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Determine the number of kilomoles and the mass of helium in the balloon. | 1 |
Assuming uniform gravitational force latex4 , find an expression for the charge Q as a function of latex4 , latex1 , and latex3 . | 1 |
What mass of diesel would be required to propel the ship across the Atlantic Ocean from Bristol to New York? | 1 |
In the diagram, a mass latex0 kg is placed on a hole of diameter latex1 cm. | 0 |
What are the length and velocity scales of the mean flow? | 1 |
What do the Earth observers conclude about the relative velocity of one ship with respect to the other? | 1 |
[embedded] The gearbox you have been supplied only came with the gear part numbers, which are as follows… * G1 - 12 * G1 - 30 * G2 - 8 * G2 - 28 What is the step-down ratio of the gearbox? | 1 |
Find the area of one loop latex0 of the lemniscate latex1 | 1 |
Solve Question 2.2 using Mohr's Circle *only*. | 1 |
Give an alternative interpretation of this combined transformation. | 1 |
What are the partial pressures of each component of the air- latex4 mixture? | 1 |
For this question, the river is discharging latex0 of phosphorus into the sea as a continuous release. | 0 |
For very light damping ( latex11 ), show the following: * (i) latex12 . | 1 |
Latitude, latex3 (phi), is conventionally defined to have a value of latex4 at the equator, and latex5 at the North and South poles: we can therefore arbitrarily define the north pole as latex6 and the south pole as latex7 if we wish. | 0 |
Find the velocity of the particle after the collision with the wall, assuming the collision is elastic. | 1 |
This is shown in the image, below, where a Cartesian frame of reference with latex1 -axis normal to the plate has been defined. | 0 |
Consider Laplace's equation for a function latex0 : latex1 Find the relation between the constants latex2 and latex3 if the function latex4 satisfies Laplace's equation: Show that the function latex5 satisfies Laplace's equation. | 1 |
*(Take rotation in the clockwise direction to be positive)* | 0 |
Show that the wavefronts are spheres centred on the origin. | 1 |
Using the normal-flow model discussed in class, describe the new equilibrium situation that the river will adopt after the mining disposal. | 1 |
(Based on P4.29, White) Consider a steady, two-dimensional, incompressible flow of a Newtonian fluid in which the velocity field is known: latex0 , latex1 , latex2 . | 0 |
The figure below shows a symmetrical diamond shaped aerofoil with a total wedge angle of latex0 in a Mach 3 supersonic flow at an incidence of latex1 Determine the flow angle in regions 3, 4, and 5. | 0 |
Calculate the magnitude of the stress in the latex4 -direction that must be superimposed on this system to restore the length of the block in that direction to its original free length. | 1 |
( i ) Explain why latex5 , where latex6 is the velocity of the centre-of-mass frame relative to the lab frame ( ii ) Using the data given at the beginning of the question, find latex6 and latex8 . | 1 |
\[**Hint:** you will need the formula for the sum of a geometric series: latex17 | 0 |
Here follows some additional examples. | 0 |
What is the probability that both Cs in positions 3 and 4 will mutate to T? | 1 |
Consider two events latex0 and latex1 which correspond to two consecutive ticks of a clock with period latex2 in its rest frame. | 0 |
Suggest a set of dimensionless groups for this problem, including a Reynolds number and a factor latex13 representing the rotational speed. | 1 |
Find latex10 in terms of latex5 for the *tip* case and the *base* case ( latex12 and latex13 respectively). | 1 |
Consider the psychrometric chart. | 0 |
In preparation to calculate the entire pressure field, calculate the vorticity, latex3 , of the flow field. | 1 |
Let us take an example. | 0 |
**(L8)**: Use Gaussian elimination to find the general solution of the following equations: latex0 | 1 |
Calculate the applied bending moment. | 1 |
The siren of a police car emits sound waves at a frequency of latex0 . | 0 |
The surface tension force can be resolved into vertical and horizontal components. | 0 |
An (infinitely thin plate) placed tangent to the North pole in this diagram would not intercept any sunlight at all: the beams would skim parallel across its surface: Image incorporates orthographic projection of Earth CC-BY-SA-3.0 Strebe (English language Wikipedia) The solar constant - the amount of solar energy falling on a plane held perpendicular to the sun’s beams at the top of the Earth’s atmosphere is latex2 . | 0 |
You were probably taught this as a child, which was your parents or school or community implementing a control measure to reduce the risk. | 0 |
We have seen that there are similarities and differences between latex0 and latex1 , where latex2 is real and latex3 is complex. | 0 |
Write out each component of the Euler Equations (i.e write three equations) using cylindrical coordinates latex0 . | 1 |
Solve the two separate ODEs in latex5 and latex6 and use this to find the general solutions for latex9 and latex10 . | 1 |
**NOTE: You should only include one example in each field, e.g for the 'Mitigation' field, only list one mitigation, e.g "Wear a lab coat". | 0 |
All other velocity components are zero. | 0 |
Using your answer to part a, determine this maximum speed you will need to limit the motor to. | 1 |
Find the volume flow rate of the refrigerant at the compressor exit. | 1 |
The creep rupture properties of the steel at this temperature are given by: latex1 Where latex2 is the rupture life in hours and latex3 is the applied stress in latex4 . | 0 |
A triangular laminate is bounded by the coordinate axes and the line latex0 . | 0 |
A ball is dropped onto a table from an initial height latex0 . | 0 |
