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Consider the integral latex0 By using the substitution latex1 , show that latex2 can also be written latex3 In part (a), you have shown that latex4 Use this relationship to find latex2 . | 1 |
(Based on P4.20, White) A two-dimensional incompressible velocity field has latex0 -component latex1 , for latex2 and latex3 . | 0 |
(Answer to 3 sf) | 0 |
The speed of a D.C. motor is governed by a proportional control system with unity feedback. | 0 |
An equalizer is to be used to process a sound signal with a range of latex0 to boost spoken language while suppressing background noise i.e the equalizer should amplify those frequencies within the normal range of speech ( latex1 ), while suppressing lower and higher frequencies which are outside this range. | 0 |
Which of the following statements correctly describes a fluid? | 1 |
Gas enters the turbine of a gas turbine engine at latex0 , with a mass flow rate of latex1 , and expands adiabatically through a pressure ratio of latex2 . | 0 |
What is the blade length (or height)? | 1 |
Simplify the Euler Equations in the following scenarios,Hydrostatic ( latex0 ). | 1 |
A mild steel beam of rectangular cross-section, latex0 wide, latex1 deep, carries loads which cause a bending moment latex2 and a shear force latex3 at a section latex4 along its length. | 0 |
If latex4 and latex2 is pure imaginary, find latex6 . | 1 |
A real silicon diode with the polarity shown in the diagram above A real C6V3 Zener diode, with the polarity shown in the diagram above An internally short-circuited (i.e blown) diode. | 0 |
Time averages were calculated using all the data recorded. | 0 |
In order for the car to remain on the track, a set performance level must be achieved. | 0 |
Give an expression for: The work done by a fluid between two points with total head, latex0 and latex1 . | 1 |
In ordinary derivatives a function latex0 implicitly defines latex1 and their derivatives obey: latex2 (check e.g for latex3 ). | 0 |
Assuming that there is only molecular diffusion: latex2 . | 0 |
How many parameters are in the equations? | 1 |
The angular momentum of the particle around latex2 is given by latex6 , where latex7 is the velocity of the particle. | 0 |
The velocity in a Poiseuille flow between two parallel plates is characterised by a parabolic profile. | 0 |
We will say that a good approximation is one where the inner product of the difference between the two is small, so the best approximation with latex3 terms is the one that leaves: latex5 the smallest. | 0 |
It is made of titanium alloy ( latex2 , failure stress latex3 ). | 0 |
By what factor is the oscillation amplitude reduced by this slight change in latex14 ? | 1 |
What is the most appropriate "framework" for thermodynamic analysis, i.e closed system (or system or fixed mass) or open system (or control volume), in each of the following situations: An air-standard Otto cycle, modelling the processes in the cylinders of a spark ignition engine? | 1 |
Consider the following two initial values (note that they differ only by the latex22 -th bit): latex94 (i) Apply (6) over latex22 iterations to find latex96 and latex97 (ii) Find latex98 , latex99 , latex100 and latex101 using (5), and comment on their differences No matter how small the difference betwe... | 1 |
The filter should have an input resistance of latex6 . | 0 |
In order to maximise excitement, passengers should feel three times their normal weight at point C. How far below point B should point C be placed? | 1 |
The amount of oxygen and blood pumped by the mammalian heart can be modelled by the following: latex0 latex1 * latex2 Volume of oxygen consumed latex3 * latex4 Cardiac output ( latex5 ) * latex6 Oxygen content in arterial blood ( latex7 ) * latex8 Oxygen content in venous blood ( latex7 ) * latex10 Hear... | 0 |
If yes, why? | 1 |
What is the Mach number of the train in the tunnel? | 1 |
Compare your solution with the one in the worked solutions. | 1 |
The specific enthalpy of steam at latex10 and latex11 bar. | 0 |
Given that those who have CF have twice as many copies of the *cf* allele as CF carriers, what is the frequency of the *cf* allele (*i.e * what is latex1 ?) | 1 |
* For **(a)** latex6 , while for **(b)** latex7 . | 0 |
In search of an Arts Council grant, the artist Damien Worst wishes to paint the **inside** surface of the musical funnel obtained by rotating the curve latex0 for latex1 about the latex2 -axis. | 0 |
You will also need to use the fact that the boundary conditions are as follows: * At latex1 , latex15 , latex16 , latex17 , * At latex2 , latex19 , latex20 , latex17 . | 0 |
We shall call this toy problem the *logistic map*. | 0 |
Two identical pendulums, each of length 1 m with a mass of 0.5 kg, are coupled with a spring of spring constant 15 Nm latex0 . | 0 |
Show that for a charge moving in the latex4 - latex5 plane under the influence of a magnetic field latex6 , the equations of motion are: latex7 By introducing the complex variable latex8 , show that the equation pair (2) may be written as a single equation: latex9 where latex10 . | 1 |
The car's velocity is in the direction labelled 2, direction 1 is perpendicular to the car's velocity and directed away from the car's position, whilst 3 is the upward normal to the road surface. | 0 |
Advection and diffusion; both in latex0 , latex1 , and latex12 directions. | 0 |
Use latex8 . | 1 |
Note that latex8 and latex10 rotate as the mass rotates. | 0 |
Assume that the fluid velocity is uniform in latex0 and latex1 . | 0 |
Determine the minimum value of latex2 necessary to contain the steady state error within latex3 , when a step input of amplitude latex4 is applied. | 1 |
