Hydraulics provides a foundation for students who specialize in the field of Water Resources Engineering. This lab manual will deal with application of basic principles of fluids at rest and in motion for analysis and design of hydraulic systems and will p rovide an advanced understanding of fluid mechanics, open channel flow, pipe flow, water pumps, and some engineering applications of these concepts. This lab manual is the basic laboratory procedure of fluid movement in pipes and open channel. This Lab wil l implement an active learning laboratory environment to assess students’ understanding and while covering experiments of pipe and open channel flow. Practical engineering problems and design applications will be emphasized. 2 Table of Contents ABSTRACT ................................ ................................ ................................ ................................ ........... 1 Chapter 1: Specific Energy and Critical Depth ................................ ................................ .................... 6 Purpose ................................ ................................ ................................ ................................ ............... 6 Equipment ................................ ................................ ................................ ................................ ........... 6 General ................................ ................................ ................................ ................................ ................ 6 Objectives ................................ ................................ ................................ ................................ ........... 7 Procedure ................................ ................................ ................................ ................................ ............ 7 Theory ................................ ................................ ................................ ................................ ................. 7 Specific energy curve ................................ ................................ ................................ .......................... 8 Raw Data ................................ ................................ ................................ ................................ ............. 9 Analyzed Data ................................ ................................ ................................ ................................ ... 10 Lab Questions ................................ ................................ ................................ ................................ .... 11 Report format ................................ ................................ ................................ ................................ .... 12 Chapter 2: Velocity Distribution and Measurement ................................ ................................ .......... 13 Purpose ................................ ................................ ................................ ................................ ............. 13 Equipment ................................ ................................ ................................ ................................ ......... 13 General ................................ ................................ ................................ ................................ .............. 13 Objectives ................................ ................................ ................................ ................................ ......... 13 Procedure ................................ ................................ ................................ ................................ .......... 14 Theory ................................ ................................ ................................ ................................ ............... 14 Velocity measurement ................................ ................................ ................................ ....................... 16 Raw Data ................................ ................................ ................................ ................................ ........... 17 Analyzed Data ................................ ................................ ................................ ................................ ... 17 Lab Questions ................................ ................................ ................................ ................................ .... 18 Report format ................................ ................................ ................................ ................................ .... 18 Chapter 3: Study on Hydraulic Jump ................................ ................................ ................................ . 20 Purpose ................................ ................................ ................................ ................................ ............. 20 Equipment ................................ ................................ ................................ ................................ ......... 20 General ................................ ................................ ................................ ................................ .............. 20 Objectives ................................ ................................ ................................ ................................ ......... 21 Procedure ................................ ................................ ................................ ................................ .......... 21 Theory ................................ ................................ ................................ ................................ ............... 21 3 Types of hydraulic jump: ................................ ................................ ................................ ................... 21 Initial and sequent depths: ................................ ................................ ................................ .................. 21 Length of the jump (L) ................................ ................................ ................................ ...................... 22 Energy loss in the jump ................................ ................................ ................................ ..................... 22 Efficiency of the jump ................................ ................................ ................................ ....................... 23 Height of the jump ................................ ................................ ................................ ............................. 23 Typical shapes of graphs ................................ ................................ ................................ .................... 23 Raw Data ................................ ................................ ................................ ................................ ........... 24 Analyzed Data ................................ ................................ ................................ ................................ ... 24 Lab Questions ................................ ................................ ................................ ................................ .... 26 Report format ................................ ................................ ................................ ................................ .... 26 Chapter 4: Flow over Hydraulic Structures ................................ ................................ ....................... 