This is because the approximation assumes a velocity latex5 at latex4 as indicated in the diagram; this is in contrast to using latex7 and latex8 in the lecture. | 0 |
The area of the tank to the left of the partition is latex4 and that to the right equals latex5 , whilst the heights of the spouts are latex6 . | 0 |
A small ball is thrown with positive velocity components latex0 from the origin in the vertical latex1 plane under the action of gravity latex2 . | 0 |
Find an expression for the amplitude and intensity again and comment on the effect. | 1 |
o For latex4 , latex5 . | 0 |
The first stage is then detached. | 0 |
*prime* or *dash* (i.e latex16 ) represents the fluctuating component of the function, that is: latex17 Show that: latex18 latex19 latex20 latex21 latex22 latex23 latex24 latex25 if latex26 *Hint: you need to use the assumption that latex0 is bounded. | 1 |
What is the efficiency of a Carnot cycle having the same maximum and minimum temperatures as this Otto cycle? | 1 |
\[No response area - this is freeform text!] | 0 |
Derive an expression for the sound-wave frequency perceived by the pedestrian in terms of latex3 , latex2 and the car's Mach number latex5 (insert latex3 as fs). | 1 |
Show that for *small* angles the equation of motion can be written as latex8 where latex9 . | 1 |
The force on the surface, latex0 due to pressure is always in the latex1 direction. | 0 |
Any object moving in a circle is continuously being accelerated towards the centre with centripetal acceleration is given by the formula latex0 where latex1 is the angular velocity and latex2 is the speed of the mass around the circumference of the circle. | 0 |
The flow is conditioned to enter the working section with a steady, uniform velocity profile at speed, latex1 . | 0 |
The magnitude of the heat transfer. | 0 |
Water from a tap with a diameter of 2 cm flows with an average velocity of 2 m/s. | 0 |
If we are to test a model of the ship to determine the drag, what are the requirements for dynamic similarity? | 1 |
How do they differ? | 1 |
At the throat latex3 . | 0 |
*(Hint: notice from (i) that latex86 -- in the decimal system, it is the well-known equality latex87 )* (vi) Show that if latex77 , then latex89 Therefore, the tent map (3) in binary reads: latex90 It is clear from (6) why the tent map is also called the *bit shift map* since each iteration consists in shifting the bits from right to left, "flip'' all bits if the left most bit (the one on the left of the dot) is a latex3 , and set it to latex14 . | 1 |
Is the channel bed stable for this flow? | 1 |
The angular position of the aircraft is described by the function latex1 . | 0 |
What ram force is required, and how much work is expended in the bending process? | 1 |
A large stationary mass latex0 is suspended by a wire from the ceiling and a projectile of mass latex1 is fired into it at an unknown speed latex2 . | 0 |
Use the Navier--Stokes equations to derive equations for latex14 and latex15 . | 1 |
The turbine has an isentropic efficiency of latex3 and there is a heat loss of latex4 from its casing to the atmosphere. | 0 |
The fluids can be taken to be the same gas on each side, assumed to behave as a perfect gas with constant-pressure specific heat latex3 . | 0 |
Calculate the air requirements and the atmospheric nitrogen in the products if air is used for stoichiometric combustion of latex0 of oil. | 1 |
Repeat this swapping the forms of latex7 and latex8 . | 1 |
The equilibrium configuration is shown in the figure. | 0 |
A supersonic wind tunnel has a rectangular throat latex0 . | 0 |
In which direction are the streamlines? | 1 |
What will be the the shock wave angle when a flow at Mach 3 is deflected by latex5 ? | 1 |
The width, latex14 , of a resonance can be characterized as the difference between the two half-power frequencies, i.e the full width at half the maximum power. | 0 |
Consider combustion of oil and wood in air. | 0 |
What is the pressure at latex4 ? | 1 |
Hence calculate the drag force exerted on the block by the water. | 1 |
Plot the latex5 component of latex28 , against latex29 . | 1 |
Calculate the determinants of the matrices latex9 and show that in all cases latex10 State the effect on the determinant of matrix latex11 that results from applying each of the elementary matrices given in part (a) to A. | 1 |
latex0 where latex1 is some initial condition (a real number between latex2 and latex3 ), and latex4 is the value of the variable latex5 at the latex6 -th iteration. | 0 |
There is no support (i.e the end is free.) | 0 |
The car is moving at a constant speed latex1 . | 0 |
Calculate the concentration at the school for an observer latex3 above the ground surface, for a wind speed latex4 . | 1 |
What does it mean if a fluid is static? | 1 |
(Treat the unit symbols as algebra: use a '\*' to represent a multiplication, *i.e * write latex26 as 'kg\*m\*s\*\*-2' or 'kg\*m/s\*\*2'.) | 0 |
Write the Euler Equations in two-dimensional Cartesian coordinates and simplify them for this situation. | 1 |
Using the given assumptions, explain why the velocity of the fluid in the gap is a function of the radial coordinate, latex10 , only. | 1 |
Consider a generic velocity vector latex0 in a Cartesian frame of reference.Write the velocity gradient tensor in Cartesian coordinates Write the deformation tensor in Cartesian coordinates Write the spin tensor in Cartesian coordinates Write the vorticity vector in Cartesian coordinates | 1 |
Let latex7 and latex8 be sine or cosine functions and use them to construct a standing wave, i.e , a form such that latex4 is always zero at fixed points latex19 . | 1 |
Assuming steady, fully-developed and incompressible flow, with latex3 -component latex4 find an expression for the latex5 -component of velocity perpendicular to the plates, latex6 . | 1 |
Write the most general form of latex10 . | 1 |