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Use the equation to find the stress which will produce the same value of latex17 at a temperature of latex18 . | 1 |
He decides to build a Sakai top by bending the clip to include a circular arc of radius latex2 and angle latex3 . | 0 |
Derive an expression for the acceleration, latex5 , on latex4 . | 1 |
Both fluids are Newtonian. | 0 |
A reflection in the latex1 -axis followed by a reflection in the latex2 -axis. | 0 |
Determine approximately an expression for the first time after release when the peak concentration shifts to the boundary. | 1 |
Steady contaminant release from an industrial chimney into a horizontal wind. | 0 |
Find the eigenvector latex9 associated with the smallest eigenvalue latex10 . | 1 |
Solve Question 2.1 using Mohr's Circle *only*. | 1 |
For a signal at latex2 , the output of the sensor is latex3 plus ripple (i.e latex3 DC plus ripple voltage). | 0 |
The power latex5 required to tow the submarine. | 0 |
In the binary system, we follow exactly the same approach: latex66 where the latex67 's are either set to latex14 or latex3 . | 0 |
The position of latex4 is given by latex5 and the position of latex6 by latex7 . | 0 |
The moment of inertia of the car about its centre of mass is latex3 . | 0 |
The inertia of the rotating parts other than the disc may be neglected. | 0 |
The correct relation is latex4 but e.g latex5 The reciprocal rule only holds if the same variable is being kept constant on both sides of the equation. | 0 |
A set of Earth observers see a rocket ship moving to the right with an latex0 velocity latex1 and a second ship moving to the left with an latex0 velocity latex3 . | 0 |
You may assume (because you proved it in the previous question) that the total momentum of the latex0 particles is zero in the centre-of-mass frame. | 0 |
You need to use a control volume analysis to answer this question. | 1 |
When calibrated with the shaft in pure torsion, the gauge records a strain of latex3 . | 1 |
Consider a different potential exists in 3D space - latex3 . | 0 |
A vector field latex0 is given in cylindrical polar coordinates by latex1 where latex2 is a constant. | 0 |
If the wheel has a moment of inertia of latex3 , what is its angular acceleration? | 1 |
The dominant wind direction is from the South West and the ground surface can be considered a perfect reflector. | 0 |
Calculate the temperature latex8 behind the oblique shock wave. | 1 |
Find an expression for the height of the water/air interface latex9 . | 1 |
**(L13)**: Find transformation matrices for the following operations in two dimensions: A reflection in the line latex0 . | 1 |
The shaft of the motor is subject to an external torque causing a maximum speed reduction of latex0 . | 0 |
Hence, find the integral of latex1 . | 1 |
Suppose that latex3 but latex4 . | 0 |
Complete the following table, using the psychrometric chart: | 1 |
Plot latex16 and latex17 versus latex18 . | 0 |
Note one constant will remain unknown due to the second boundary condition not being given. | 0 |
Now assume that the compressor and the turbine both have an isentropic efficiency of latex17 instead of latex18 (but are still adiabatic). | 0 |
The question is long but provides very good practice in converting from one frame to another and handling the associated algebra. | 0 |
(Hint: use the binomial expansion.) | 1 |
Determine the corner frequency of a filter that would eliminate the chance of aliasing. | 1 |
ITER is an experimental facility currently under construction in Cadarache, France ([embedded]) It is designed to prove the feasibility of commercial fusion reactors. | 0 |
What would the stagnation pressure be, if it were estimated using the Bernoulli equation? | 1 |
A uniform rod of length latex0 and mass latex1 has one end attached to a smooth hinge, whose axis is horizontal and is allowed to fall from a horizontal position. | 0 |
To calculate the ratio of acid to base needed for a buffer of a particular latex4 , we use the Henderson-Hasselbalch equation, which you are now going to derive. | 1 |
What is the voltage at point “X” under these conditions? | 1 |
The seed weighed latex36 , and contained about latex37 carbon (on a dry-weight basis). | 0 |
What is the probability that there will be *no mutations whatsoever*? | 1 |
You can see the edges of the plates poking through in this image (the six little rectangles) - these tabs are fixing them onto the spool. | 0 |
Write down the equation of the plane in vector form. | 1 |
**26**(3), 442 (1963)] established the equality of gravitational and inertial mass, latex0 and latex1 , to an accuracy of 3 parts in latex2 . | 0 |
The 540 ore cars had a combined mass of latex0 kg. | 0 |
In the case of a block with mass latex17 kg and surface area latex18 m latex19 moving over a film of water of viscosity latex20 Pa s and depth latex21 mm on a slope angled at latex22 to the horizontal, find the terminal velocity. | 1 |
To write latex20 , write 'ln(x)'. | 1 |
A direct consequence of the bit-shifting process is an extreme sensitivity of the map to the initial condition. | 0 |
\[Let the constant of proportionality be latex3 .] | 0 |
Generalise this derivation to the case of latex3 particles. | 1 |
If latex10 denotes the water level in the tank in the absence of rotation and latex11 is the tank radius, find latex12 in terms of latex2 , latex14 , latex11 and latex10 . | 1 |