28 Purpose ................................ ................................ ................................ ................................ ............. 28 Equipment ................................ ................................ ................................ ................................ ......... 28 General ................................ ................................ ................................ ................................ .............. 28 Practical application ................................ ................................ ................................ .......................... 29 Experimental setup ................................ ................................ ................................ ............................ 29 Theory ................................ ................................ ................................ ................................ ............... 29 Raw Data ................................ ................................ ................................ ................................ ........... 32 Analyzed Data ................................ ................................ ................................ ................................ ... 33 Lab Questions ................................ ................................ ................................ ................................ .... 33 Report format ................................ ................................ ................................ ................................ .... 33 Chapter 5: Head losses in a pipe flow ................................ ................................ ................................ . 35 Purpose ................................ ................................ ................................ ................................ ............. 35 Equipment ................................ ................................ ................................ ................................ ......... 35 General ................................ ................................ ................................ ................................ .............. 35 Practical application ................................ ................................ ................................ .......................... 35 Objectives ................................ ................................ ................................ ................................ ......... 35 Experimental setup ................................ ................................ ................................ ............................ 36 Procedure ................................ ................................ ................................ ................................ .......... 36 Major Loss due to Pipe Friction: ................................ ................................ ................................ ........ 36 Minor loss due to fittings: ................................ ................................ ................................ .................. 36 Theory ................................ ................................ ................................ ................................ ............... 37 4 Moody diagram ................................ ................................ ................................ ................................ . 40 Raw Data ................................ ................................ ................................ ................................ ........... 40 Analyzed Data ................................ ................................ ................................ ................................ ... 41 Lab Questions ................................ ................................ ................................ ................................ .... 42 Report format ................................ ................................ ................................ ................................ .... 42 Chapter 6: Pipes in Series and Parallel ................................ ................................ ............................... 44 Purpose ................................ ................................ ................................ ................................ ............. 44 Equipment ................................ ................................ ................................ ................................ ......... 44 General ................................ ................................ ................................ ................................ .............. 44 Practical application ................................ ................................ ................................ .......................... 45 Objectives ................................ ................................ ................................ ................................ ......... 45 Experimental setup ................................ ................................ ................................ ............................ 45 Procedure ................................ ................................ ................................ ................................ .......... 45 Pipe in Series ................................ ................................ ................................ ................................ ..... 46 Pipes in Parallel ................................ ................................ ................................ ................................ . 46 Theory ................................ ................................ ................................ ................................ ............... 46 Raw Data ................................ ................................ ................................ ................................ ........... 48 Analyzed Data ................................ ................................ ................................ ................................ ... 48 Lab Questions ................................ ................................ ................................ ................................ .... 50 Report format ................................ ................................ ................................ ................................ .... 51 Chapter 7: Pipe network design and analysis ................................ ................................ ..................... 52 Lab instructions ................................ ................................ ................................ ................................ . 52 Problem Definition ................................ ................................ ................................ ............................ 52 Procedure (Program Execution) ................................ ................................ ................................ ......... 52 Lab Questions ................................ ................................ ................................ ................................ .... 55 Report format ................................ ................................ ................................ ................................ .... 55 Chapter 8: Water Hammer effect in a pipe system ................................ ................................ ............ 57 Purpose ................................ ................................ ................................ ................................ ............. 57 Equipment ................................ ................................ ................................ ................................ ......... 57 General ................................ ................................ ................................ ................................ .............. 57 Practical application ................................ ................................ ................................ .......................... 58 Experimental setup ................................ ................................ ................................ ............................ 58 Procedure ................................ ................................ ................................ ................................ .......... 59 5 Theory and Calculations ................................ ................................ ................................ .................... 61 Raw Data ................................ ................................ ................................ ................................ ........... 63 Analyzed Data ................................ ................................ ................................ ................................ ... 63 Lab Questions ................................ ................................ ................................ ................................ .... 63 Report format ................................ ................................ ................................ ................................ .... 64 6 Chapter 1: Specific Energy and Critical Depth Purpose The purpose of this experiment is to derive the specific energy equation and to show that the critical depth is a function of the flow per width . Equipment 1. S16 Armfield Hydraulic Flow Demonstrator 2. Stopwatch General The concept of specific energy is extremely useful in the solution of many problems in open channel flow. This experiment deals with the development of specific energy curves. These curves are useful in determining the state of flow in a channel, i.e., whether the flow is critical, subcritical, or supercritical. Flow is critical when the Froude number is equal to unity. When the depth of flow is above the critical depth, the subcritical state of flow exists in the channel. When the depth of flow is below th e critical depth, the supercritical state of flow exists. Also, the critical state of flow gives us several important conditions, such as, the specific energy is minimum for a given depth . When the flow is dominated by the gravity, then the type of flow c an be identified by a dimensionless number, known as Froude Number. Given by : 𝐹𝑟=𝑣 √𝑔𝐷 Where, 𝑣 is the mean velocity of flow, 𝐷 is the hydraulic depth ( 𝐷=𝐴/𝑇=𝑦 for wide rectangular channel ), 𝐴 is the cross -sectional area, 𝑇 is the top width and 𝑔 is the acceleration due to gravity. Depending on the effect of gravity relative to inertia, the flow may be subcritical, critical or supercritical - When, 𝐹𝑟<1 the flow is subcritical 𝐹𝑟 =1 the flow is critical 𝐹𝑟>1 the flo w is supercritical . All these conditions are used in designing the various types of transitions and in controlling the flow using different control structures, for example, in determining the height of a weir, the width of a flume, opening of sluice gate, etc. For details please see (Sarker, 2021a) . 7 Fig 1. Open channel flow Objectives 1. To develop the specific energy curve. 2. To determine critical depth ( 𝑦𝑐). 3. To determine the state of flow . 4. To observe the subcritical and the supercritical flows . Procedure 1. Adjust the height of the sluice gate 𝑦𝑔 = 10 mm above the bed . 2. Gradually open the flow control valve to reach a depth of 𝑦0 = 170 mm at the upstream side of the gate . 3. Measure and record the inflow rate (Q) . 4. Without changing the inflow, raise the gate in 5 mm increments until 𝑦𝑔 = 25 mm and for each value of 𝑦𝑔, record 𝑦0 and 𝑦1. 5. Repeat steps (1 to 4), for a different flow, Q (so that 𝑦0 = 150 mm). It should be noted that 𝑦0 can be adjusted by changin g the inflow rate . Theory Energy conservation is an important concept when analyzing open channel flows. If we consider the datum located at the bottom of the channel, the energy in each section is calculated based on the following equation : 𝐸=𝑦+𝑣2 2𝑔 In this equation, 𝑣 is velocity, 𝑦 is depth and 𝑔 is acceleration due to gravity . In a rectangular channel (width = b) with an inflow rate of Q the energy can be calculated using the following equation: 8 𝐸=𝑦+𝑄2 2𝑔𝑏2𝑦2 For given values of discharge, 𝑄, a specific energy diagram depicting energy and the depth of water, y, can be developed. The specific energy is the energy above the datum, which we have chosen as the bottom of the channel . For each value of unit discharg e, there is an associated critical depth, 𝑦𝑐. Flow travelling at a depth greater than the critical depth is subcritical, and flow travelling at a depth less than the critical depth is supercritical. The critical depth is the smallest energy value. Theref ore, we can take the first derivative of the energy equation with respect to depth to determine the critical depth ( 𝑑𝐸/𝑑𝑦) and equate it to zero to determine the minimum value. For details please see (Sarker, 2021a) . 𝑑𝐸 𝑑𝑦=0 𝑑 𝑑𝑦(𝑦+𝑄2 2𝑔𝑏2𝑦2)=0 1+𝑑 𝑑𝑦{𝑄2 2𝑔𝑏2(1 𝑦2)}=0 1+𝑄2 2𝑔𝑏2𝑑 𝑑𝑦{(𝑦−2)}=0 1−2𝑄2 2𝑔𝑏21 𝑦𝑐3=0 1=2𝑄2 2𝑔𝑏21 𝑦𝑐3⟹𝑦𝑐=√𝑄2 𝑔𝑏23 Specific energy curve Specific energy curve shown in Fig. 2. 9 Fig 2. Specific Energy Curve for a given discharge Raw Data Fig 3. Experimental data measurement Record the depths at the upstream and downstream sections of the gate and the streamflow. Then, fill in the following tables . Table 1 - Initial 𝑦0 = 170 mm, t = _________ s, V = 20 L 𝑦𝑔 (mm) 𝑦0 (mm) 𝑦1 (mm) 1 10 170 2 15 3 20 4 25 10 Table 2 - Initial 𝑦0 = 150 mm, t = _________ s, V = 20 L 𝑦𝑔 (mm) 𝑦0 (mm) 𝑦1 (mm) 1 10 150 2 15 3 20 4 25 Analyzed Data Using all the data collected in the previous step and for each value of Q, fill in the following tables : Table 3 - Initial 𝑦0 = 170 mm, Q = _________ 𝑚𝑚3/𝑠 𝑦𝑔 (mm) 𝑦0 (mm) 𝑦1 (mm) 𝐸0 (mm) 𝐸1 (mm) 𝑦𝑐 (mm) 1 10 2 15 3 20 4 25 Table 4 - Initial 𝑦0 = 150 mm, Q = _________ 𝑚𝑚3/𝑠 𝑦𝑔 (mm) 𝑦0 (mm) 𝑦1 (mm) 𝐸0 (mm) 𝐸1 (mm) 𝑦𝑐 (mm) 1 10 2 15 3 20 4 25 11 Using the data, compute the following : 1. For each discharge value, sort the data in descending order of depth, Y and fill in the following tables. 2. Plot the (y -E) line for two different inflows in one graph. 3. Estimate the critical depth based on the specific energy curves. Table 5 - Initial 𝑦0 = 170 mm, Q = _________ 𝑚𝑚3/𝑠 Table 6 - Initial 𝑦0 = 150 mm, Q = _________ 𝑚𝑚3/𝑠 Lab Questions 1. Why the state of flow and the critical depth of a river or canal need to be determined? 2. How is the critical depth affected by Q? 3. Theoretically, what should be the relation between 𝐸0 and 𝐸1? Do the calculated values agree with the theory? 4. Do the calculated values of critical depth agree with the corresponding values extracted from the plotted curves? If not, explain why. 12 Report format Students are expected to submit the lab report in the following format. Report will be evaluated in 100%. The distribution of total marks is shown in bracket in the table below. Please submit a soft copy (pdf) in the webcourse assignment section. You can send any questions regarding Lab by webcourse s inbox. Please prepare a pdf file in the following format and mention the course number in the subject line. “CWR4202CLab -LastName -FirstName -Labno.pdf” (For example, CWR4202CLab -Sarker Shiblu -Lab0 1.pdf) Cover Page Please provide the course number, course name, experiment name, your name and submission date. 1 Introduction ( 5%) Not more than 200 words. It may include the background and scope of the experiment. 