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Spreading jam on bread (viscosity of jam is about 8 Pa s) | 0 |
A solid, rectangular cross-section, steel beam, latex0 long, latex1 deep, is simply supported at its ends and is to carry a total uniformly distributed load of latex2 . | 0 |
Find expressions for the force on another charge latex3 as a function of position along the latex4 axis. | 1 |
Calculate the mass flow rate passing through the wind tunnel. | 1 |
What would be the angle of twist per metre length of the shaft when under full load? | 1 |
In its daily schedule, an engineering company can manufacture quantities latex0 of its main products, giving a projected profit of latex1 . | 0 |
We then proceed with the same counting procedure as for the integer numbers (as explained above), but applied to the figures after the "dot''. | 0 |
If sediment motion is present write the condition for a stable bed. | 1 |
Select a resistor which, in combination with a latex5 capacitor, will reduce the ripple by latex6 . | 1 |
The pressure, latex2 , as a function of the upstream pressure latex3 . | 0 |
State the significance of the negative sign in Fick's Law, using a diagram (student's are expected to draw the diagram on paper, and compare with final answer). | 1 |
Integrate equations (4) to show that the trajectory of the charge is given by: latex14 where latex15 and latex16 are the coordinates of the charge's initial position. | 1 |
Which view is consistent with a Lagrangian description and which view is consistent with a Eulerian description? | 1 |
(ii) Sketch the processes of the open cycle on a latex12 diagram. | 1 |
To match the available power, it is desired that the specific work transfer to the air at this stage be latex3 . | 0 |
What is the requirement for a real gas to be liquefied by throttling in a Linde process? | 1 |
A 'comprehensive' risk assessment, for more serious risks like nuclear energy, cyber security, or pandemics As engineers it is useful to develop a habit of writing a 'comprehensive' risk assessment, which separates the consideration of likelihood and severity What is the definition of a risk? | 1 |
An explosion on a ship latex0 away from the coast releases a quantity latex1 of contaminant. | 0 |
What is the centre of mass of the cube? | 1 |
Two uniform discs latex0 (wit mass latex1 and radius latex2 ) and latex3 (with mass latex4 and radius latex5 ), and a uniform rod-shaped carrier latex6 (with mass latex7 and length latex8 ), are freely pivoted together as shown in the diagram. | 0 |
What is the horizontal limit in terms of its variables? | 1 |
If the cross-sectional area at the test section is latex5 , what is the mass rate of the flow? | 1 |
Note that latex16 and latex17 rotate as the mass rotates. | 1 |
The ground temperature varies with position through a cold front, falling at the rate of latex3 per km. | 0 |
If we denote latex0 as the `traction force' per unit area on each face of a particle; latex1 as the stress tensor; and latex2 as a unit normal; what is the order and physical dimensions ([ latex3 ],[ latex4 ],[ latex5 ]) of each of the following terms?As an example, the answer for latex6 is Order 1, latex7 , latex8 , latex9 . | 1 |
Hint: we only require an average over the control volume. | 0 |
Consider the equation of motion of a classical undamped harmonic oscillator with natural frequency latex0 , latex1 with the initial conditions, latex2 Show that the solution to this initial value problem is, latex3 | 1 |
The specific heat ratio of latex0 is latex1 and its gas constant is latex2 . | 0 |
This question takes you through an observation which provides a direct experimental confirmation of time dilation and length contraction. | 0 |
Cite the main assumptions behind your bed shear computations in parts (a) and (b). | 1 |
Is kinetic energy conserved? | 1 |
With a steam consumption of latex2 , the stage develops a power of latex3 . | 0 |
Calculate the normal mode frequencies (in Hz), assuming latex11 N m latex12 and latex13 \~kg | 1 |
Consider a straining flow as in Q2.1 and Q2.5, i.e latex0 and assume constant, uniform density, and no body forces.To prepare for this question, write the Euler Equations in two-dimensional Cartesian coordinates latex1 . | 1 |
There is a tolerance permitted of up to 5% under this speed but no tolerance for going over. | 0 |
The tracks near points C and D are arcs of circles of radius 10 m. Assume for simplicity that latex0 . | 0 |
The fluid density is 1032 kg/m latex0 and kinematic viscosity is 0.95 x 10 latex1 m latex2 /s. | 0 |
What do each of the assumptions imply about the velocity components latex8 , latex9 and latex10 and the pressure latex11 ? | 1 |
Compute the bed shear stress, latex3 . | 1 |
Now we generalize this to a line of latex1 identical point sources, each separated by a distance latex0 and spanning a total distance latex3 . | 0 |
**(L11)** Consider the system of 3 equations in 3 unknowns latex0 Identify the matrix latex1 of coefficients and then: Find the inverse latex2 . | 1 |
A unit cube has an inhomogeneous density distribution. | 0 |
In these conditions the specific flow discharge is latex0 , the normal flow depth is latex1 , the section slope is latex2 and the sediment size is latex3 . | 0 |
Show that its volume is latex2 . | 1 |
\[Assume that the friction force of the damper is proportional to latex4 and that the spring force is proportional to latex5 ]. | 0 |
The bit-shifting process that we have now understood leads to one fundamental question: electronic devices have a finite amount of memory, and numbers are therefore represented by a finite amount of bits. | 0 |
What is the tensile failure strength of the iron? | 1 |
As the person accelerates, their muscles do work , converting stored chemical energy into kinetic energy. | 0 |
Let latex9 y latex10 \vec{u}_a=\vec{u}_a(y) latex11 \vec{u}_b=\vec{u}_b(y) latex12 v_a(y)=0 latex11 v_b(y)=0$. | 0 |