A thin-walled steel pressure vessel consists of a cylinder fitted with hemispherical end caps. | 0 |
The material of the spool (discs and inner cylinder) is a medium density fibreboard. | 0 |
(Inspired by chapter 3.2 of \`\`Turbulence, the legacy of AN Kolmogorov'' (1995) by U. Frisch -- CUP) In order to get some insight into the behavior of dynamical systems such as turbulence, we study a recursive system which mimics some of the key components of the Navier--Stokes equations. | 0 |
latex1 latex2 latex3 latex4 | 0 |
**\[Boas 5.2.28]** Sketch the area of integration for the following integral, and write an equivalent integral with the integration in the opposite order. | 1 |
When diffusion is negligible. | 1 |
What is the electrostatic potential energy due to the three charges in terms of latex1 and latex2 ? | 1 |
Consider the integral latex0 where latex1 is the wedge of the circle bounded by latex2 , latex3 , and latex4 . | 0 |
Find the total mass of the fluid inside the torus. | 1 |
The flow in this question is a famous exact solution of the Navier latex0 Stokes equations, and it is the characteristic flow that appears between parallel moving plates, and it is called *Couette flow*. | 0 |
(ii) Express this as a fraction of the specific work output from the turbine of this plant, assuming that: * The turbine inlet state is latex1 bar and saturated vapour [embedded] * The turbine expansion process is isentropic (i.e the plant operates on the basic Rankine cycle without superheat). | 1 |
The force varies with rotational position, latex7 , however in this question we simplify the variation by assuming each cup experiences one value of force, latex8 , for half the rotation, and a second value, latex9 , for the other half of the rotation. | 0 |
Compare the group velocity with the phase velocity for this type of wave. | 1 |
Suppose that a fluid element is displaced sufficiently quickly by some height latex7 such that its expansion is adiabatic. | 0 |
This exercise gives feedback on Risk Assessments. | 0 |
Show that the pressure gradient is equal to the null vector throughout the flow. | 1 |
* Can you see how this relates to the Fourier series? | 1 |
Consider the elliptical lamina bounded by the curve latex0 . | 0 |
Rearrange the second equation, latex15 so that we could work out stroke volume when cardiac output and heartbeat frequency are known. | 1 |
The time taken for a pendulum to perform a complete oscillation is given by: latex0 * latex1 Time period of oscillation ( latex2 ) * latex3 Length of the pendulum ( latex4 ) * latex5 Standard acceleration of gravity ( latex6 ). | 0 |
What limiting value of Reynolds number is considered? | 1 |
This allows you to split the problem into pieces in which you can move some parts past the derivative aspects of latex0 . | 0 |
Each log inserted into the burner heats with a constant power latex0 for a fixed period of time latex1 . | 0 |
Assume air to be a perfect gas with latex3 and latex4 . | 0 |
The radius of latex3 is latex8 . | 0 |
A hand-held rotary sanding machine is shown in the diagram below. | 0 |
What is the air speed at the test section? | 1 |
Complete the table below to check you answers. | 1 |
Consider a counterflow heat exchanger in which the fluids on the hot and cold sides have inlet temperatures latex0 and latex1 respectively, while the temperature of the environment is latex2 . | 0 |
latex2 in the interval latex3 . | 0 |
Do not worry about normalisation factors. | 0 |
Find the trigonometric Fourier series for the following three functions. | 1 |
Although this looks complicated, you will find several of the terms drop out. | 1 |
How is it related to the calorific value of carbon (graphite)? | 1 |
By solving equation (3) show that the general solution to equation pair (2) is: latex11 where latex12 and latex13 are the charge's initial velocity components. | 1 |
Water (density latex0 kg/m latex1 ) flows up the slanted pipe, which is at an angle of latex2 to the horizontal, as shown below. | 0 |
How many photons per second are emitted? | 1 |
Using your answer to Part (a), deduce an expression for the constant latex6 in latex7 , in terms of latex8 and latex9 . | 1 |
Consider the mass flux of a contaminant. | 0 |
Sketch this Rankine cycle with superheat, on a latex2 diagram, then find the turbine specific work latex10 and latex11 for the cycle with superheating. | 1 |
Determine whether the dimensions of this specimen provide a valid plane strain fracture toughness value given the yield strength of the materials was latex12 for the: * Crack length and fracture toughness determined in (a). | 1 |
Plot diagrams to show the distribution of hoop and radial stresses through the cylinder. | 0 |
Show that the simplest expression for latex13 is: latex14 Sketch the boundary layer in the latex15 plane. | 1 |
Let's look at this in the muon's rest frame: for the muon the path length through the atmosphere to the surface is length contracted. | 0 |
Find the strain energy, latex7 , stored in the rope. | 1 |
Rearrange the first equation to give an expression for latex5 in terms of latex6 , latex7 and latex8 Take the base-10 logarithm of this equation, and simplify it, so the right hand side contains one term in latex0 and a second in latex8 and latex7 . | 1 |
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