2 Objective (5%) Please formulate the main objective (goal, aim) of the experiment . 3 Procedure ( 5%) Please provide step by step procedure how the experiment can be done. 4 Experimental data (10%) Please present the raw data in tabular format mentioning the proper unit and symbol. 5 Sample calculation (20%) In this section, please present the calculation of different parameters from the experimental data along with mathematical equations provided in the manual. 6 Results (15%) Please present your results in tabular format . If it is required to present it by graph, chart etc., please put those in this section . 7 Answer to the lab questions ( 20%) Please provide the answers to the lab questions. Please try to answer what is asked for. 8 Discussion ( 15%) In this part, please discuss your results. If any kind of error, unusual results etc. are found, please discuss it in this section. Try to be precise and write to the point w hich is asked for. Also write the practical value of the experiment . 9 Conclusions (5%) Please write a short conclusion (not more than 50 words). 13 Chapter 2: Velocity Distribution and Measurement Purpose The purpose of this experiment is to measure the velocity in the working section using Pitot tube and manometer and to compare it with the actual value. Having known the total pressure in two points in a specific section of channel, the velocity can be calculated using the Bernoulli equation . Equipment 1. S16 Armfield Hydraulic Flow Demonstrator 2. Stopwatch 3. Pitot tube General Velocity of flow is an important parameter in open channel flow. In order to find out the channel discharge, the velocity distribution needs to be known. In an open channel the velocity is not uniform over the cross -section. The velocity is zero at the cha nnel boundary and maximum at or near the free surface. This experiment deals with the velocity distribution in an open channel and determination of the velocity using pitot tube . Practically the energy equations require to determine velocity using pitot tu be (figure 1). Fig 1. Velocity measurement with pitot tube Objectives 1. To understand the function of pitot tube. 2. To understand the velocity distribution of open channel . 3. To determine the mean velocity of channel . 4. To compare the measured velocity with theoretical velocity . 14 Procedure 1. Lower sluice gate until the tip is 10 mm above the bed . 2. Raise overshot weir at outlet until tip is 80 mm above the bed . 3. Move upstream Pitot to the height of the sluice gate . 4. Measure the pressures at the bed ( 𝐻𝐵) and the sl uice gate height ( 𝐻𝐴) using the corresponding pitots . 5. Measure the depth (y) . 6. Use a stopwatch to find the time that it takes to have 20 liters of water in the outlet tank (t) . 7. Change the discharge and carry out the first three steps for two more discharges . 8. Carry out the above -mentioned steps when the sluice gate is open for 20 mm . Theory When water enters a channel the velocity distribution across the channel section will vary with distance due to the presence of boundary roughness as shown in Fi g. 2: Fig 2. Development of boundary layer The effect on the velocity distribution due to boundary roughness is indicated by the line ABC. Outside the surface represented by ABC, the velocity distribution is practically uniform. Near the channel surface and within the region ABC, velocity varies ac cording to distance from channel surface. The region inside ABC is known as boundary layer. At the beginning of the flow in the channel, the flow is entirely laminar, and a laminar boundary layer is developed along the channel surface, as shown by the curv e AB. The velocity distribution in this layer is approximately parabolic. As water travels further along the channel, the flow in the boundary layer will eventually change to turbulent (at point B). Downstream from B a turbulent boundary layer is developed , as shown by the curve BC. The velocity distribution in this layer is approximately logarithmic. The 15 turbulent boundary layer intersects the free water surface at a distance where the flow is assumed to be fully developed. Even in a turbulent boundary lay er, there is a very thin layer near the boundary in which the flow is laminar and is known as the laminar sublayer. The thickness of this layer is given by : 𝛿0=11.6𝜈 𝑣𝑓 Where, 𝑣𝑓 is the shear or friction velocity, given by : 𝑣𝑓=√𝑔𝑅𝑆 𝑅 is the hydraulic radius, 𝑆 is the slope of the energy line (taken to be equal to the slope of the channel bottom) and 𝜈 is the kinematic viscosity of water. The surface of a channel is composed of irregular peaks and valleys. The effective height of th e irregularities is called the roughness height k. If the roughness height is less than the thickness of the laminar sublayer, the surface irregularities will be so small that all roughness elements will be submerged in the laminar sublayer and have no eff ect upon the flow outside the layer. Then the channel is said to be hydraulically smooth. For hydraulically smooth channel . 0≤𝑘𝑣𝑓 𝜈≤5;𝑖𝑓 𝑘<𝛿0 However, if the roughness height k is greater than the thickness of the laminar sublayer, the roughness ele ments extend their effects beyond the laminar sublayer and the channel is said to be hydraulically rough. For hydraulically rough channel . 𝑘𝑣𝑓 𝜈≥70;𝑖𝑓 𝑘>𝛿0 There exists a transition zone in which the channel is neither smooth nor rough. For this zon e: 5<𝑘𝑣𝑓 𝜈<70 The flow of water in open channel is turbulent and the bed is normally rough. On the basis of Prandtl -von Karman logarithmic velocity distribution law, the velocity distribution in an open channel having hydraulically rough surface is given by : 𝑉=5.75𝑣𝑓log30𝑦 𝑘 Where, v is the velocity at any point at a vertical distance of y from the channel bottom. 16 The velocity varies in the vertical direction as well as in the lateral direction due to boundary friction. Cross -sectional mean veloc ity represents the average velocity over the cross -section. Using the velocity distribution given by above equation , the cross -sectional mean velocity V is given by 𝑉=𝑣𝑓(6.25+5.75log𝑅 𝑘) Velocity measurement The velocity in point A can be calculated using the Pitot tube and manometer in point A and B (figure 3) . From Bernoulli equation the total head in points A and B is as follows: Fig 3. Experimental data measurement 𝐻𝐴=ℎ𝐴+𝑦+𝑢2 2𝑔 ⟹ℎ𝐴=𝐻𝐴−𝑦−𝑢2 2𝑔 𝐻𝐵=ℎ𝐵+0+0⟹ℎ𝐵=𝐻𝐵 The static head of points A and B are related based on the following equation (figure 3): ℎ𝐵=ℎ𝐴+𝑦 Finally, substituting the value of the static head ℎ𝐴 and ℎ𝐵, we can easily calculate the velocity in point A : 𝐻𝐵=𝐻𝐴−𝑦−𝑢2 2𝑔+𝑦 ⟹𝑢=√2𝑔(𝐻𝐴−𝐻𝐵) 17 Raw Data For upstream section fill the following tables. Table 1 - Sluice gate tip 10 mm above the bed 𝑡 (sec) 𝑦 (mm) 𝐻𝐴 (mm) 𝐻𝐵 (mm) 1 2 3 Table 2 - Sluice gate tip 20 mm above the bed 𝑡 (sec) 𝑦 (mm) 𝐻𝐴 (mm) 𝐻𝐵 (mm) 1 2 3 Analyzed Data Using all the data collected in the previous step, fill in the following tables : Table 3 - Sluice gate tip 10 mm above the bed 𝑡 (sec) Volume (𝑚𝑚3) 𝑄𝑎 (𝑚𝑚3/𝑠) 𝑦 (mm) 𝐻𝐴−𝐻𝐵 (mm) 𝑢 𝑄𝑡 (𝑚𝑚3/𝑠) 1 2 3 18 Table 4 - Sluice gate tip 20 mm above the bed 𝑡 (sec) Volume (𝑚𝑚3) 𝑄𝑎 (𝑚𝑚3/𝑠) 𝑦 (mm) 𝐻𝐴−𝐻𝐵 (mm) 𝑢 𝑄𝑡 (𝑚𝑚3/𝑠) 1 2 3 Lab Questions 1. What is the main assumption when the value of discharge is calculated using Bernoulli’s equation? 