Give a quantitative answer by examining how much original latex3 mass would remain at this point in terms of latex27 . | 1 |
This corresponds to a local maximum in the latex0 vs. latex1 plot. | 0 |
Show that for these initial conditions latex9 and latex10 . | 1 |
Find the angular velocity latex5 of the wheel at the instant when it leaves the path and starts to mount the step. | 1 |
Find the directional derivative latex2 in the direction of the (un-normalised) vector latex3 at the point latex4 . | 1 |
Neglecting friction, what is the minimum height, latex8 , of latex4 above latex5 at which the car can start from rest without falling off the track at latex11 ? | 1 |
Since then, bridge designers test their designs in wind tunnels. | 0 |
The fluids are Newtonian with constant and uniform densities ( latex7 ) and dynamic viscosities ( latex8 ). | 0 |
The carrier, which is freely pivoted about latex4 , has a total mass of latex5 and may be considered as two uniform rods, each of length latex6 . | 0 |
After leaving Waterloo station the driver requires a steady speed of latex1 . | 0 |
What is the critical bed shear stress, latex4 , for this channel? | 1 |
Ignore all forces other than gravity. | 0 |
Don’t forget that $1/x latex6 x^{-1} latex7 \frac{A}{B}=0 latex8 A latex9 A latex10 B$ is not zero too, but it isn’t in this case because all the terms in the denominator are positive). | 0 |
For what values of latex4 does latex7 ? | 1 |
If a latex6 scale model were to be tested in a wind tunnel and full dynamic similarity was required: What air velocity would be necessary in the wind tunnel compared to the wind velocity experienced in real life (use latex7 for velocity)? | 1 |
As it falls, it undergoes both linear and rotational acceleration. | 0 |
What is: The change in energy flow rate. | 1 |
The situation is modelled as follows: In the diagram, the coordinate system is at the centre of the car's circular motion. | 1 |
The figure shows the train in the tunnel, in a frame of reference attached to the train. | 0 |
An electric resistance heater with latex0 efficiency. | 0 |
Sketch the processes on a latex9 diagram, numbering the state points to correspond with the figure above. | 1 |
Having now seen the Lorentz transformations, we will check that we can reproduce these results explicitly.We will start with time dilation. | 0 |
What would have happened if, instead of throwing the rock sideways, Biff had thrown it up at an angle? | 1 |
Find the maximum deflection of the loaded beam. | 1 |
The sanding disc, which may be considered to be a uniform disc of mass latex1 , has a diameter latex2 . | 0 |
That is, the power spectrum is the same if latex8 is replaced by latex9 , where latex10 is an arbitrary phase. | 0 |
The latex0 roots of unity are the solutions to the equation latex1 for any **positive integer latex2 . | 0 |
Does the length of the rod matter? | 1 |
Can you work out the boat’s velocity latex2 and displacement latex3 in this case? | 1 |
* Gravity can be neglected. | 0 |
There are two ways to get the answer, and one of them requires an infinite sum. | 0 |
As with the petrol engine, you need to evaluate the conditions at each stage in the engine. | 1 |
At latex3 , Matt emits a light pulse to Rick and another to Lucy. | 0 |
How many conditions on latex17 do you need to find to determine the coefficients? | 1 |
Calculate the wall shear-stress latex24 . | 1 |
Sketch a diagram of the plant layout. | 1 |
There is a dam at one end of width latex1 m as shown. | 0 |
In practice, the repeated sequence will be truncated to fit in memory. | 0 |
If a population of cells is exposed to radioactive UTP labelled with latex0 (a radioactive isotope of phosphorus), the mRNA being formed at that moment will be labelled. | 0 |
State whether this cycle is suitable for maintaining a temperature of latex4 in the cold space. | 0 |
Find the inverse of each of these functions and the domain of each inverse; latex0 , for all real latex1 latex2 , where latex3 | 1 |
(Based on P4.10, White) The flows in this question are all two-dimensional, incompressible and steady. | 0 |
Use an analytical method to confirm the answers found in (a). | 1 |
What is the distance latex2 between Earth and the centre of the Milky Way as seen by an observer in the spaceship's inertial reference frame? | 1 |
In lectures, we worked out a formula for the distance travelled by a boat initially moving at speed latex0 , gradually brought to rest by a drag force of the form latex1 . | 0 |
In doing so we derived the values of the constants needed to match the general solution; however more generally we need a method to do this matching when the general solution is not known. | 0 |
Choose the appropriate set of equations to solve the problem and show that the component of the velocity normal to the wall is strictly zero, i.e latex13 . | 1 |
Using the Cartesian frame of reference shown: If latex5 , show that latex6 . | 1 |
A mass of 1.5 kg is on a spring of spring constant 80 N/m. | 0 |
What does it mean if the filter function is real but negative, i.e $G(\omega) [embedded] * If aircraft humming (below 200 Hz) should be seriously reduced, what is the longest the delay can be before the signal is (negatively) replayed? | 1 |
The mass of the wheels may be ignored. | 0 |
A damped harmonic oscillator has the equation of motion latex0 When latex1 , the damping is light. | 0 |
To answer this question, note carefully the definitions of latex17 and latex18 in Figure 16.4. latex22 where latex23 is the frontal projected area and latex24 is the relative flow speed. | 0 |
Three-quarters of its initial mass is fuel. | 0 |
Contrast these results with a heat loss of approximately latex7 under normal room conditions. | 1 |
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