Describe the morphological impact of the development on the river, stating any equations used. | 1 |
Determine the maximum allowable side slope, latex4 . | 1 |
Other losses from the GT and HRSG can be ignored. | 0 |
They join at latex0 , where latex1 is an integer. | 0 |
Rewrite dy in terms of latex7 Integrate to find an expression for the field latex8 in terms of latex9 . | 1 |
In the first case, for the beam with no holes in the vertical web, identify two possible failure modes, and calculate the safety factors against yielding if the steel had a yield strength of latex2 . | 1 |
Calculate the end load which must be applied. | 1 |
The following data were obtained during a run of this experiment: [table] Calculate the latex2 percentage survival for each time period. | 1 |
The ratio of latex7 with latex1 is known as the Froude number (noted latex10 ). | 0 |
One key element of the design is to account for the variation of the atmospheric density ( latex0 ) as the drone is gaining altitude. | 0 |
The 3PB sample consists of a simply supported beam of span latex0 , width latex1 , thickness, latex2 . | 0 |
Consider a supersonic flow ( latex0 ) with latex1 , latex2 atm and latex3 K. This flow is deflected at a compression corner of latex4 . | 0 |
Derive an expression linking latex2 to latex4 via Tresca and Von Mises yield criteria. | 1 |
Show that the shells fly furthest when latex2 . | 1 |
By using results we found in lectures and without doing any integrations, can you determine (approximately) its moment of inertia? | 1 |
Find the refrigerant mass flow rate in the evaporator which is necessary for a heat transfer rate of latex18 from the cold space. | 1 |
14.7),What limiting value of Mach number is considered? | 1 |
If latex0 and latex1 By using the chain rule, calculate latex2 . | 1 |
For a steel cylinder, latex1 and latex2 . | 0 |
We will now draw out a spacetime diagram of this situation to illustrate which events happen simultaneously in which reference frame.Draw a spacetime diagram in which Rick, Lucy, and Matt are stationary, with Lucy at latex0 , Rick at latex1 , and Matt at latex2 . | 1 |
*** \[This is simply the cube in the corner of the first octant, with diagonal latex4 but without the face in the latex5 plane. | 0 |
Using the expressions you have found, calculate the area ratio and Mach number at a section located a distance latex9 from the throat. | 1 |
Let latex0 be given by: latex1 . | 0 |
The flow is assumed to be steady, fully-developed in latex5 and latex7 with no flow in latex7 , i.e latex9 . | 0 |
*** Be careful to re-cast this, i.e change variables, into a cylindrical form in which the axis of revolution is the new latex4 -axis. | 0 |
Part of a machine drive system is shown below. | 0 |
Rearrange the equations so we can calculate stroke volume if we know the difference in oxygen content between arterial and venous blood, as well as the volume of oxygen consumed and the heartbeat frequency? | 1 |
Show that the pressure is uniform throughout the flow field (the same value in both fluids). | 1 |
Why does he not pull at a shallower angle (closer to the horizontal)? | 1 |
Atmospheric pressure is What is the total vertical force of the fluid on the beaker? | 1 |
The rate of a population's growth at different times is not directly measurable; however, with a time series for a population, we can use differentiation to work out an equation for the rate of population growth at any time. | 0 |
For a spherical bubble with spherical oscillations, a simple model of the motion of the water is given by a scalar velocity potential expressed by latex5 where latex6 is time, latex7 is radial position, latex2 is a constant, and latex9 is a wave number, i.e a constant with dimensions latex10 \vec{u}=\overrightarrow{\mathrm{grad}}{\phi}$. | 0 |
Calculate the safety factors against **yielding. | 1 |
In this question you need a basic understanding of turbulent boundary layers and you will use it, in combination with publically available information (that you may need to Google) to make some practical estimates about an engineering system. | 0 |
A 2-stage transmission is required, made up of a belt and a chain drive. | 0 |
Consider a conical, supersonic nozzle, in which the area expands from latex0 at the sonic throat to latex1 at the exit, which is a distance latex2 from the throat. | 0 |
Compute the bed shear stress and friction coefficient assuming a velocity profile following the log-law. | 1 |
Why are lines of constant specific humidity and constant partial pressure of vapour parallel? | 1 |
Compare the value obtained in part (a) with the turbine power in units of latex7 . | 1 |
Mark the region where the continuum assumption is valid. | 1 |
Explain the role of the roughness Reynolds number, latex0 , in determining if the flow regime at the boundary layer is rough or smooth turbulent. | 1 |
Choose the correct equation, in vector form, that governs the transport of a neutrally-buoyant and passively released contaminant in the situations that follow. | 1 |
Show that the pressure, latex12 , is a function of latex1 only and compute latex14 . | 1 |
Using a control-volume analysis, we want to find the required power to tow the submarine. | 1 |
Find a second order polynomial latex6 which is orthogonal to both latex7 and latex8 , and is normalised. | 1 |
The pressure at the origin is fixed at latex3 . | 0 |
Compute the following: The fluid particle acceleration at latex1 The time required for a fluid particle to travel from latex2 to latex1 . | 1 |
In our case, the body rotates mainly about principal axis 3. | 0 |
Is it a function of the temperature? | 1 |
Now find expressions for the torque and angular momentum about latex1 , expressing them in terms of the same unit vectors used in parts (b) and (c). | 1 |
In each case either prove your answer or provide an example where the statement is false. | 1 |