2. What do you mean by hydraulically smooth and rough channels? What is the criterion used to determine whether a surface is hydraulically smooth or rough? 3. Explain why the velocity distribution over a channe l section is not uniform. 4. Plot the theoretical discharge on the X -axis and the experimental discharge on the Y -axis. Do these two values agree with each other? If not, what are the main reasons? 5. Calculate the percentage of error in your velocity measurement ? Report format Students are expected to submit the lab report in the following format. Report will be evaluated in 100%. The distribution of total marks is shown in bracket in the table below. Please submit a soft copy (pdf) in the webcourses assignment section. You can send any questions regarding Lab by webcourse s inbox. Please prepare a pdf file in the following format and mention the course number in the subject line. “CWR4202CLab -LastName -FirstName -Labno.pdf” (For example, CWR4202CLab -Sarker Shiblu -Lab0 2.pdf) Cover Page Please provide the course number, course name, experiment name, your name and submission date. 1 Introduction ( 5%) Not more than 200 words. It may include the background and scope of the experiment. 19 2 Objective (5%) Please formulate the main objec tive (goal, aim) of the experiment . 3 Procedure ( 5%) Please provide step by step procedure how the experiment can be done. 4 Experimental data (10%) Please present the raw data in tabular format mentioning the proper unit and symbol. 5 Sample calculation (20%) In this section, please present the calculation of different parameters from the experimental data along with mathematical equations provided in the manual. 6 Results (15%) Please present your results in tabular format. If it is required to present it by graph, chart etc., please put those in this section . 7 Answer to the lab questions ( 20%) Please provide the answers to the lab questions. Please try to answer what is asked for. 8 Discussion ( 15%) In this part, please discuss your results. If any kind of error, unusual results etc. are found, please discuss it in this section. Try to be precise and write to the point w hich is asked for. Also write the practical value of the experiment . 9 Conclusions (5%) Please write a short conclusion (not more than 50 words). 20 Chapter 3: Study on Hydraulic Jump Purpose The main purpose of this experiment is to study hydraulic jump and to use momentum equation to describe this phenomenon . Equipment 1. S16 Armfield Hydraulic Flow Demonstrator 2. Stopwatch General In an open channel when a supercritical flow is made to change abruptly to subcritical flow, the result is usually an abrupt rise of the water surface. This feature is known as the hydraulic jump. It results when there is a conflict between upstream and downstream controls which influence the same reach of the channel. For example, if the upstream control causes super critical flow and downstream control dictates subcritical flow, then this conflict can be resolved by a hydraulic jump, which passes the flow from one flow regime to other . This experiment deals with observation of hydraulic jump in a horizontal rectangula r channel and development of different relationships between height, length, efficiency and energy loss of a jump. Hydraulic jump is useful in dissipation of excess energy in flows over dams, weirs, spillways and other hydraulic structures to prevent scour ing downstream, maintaining high water levels in channels for irrigation and other water distribution purposes, increasing discharge of a sluice gate and thus increasing the effective head across the gate, mixing chemicals for water purification or wastew ater treatment, increasing aeration of flows and dichlorination of waste water, identification of special flow conditions, etc . For details please see (Sarker, 2021a) . Fig 1. Hydraulic Jump in a horizontal rectangular channel 21 Objectives 1. To determine the type of the jump according to USBR classification. 2. To measure the initial depth ( 𝑦1), sequent depth ( 𝑦2), length ( 𝐿) and height ( ℎ𝑗) of the jump and compare them with the theoretical values. 3. To determine the total energy loss, kinetic energy loss and efficiency of the jump and compare them with the theoretical values. 4. To develop the theoretical characteristic curves of the hydraulic jump. Procedure 1. Open the upstream gate for 10 mm . 2. With a constant value of downstream height of the gate, change the discharge to get a stable hydraulic jump in the middle of the channel . 3. Measure the depth in upstream of the gate ( 𝑦0), before the jump ( 𝑦1) and after the jump (𝑦2), the length of the jump ( 𝐿) and the time ( 𝑡) it takes to have 20 liters of water in inlet tank. 4. Repeat the experiment for 5 different conditions (discharge and gates’ opening) . Theory Types of hydraulic jump: Depending on the Froude number before the jump (F1), the United States Bureau of Reclamation (USBR) cl assified the hydraulic jumps in horizontal rectangular channels into the following five categories : Type 1: 𝐹1 = 1 ~1.7 Undular jump Type 2: 𝐹1 = 1.7 ~2.5 Weak jump Type 3: 𝐹1 = 2.5 ~4.5 Oscillating jump Type 4: 𝐹1 = 4.5 ~9.0 Steady jump Type 5: 𝐹1>9.0 Strong jump Initial and sequent depths: The depth of flow before the jump is known as the initial depth ( 𝑦1) and the depth after the jump is known as the sequent depth ( 𝑦2). Consider a hydraulic jump occurring i n a horizontal rectangular channel (Fig. 1). Since the jump takes place in a short reach of the channel, 𝐹𝑓≈0 and since the channel is prismatic, we can assume that 𝛽1=𝛽2=1. The hydrostatic forces 𝐹𝑝1 and 𝐹𝑝2 may be expressed as 𝐹𝑝1=𝛾𝑧1̅𝐴1 and 𝐹𝑝2=𝛾𝑧2̅𝐴2 22 Where, 𝑧1̅and 𝑧2̅ are the vertical distances of the centroids of the respective water areas 𝐴1 and 𝐴2 from the free surface. Now applying momentum equation (Reza et al., 2014; Sarker, 2021e, 2021a) between sections 1 and 2, we obtain 𝑄2 𝑔𝐴1+𝑧1̅𝐴1=𝑄2 𝑔𝐴2+𝑧2̅𝐴2 Since for a rec tangular channel 𝑄=𝐴1𝑉1=𝐴2𝑉2; 𝐴1=𝐵𝑦1 and 𝐴2=𝐵𝑦2 𝑧1̅=𝑦1/2 and 𝑧2̅= 𝑦2/2 above equation gives 𝑄2 𝑔𝐵2(1 𝑦1−1 𝑦2)=1 2(𝑦22 −𝑦12) Using 𝑄=𝐵𝑦1𝑉1=𝐵𝑦2𝑉2 above equation may be recast as 𝑉12 𝑔𝑦1=𝐹12=1 2𝑦2 𝑦1(𝑦2 𝑦1+1) Which may be solved to yield 𝑦2 𝑦1=1 2(√1+8𝐹12 −1) Where, 𝑦2 𝑦1 is known as the ratio between the sequent and the initial depths . Length of the jump (L) The length of a hydraulic jump is the horizontal distance from the front face of the jump to a point immediately downstream from the roller. This length cannot be determined by theory. Silvester (1964) demonstrated that for free hydraulic jumps in horizontal rectangular channels 𝐿 𝑦1=9.75(𝐹1−1)1.01 Energy loss in the jump The total loss of energy in the jump is equal to the difference in specific energies before and after the jump. It can be shown that the total energy loss involved in a hydraulic jump in a horizontal rectangular channel is given by ∆𝐸=𝐸1−𝐸2=(𝑦2−𝑦1)3 4𝑦1𝑦2 Where, 𝐸1 is the specific energy before the jump and 𝐸2 is the specific energy after the jump. The kinetic energy loss in the jump is given by the difference in velocity head before and after the jump. Thus 23 ∆𝐸𝐾.𝐸.=1 2𝑔(𝑉12−𝑉22) Where, 𝑉1 is the velocity before the jump and 𝑉2 is the velocity after the jump. Efficiency of the jump The ratio of the specific energy after the jump to that before the jump ( 𝐸2/𝐸1) is known as the efficiency of the jump. It can be shown that the efficiency of the jump is given by 𝐸2 𝐸1=(1+8𝐹12)3/2−4𝐹12+1 8𝐹12(2+𝐹12) Height of the jump The difference between the depths after and before the jump is known as the height of the jump. It is given by ℎ𝑗=𝑦2−𝑦1 The ratio of the height of jump to the specific energy before jump is known as the relative height of the jump and is given by ℎ𝑗 𝐸1=(1+8𝐹12)1/2−3 2+𝐹12 Typical shapes of graphs Characteristic graphs of hydraulic jumps are a combination of four graphs shown in Fig. 2. Fig 2. Characteristics curves of hydraulic jumps in horizontal rectangular channels 24 Raw Data Fig 3. Experimental data measurement Record the values of 𝑦1, 𝑦2, ℎ𝑗, 𝐿 and 𝑡 in the following table . Table 1 𝑦1 (mm) 𝑦2 (mm) ℎ𝑗 (mm) L (mm) t (s) 1 2 3 4 5 Analyzed Data First, having known the time and volume, calculated the discharge and then estimate the following table: 25 Table 2 Q (𝑚𝑚3/𝑠) 𝑦1 (mm) 𝑣1 (mm/s) 𝐸1 (mm) 𝑦2 (mm) 𝑣2 (mm/s) 𝐸2 (mm) ∆𝐸=𝐸1−𝐸2 (mm) 1 2 3 4 5 Calculate the theoretical values ( i.e., sequent depth, length, e nergy loss, efficiency and height) for your observed hydraulic jump in the following table: Table 3 𝑦1 (mm) 𝑣1=𝑄 𝑏𝑦1 (mm/s) 𝐹1=𝑣1 √𝑔𝑦1 𝑦2 (mm) L (mm) 𝑦1 𝐸1 𝑦2 𝐸1 ℎ𝑗 𝐸1 𝐸2 𝐸1 ∆𝐸 (mm) 1 2 3 4 5 Note. The highlighted columns are values that are measured. So, you have to use them to complete the rest of the table. 26 Lab Questions 1. What is the type of your hydraulic jump according to USBR classification? 2. We assume that the loss in two sides of the gate in negligible when we use energy equation. Does this assumption seem realistic ? 3. Do the calculated values for 𝑦2, agree with the measured va lues? What can be the reason for the differences ? 4. Plot the curve of 𝐿 versus 𝑦2−𝑦1. Using this curve, find the value of α (slope of the straight line).The value of 𝑦2−𝑦1should be in horizontal axes . 5. Plot 𝐸2 𝐸1,ℎ𝑗 𝐸1,𝑦1 𝐸1 𝑎𝑛𝑑 𝑦2 𝐸1 vs 𝐹1 to get the characteristics curves ? Note. In order to draw the curves, use “scatter with only markers” chart in excel. To find out the value of α, you can use “add trendline” option in Excel. The slope of the curve is the value of α. Report format Students are expected to submit the lab report in the following format. Report will be evaluated in 100%. The distribution of total marks is shown in bracket in the table below. Please submit a soft copy (pdf) in the webcourse assignment section. You can send any questions regarding Lab by webcourse s inbox. Please prepare a pdf file in the following format and mention the course number in the subject line. “CWR4202CLab -LastName -FirstName -Labno.pdf” (For example, CWR4202CLab -Sarker Shiblu -Lab0 3.pdf) Cover Page Please provide the course number, course name, experiment name, your name and submission date. 1 Introduction ( 5%) Not more than 200 words. It may include the background and scope of the experiment. 2 Objective (5%) Please formulate the main objective (goal, aim) of the experiment . 3 Procedure ( 5%) Please provide step by step procedure how the experiment can be done. 4 Experimental data (10%) Please present the raw data in tabular format mentioning the proper unit and symbol. 27 5 Sample calculation (20%) In this section, please present the calculation of different parameters from the experimental data along with mathematical equations provided in the manual. 6 Results (15%) Please present your results in tabular format. If it is required to present it by graph, chart etc., please put those in this section . 7 Answer to the lab questions ( 20%) Please provide the answers to the lab questions. Please try to answer what is asked for. 8 Discussion ( 15%) In this part, please disc uss your results. If any kind of error, unusual results etc. are found, please discuss it in this section. Try to be precise and write to the point which is asked for. Also write the practical value of the experiment . 9 Conclusions (5%) Please write a short conclusion (not more than 50 words). 28 Chapter 4: Flow over Hydraulic Structures Purpose The purpose of this experiment is to determine the theoretical discharge of the weir (1. Sharp crested weir, 2. Broad crested weir) and measure the actual discharge and hence to find out the coefficient of discharge . Equipment 1. S16 Armfield Hydraulic Flow Demonstrator 2. Stopwatch 3. Flow meter 4. Sharp crested weir 5. Broad crested weir General A weir is an overflow structure built across an open channel for the purpose of measuring the flow. Weirs are commonly used to measure flow of water, but their use in measurement of other liquids is increasing. Classified with reference to the shape of the opening through which the liquid flows, weirs may be rectangular, triangular, trapezoidal, circular, parabolic or of any other regular form. The first three forms are most commonly used for measurement of water. Classified with reference to the form of crest (the edge or the top surface with which liquid comes in contact) weirs may be sharp - crested or broad -crested. The sharp -crested rectangular weir has a sharp upstream edge so formed that the liquid in passing touches only a line. The overfalling stream is termed as ‘nappe’. The nappe of a sharp crested weir as shown in fig is contracted at its underside by the action of the vertical components of the velocity just upstream from the weir. This is called cres t contraction. If the sides of the opening also have sharp upstream edge so that the nappe is contracted in width, the weir is said to have end contractions and is usually called a contracted weir. Fig 1. Path lines of flow over rectangular sharp crested weir 29 A broad -crested weir is an overflow structure with a truly level and horizontal crest. It is widely used in irrigation canals for the purpose of flow measurement as it is rugged and can stand up well under field conditions. But practically som e problems arise with the weir, as there exists a dead water zone at the upstream of the weir and the head loss is mo re comparable to other devices. By virtue of being a critical depth meter, the broad cre sted weir has the advantage that it operates effect ively with higher downstream water levels than a sharp crested weir. This experiment deals with measurement of discharge using the broad crested weir and also calibration of the wei r. Practical application Shallow rivers are often made navigable by buildi ng, dams across the river at certain sections over which the water may flow. During a drought little or no water will flow past the dam, but after heavy rains the water flows over the dam, thus converting it into a weir. Also flow through canal is measured by weirs. Hydraulic structure formula also useful to understand the effect of structure in dynamic river (see Khan et al., 2014 ) Experimental setup 1. Open all the ga tes and m easure the height (P) and width (B) of the weir. Position the weir plate at end side of the approach channel, in a vertical plane, with sharp edge on the upstream side. 2. Allow water to the channel so that water flows over the weir and wait until water surface comes to a steady condition. 3. Ventilate the nappe. 4. Check again whether the nappe is ventilated or not. If not, ventilate it. 5. Carefully take the gauge reading (upstream water level over the weir ). The water surface may be slightly fluctuating. 6. Take the time to accumulate 20 l iters in the tank and calculate actual discharge and hence find the coefficient of discharge . Theory The relationship between discharge and head over the weir can be developed by making the following assumptions as to the flow behavior: 1. Upstream of the we ir, the flow is uniform, and the pressure varies with depth according to the hydrostatic equation 𝑃=γℎ 2. The free surface remains horizontal as far as the plane of the weir, and all particles passing over the weir move horizontally. (In fact, the free surface drops as it approaches the weir). 3. The pressure throughout the sheet of liquid or nappe, which passes over the crest of the weir, is atmospheric. 4. The effects of viscosity and surface tension are negligible. 5. The upstream approach velocity head is neg lected. 30 Fig 2. Flow Over a Sharp -Crested weir Now consider the sharp -crested weir in the figure. Let H be the working head and B is the width of the weir. Let us consider a small horizontal string of thickness dh under a head h. Therefore, the theoretica l discharge through the strip 𝑑𝑄1=𝑎𝑟𝑒𝑎𝑜𝑓𝑡 ℎ𝑒𝑠𝑡𝑟𝑖𝑝 ∗𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 =(𝐵𝑑ℎ)∗√2𝑔ℎ Integrating between the limits 0 and H, the total theoretical discharge over the weir is given by 𝑄𝑡=2 3√2𝑔∗𝐵∗𝐻(3/2) Let 𝑄𝑎 be the actual discharge. Then the co -efficient of discharge, 𝐶𝑑, is given by 𝐶𝑑=𝑄𝑎/𝑄𝑡 The broad -crested weir has a definite crest length in the direction of flow. In order to maintain a hydrostatic pressure distribution above the weir crest, i.e., to maintain the streamlines straight and parallel, the length of the weir is designed such that 0.07≤𝐻1/𝐿≤0.50 where 𝐻1 is the head above the crest and 𝐿 is the length of the weir (Fig. 3). Under this condition, critical flow occurs over the weir and the weir provides an excellent means of measuring discharge in open channels based on the principle of critical flow. The upstream corner of the weir is rounded in such a manner that flow separation does not occur. 31 Fig 3. Flow Over a Broad -Crested w eir Consider a rectangular broad crested weir shown in figure 3 Based on the principle of critical flow (𝐹𝑟=1), the theoretical discharge 𝑄𝑡 over the weir is given by 𝑄𝑡=√𝑔∗𝐵∗𝑦𝑐(3/2) Where, B is the width of the weir, 𝑦𝑐 is the critical depth and g is the acceleration due to the gravity. But t he usual difficulty to use this equation for computing discharge lies in locating the critical flow section and measuring the critical depth accurately. This dif ficulty is, however, overcome by measuring the depth of flow upstream of the weir where the flow is not affected by the presence of the weir. With reference to Fig. 3, neglecting the frictional losses and applying the energy equation between the upstream section and the critic al flow section, we obtain 𝐻1=𝑦𝑐+𝑣𝑐2 2𝑔 Where, 𝑉𝑐 is the critical velocity. Since at the critical state of flow, the velocity head is equal to one-half of the hydraulic depth ( 𝐷) and for a rectangular channel 𝐷=𝑦, the above equation gives 𝐻1=𝑦𝑐+𝑣𝑐2 2𝑔=𝑦𝑐+𝐷𝑐 2=𝑦𝑐+𝑦𝑐 2=3 2𝑦𝑐 so that 𝑦𝑐=2 3𝐻1 and the theoretical discharge 𝑄𝑡 becomes 𝑄𝑡=(2 3)3/2 √𝑔∗𝐵∗𝐻1(3/2) 32 Let 𝑄𝑎 be the actual discharge. Then the co -efficient of discharge, 𝐶𝑑, is given by 𝐶𝑑=𝑄𝑎/𝑄𝑡 Raw Data (1) Sharp crested weir Width of the weir, B = mm; Height of the weir, P = mm. Time , t (s) Head, H (mm) 1 2 3 4 5 (2) Broad crested weir Width of the weir, B = mm; Height of the weir, P = mm. Time , t (s) Head, H (mm) 1 2 3 4 5 33 Analyzed Data (1) Sharp crested weir Volume (L) Time (s) Discharge ( 𝑄𝑎) Head (mm) Discharge 𝑄𝑡 1 2 3 4 5 (2) Broad crested weir Volume (L) Time (s) Discharge ( 𝑄𝑎) Head (mm) Discharge 𝑄𝑡 1 2 3 4 5 Lab Questions 1. What are the assumptions made in deriving this equation? 2. Discuss the observation of the nappe . 3. Plot the 𝑄𝑎 vs 𝑄𝑡 and determine the value of 𝐶𝑑 for sharp crested weir. 4. What is the advantage, disadvantage and use of a broad -crested weir? 5. Plot the 𝑄𝑎 vs 𝑄𝑡 and determine the value of 𝐶𝑑 for the broad crested weir. Report format Students are expected to submit the lab report in the following format. Report will be evaluated in 100%. The distribution of total marks is shown in bracket in the table below. Please submit a soft copy (pdf) i n the webcourse assignment section. You can send any questions regarding Lab by webcourse s inbox. Please prepare a pdf file in the following format and mention the course number in the subject line. 34 “CWR4202CLab -LastName -FirstName -Labno.pdf” (For example, CWR4202CLab -Sarker Shiblu -Lab0 4.pdf) Cover Page Please provide the course number, course name, experiment name, your name and submission date. 1 Introduction ( 5%) Not more than 200 words. It may include the background and scope of the experiment. 2 Objective (5%) Please formulate the main objective (goal, aim) of the experiment . 3 Procedure ( 5%) Please provide step by step procedure how the experiment can be done. 4 Experimental data (10%) Please present the raw data in tabular format mentioning the proper unit and symbol. 5 Sample calculation (20%) In this section, please present the calculation of different parameters from the experimental data along with mathematical equations provided in the manual. 6 Results (15%) Please present your results in tabular format. If it is required to present it by graph, chart etc., please put those in this section . 7 Answer to the lab questions ( 20%) Please provide the answers to the lab questions. Please try to answer what is asked for. 8 Discussion ( 15%) In this part, please discuss your results. If any kind of error, unusual results etc. are found, please discuss it in this section. Try to be precise and write to the point which is asked for. Also write the practical value of the experiment . 9 Conclusions (5%) Please write a short conc lusion (not more than 50 words). 35 Chapter 5: Head losses in a pipe flow Purpose The objective of this experiment is to demonstrate and calculate head losses (major loss and minor loss) in a pipe system. In this demonstration, the friction coefficients for the Darcy -Weisbach ( 𝑓), the Hazen -William ( 𝐶𝐻𝑊), and the Manning ( 𝑛) equations are determined for pipes with different materials. Equipment 1. Water storage reservoir 2. Pump 3. Flow meter 4. Pipes (opaque PVC & clear PVC) 5. Pipe containing eight 900 elbows 6. Flow network panels 7. Pressure gauge 8. Timer General Head loss in a pipe flow is mainly due to friction in pipes and again friction is due to roughness of pipes. It has been proved that friction is dependent not only upon the size and shape of the projection of roughness, but also upon their distribution or spacing . For details please see (Sarker , 2021a) . Practical application Flow through a single pipeline, pipes in series and parallel and also in pipe network system, cause head loss due to friction. The head loss from source to the point of interest due to the friction along the pipe also provides the basis of pipe size (diameter) design. This experiment gives an estimate of head loss due to friction in the pipe per u nit length of the pipe . Besides pipes it has wide range of use in natural and manmade network system (Reza et al., 2014; Sarker, 2021a; Sarker et al., 2018, 2019a, 2019b; Sarker & Singh, 2017) . Objectives 1. To understand the types of flow in pipes. 2. To find the frictional loss . 3. To determine the friction coefficients for the Darcy -Weisbach ( 𝑓), the Hazen -William (𝐶𝐻𝑊), and the Manning ( 𝑛) equations . 36 Experimental setup Fig 1. Experimental pipe system Procedure Major Loss due to Pipe Friction: 1. Set up the flow network system, as shown in the diagram, so that the water will circulate from the supply reservoir through the pipe network and back to the supply reservoir . 2. Fill the supply reservoir with water. 3. Open valves A and B for each pipe so that the flow is not restricted in the system . 4. Turn on the pump. Allow suff icient time for the air to escape from the system. 5. Close valves A (2A & 3A) and B (2B & 3B) on pipes 2 and 3 . 6. Measure the flow rate through the pipe 1. 7. Insert the pressure gauges onto the pressure tap located near valve 1A and valve 1B. Read the gauge pressures. 8. Vary the flow rate and measure the gauge pressures. 9. Open valves 2A and 2B. (Note: Valves A and B should always be open for at least one pipe to avoid any damage on the pump) 10. Close valves A and B on pipe 1. 11. Repeat steps 6 through 8 for pipe 2. Minor loss due to fittings: 1. Open valves 3A and 3B on pipe 3 containing eight 900 elbows. 2. Close valves 2A and 2B on pipe 2. 3. Repeat steps 6 through 7 for pipe 3. 4. Turn off the pump . 37 Theory Friction loss is the loss of energy or head that occurs in the pipe flow due to viscous effects generated by the surface of the pipe. This energy loss is dependent on the wall shear stress between the fluid and pipe surface, and the shear stress of a flow dependent on whether the flow is turbulent of laminar. For turbulent flo w, the pressure drop is dependent on the roughness of the surface while in laminar flow the roughness effects of the wall are negligible. This is due to fact that for turbulent flow a thin viscous layer is formed near the pipe surface which causes loss of energy while in laminar flow this viscous layer is nonexistent. Friction loss has several causes: -Condition of flow , - Movement of fluid molecules against each other and - Movement of fluid molecules against inside surface of pipe . If the head loss in a g iven length of uniform pipe is measured at different values of the velocity, it will be found that, as long as the velocity is low enough to secure laminar flow. the head loss, due to friction, will be directly proportional to the velocity. But with increa sing velocity, at some point where the visual observation in a transparent tube would show that the flow changes from laminar to turbulent, there will be an abrupt increase in the rate at which the head loss varies. If the logarithms of those two variables are plotted on linear scales or if the values are plotted directly on log -log paper, it will be found that, after a certain transition region has been passed, lines will be obtained with slopes ranging from about 1.75 to 2.00. For details please see (Sarker, 2021a, 2021c) . Fig 2. Head loss due to Friction in a pipe It is thus understood that for laminar flow the drop -in energy due to friction varies as 𝑉, while for turbulent flow the friction varies as 𝑉𝑛, where 𝑛 ranges from about 1.75 to 2.00. The lower value of 1.75 for turbulent flow is found for pipes with very smooth walls; as the wall roughness increases, the value of n increases up to its maximum value of 2.00. However, velocity is not the only factor that determines whether the flow is lamin ar or turbulent. The criterion is Reynolds number. For a circular pipe the significant linear dimension L is usually taken as the diameter D, and thus : 38 𝑅𝑒=𝑉𝐷 𝜈 For circular pipe when, Re < 2000 Flow is Laminar 2000 < Re < 4000 Flow is Transitional Re > 4000 Flow is Turbulent Head loss, ℎ𝐿 can be generalized as proportional with the exponential power of velocity (Sarker, 2021c) , 𝑉 by: ℎ𝐿∞𝑣𝑛 where n is the exponent of velocity ℎ𝐿=𝐾𝑣𝑛 where K is a constant. Early experiment on the flow of water in long, straight, uniform circular pipes indicated that head loss varied directly with velocity head and pipe length and inversely with pipe dia. Darcy Weisbach proposed the formula for the turbulent flow, ℎ𝐿=𝑓𝐿 𝐷𝑣2 2𝑔 Where, 𝑓 = friction coefficient, 𝐿 = Length of pipe, 𝑣 = velocity of pipe, 𝐷 = Diameter of the pipe . For laminar flow head loss ( ℎ𝐿) given by Hagen -Poiseuille is : ℎ𝐿=32𝜇𝐿𝑣 𝜌𝑔𝐷2 For laminar flow the striking feature of the equation is that it involves no empirical coefficient or experimental factors of any kind, except for the physical properties of fluid such as, viscosity, and density. 𝑓=64 𝑅𝑒 (for circular pipe ) Therefore, friction factor (f) can be related empirically as : 𝑓=𝐶𝑅𝑒𝑚 39 Where m is the exponent of Reynolds number and 𝐶 is a constant. From this it would appear that in laminar flow the friction is independent of the roughness of the pipe wall. Moody diagram useful to relate Darcy -Weisbach friction factor 𝑓, Reynolds number 𝑅𝑒, and surface roughness (figure 4). Hazen -Williams also proposes the formula to calculate pipe friction factor as below: 𝑣=1.32𝐶𝐻𝑊𝑅ℎ0.63𝑆0.54 Where 𝑣 = mean velocity, 𝐶𝐻𝑊 = Hazen Williams Friction Coefficient, 𝑅ℎ = Hydraulic Radius, 𝑆 = Slope of the energy grade line . Manning’s equation also applicable to calculate pipe roughness as below: 𝑣=1.49 𝑛𝑅ℎ2/3𝑆1/2 Where 𝑛 = Manning’s friction coefficient . The loss of head in a sudden contraction is not only due to the contraction itself but also due to sudden expansion which follows the contraction as shown in figure 3. Head loss in sudden contraction : ℎ𝐶=𝑘1𝑣2𝑛 The loss of head in a sudden contraction is due to the formation of eddies at the corner as shown in figure 3. Head loss in a sudden expansion : ℎ𝐸=𝑘2(𝑣2−𝑣1)𝑛 The loss of head in a 900 elbows : ℎ𝑏=𝑁𝑘 3𝑣2 2𝑔 Where, N is the number of elbows and 𝑘3 is usually 0.9. Fig 3. Theoretical formula to calculate minor losses 40 Moody diagram Moody diagram is a curve that relates the Darcy -Weisbach friction factor 𝑓, Reynolds number 𝑅𝑒, and surface roughness for fully developed flow in a circular pipe shown in Fig. 4. Fig 4. Moody diagram Raw Data Table 1 Flow rate Pipe 1 Pipe 2 Pipe 3 𝑃𝑖𝑛 (psi) 𝑃𝑜𝑢𝑡 (psi) 𝑃𝑖𝑛 (psi) 𝑃𝑜𝑢𝑡 (psi) 𝑃𝑖𝑛 (psi) 𝑃𝑜𝑢𝑡 (psi) 𝑄1 𝑄2 𝑡1 𝑡2 Volume of reservoir (𝑉) 41 Analyzed Data Calculate the fluid velocity ( 𝑉) through each pipe. Determine the slope of the energy grade line (𝑆) for each of the pipes. Determine the friction coefficients ( i.e., 𝑓, 𝐶𝐻𝑊, and 𝑛) for each of the pipes (Sarker, 2021e) . Compare the measured friction coefficients with the theoretical values . Determine the total head loss through pipe 3. Determine the head loss due to pipe friction using friction coefficients obtained from the pipe friction experiments. Calculate the minor head loss (Note: 𝑚𝑖𝑛𝑜𝑟 𝑙𝑜𝑠𝑠 = 𝑡𝑜𝑡𝑎𝑙 𝑙𝑜𝑠𝑠 – 𝑚𝑎𝑗𝑜𝑟 𝑙𝑜𝑠𝑠). Compare the measured minor head loss with the one using minor loss coefficients obtained from theory . Table 2 - Major loss due to pipe friction Pipe Trial 𝑄 (𝑓𝑡3/𝑠) 𝐻𝐿=(𝑃𝑖𝑛−𝑃𝑜𝑢𝑡) 𝛾 ft 𝑣 (𝑓𝑡/𝑠) 𝑆 𝑅ℎ (ft) 𝑓 𝐶𝐻𝑊 𝑛 #1 𝑄1 𝑄2 #2 𝑄1 𝑄2 Table 3 - Minor losses due to fittings Pipe Trial 𝑄 (𝑓𝑡3 /𝑠) 𝐻𝐿= (𝑃𝑖𝑛−𝑃𝑜𝑢𝑡) 𝛾 ft 𝑣 (𝑓𝑡/𝑠) 𝑃𝑖𝑝𝑒 𝑓𝑟𝑖𝑐𝑡𝑖𝑜𝑛 𝑙𝑜𝑠𝑠 (𝑓𝑡) 𝑀𝑒𝑎𝑠𝑢𝑟𝑒𝑑 𝑚𝑖𝑛𝑜𝑟 𝑙𝑜𝑠𝑠 (𝑓𝑡) 𝑇ℎ𝑒𝑜𝑟𝑒𝑡𝑖𝑐𝑎𝑙 𝑚𝑖𝑛𝑜𝑟 𝑙𝑜𝑠𝑠 (𝑓𝑡) 𝑅𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝐸𝑟𝑟𝑜𝑟 (%) #3 𝑄1 𝑄2 42 Lab Questions 1. What are the factors upon which the frictional loss in a pipe depends? 2. Discuss the relation between fluid friction and velocity of a pipe for different flow condition? 3. Regarding the bottom pipe (Pipe #3), compare the measured minor head loss with its theoretical value (by using minor loss coefficients obtained from