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Calculate the power lost at the expansion, and express it as a fraction of both the initial kinetic power and the final kinetic power. | 1 |
There is an incompressible Newtonian fluid of density latex5 and viscosity latex6 in the gap between them. | 0 |
Draw the paths of the light pulses on the diagram. | 1 |
Assume the velocity profile at the trailing edge to be linear (in the image shown), and the flow to be two-dimensional. | 0 |
The "lenticular" aerofoil sketched below has a thickness/chord ratio of 0.08. | 0 |
Calculate the pressure behind the shock. | 1 |
The velocity is uniform along latex2 and latex0 ; the axial component of the velocity, latex4 , is zero everywhere in the gap. | 0 |
Since then, bridge designers test their designs in wind tunnels. | 0 |
If one of the vertices is placed at the origin with edges aligned along the coordinate axes, the density at the point latex0 is latex1 . | 0 |
The weather conditions are just perfect so that a Mach cone is made visible thanks to a condensation phenomenon. | 0 |
Show that latex0 is **not** an exact differential, but that it becomes exact if multiplied through by a factor latex1 , for a suitable value of latex2 . | 1 |
Take latex33 m and latex34 . | 0 |
It was tested by being pressurized until it failed, at a pressure of latex2 . | 0 |
latex2 What would be the new design life if the engine rate latex3 hotter? | 1 |
Estimate the time-averaged velocity at latex4 . | 1 |
* (ii) The number of oscillations for the amplitude to fall by a factor of latex5 is latex14 . | 0 |
At the bottom of the plate, latex3 | 0 |
There are two principle methods of recording a risk assessment: 1. | 0 |
Ignoring any time dilation, if one particular muon decayed after exactly 1 lifetime how far would it have traveled towards the Earth's surface before it decayed into an electron? | 1 |
Comment on the orientation when the cube is submerged. | 1 |
What is the flow rate latex5 that corresponds to the threshold of motion in this channel (assuming the same uniform depth)? | 1 |
What does latex7 equal? | 1 |
The car accelerates from rest as a result of the rear wheel exerting a horizontal tractive force of latex4 . | 0 |
Assuming the value found in (a) to be the maximum current to be provided by the voltage regulator circuit in figure, calculate the maximum Zener series resistor latex7 . | 1 |
*** It is worth memorizing Eqs. | 0 |
Estimate the suspended load transport latex7 when latex6 . | 1 |
latex9 latex10 \[BONUS]: latex11 | 0 |
An atom interacting with light is best described using quantum mechanics. | 0 |
Using this simplified expression, calculate the sediment concentration at the following vertical elevations with respect to the bed: latex5 , latex6 , and latex7 . | 1 |
Where is the largest acceleration and what is its magnitude? | 1 |
Explain your answer. | 1 |
On the compression stroke of an internal combustion engine, a mass of air at a fixed initial state is compressed through a certain volumetric compression ratio. | 0 |
If the ratio of outer to inner diameter is specified as latex2 and the maximum allowable shearing stress is latex3 , find the required shaft outer diameter. | 1 |
The latex0 component of velocity in a steady incompressible flow field in the latex1 plane is latex2 where latex3 and latex4 are two constants. | 0 |
Compute the vorticity. | 1 |
Complete the table below. | 1 |
Find latex0 for each of these relationships: latex1 latex2 latex3 | 1 |
What are the maximum hoop, radial and shear stresses, if the axial stress is zero **when treated as a thin cylinder**. | 1 |
Show that the shear stress latex7 acting on the wall is equal to latex8 . | 1 |
For this reason, note down the densities and viscosities for common fluids such as water and air as they will be used throughout the course and don't change.) | 1 |
How does your answer to (a) compare to manufacturer data? | 1 |
Evaluate both of these integrals and verify that they give the same answer. | 1 |
A circular section tube, outer diameter latex4 , wall thickness latex5 . | 0 |
Determine if the unit vector latex5 is the unit vector corresponding to any of the following expressions: *** latex6 | 1 |
The helicopter weighs latex6 . | 0 |
Assuming the masses have small displacements ( latex3 and latex4 ) from equilibrium, show that their equations of motion are 	 latex5 , 	 latex6 .	 We now look for normal modes of the system. | 1 |
Given that the chosen combination is the 10 tooth sprocket to the 28 tooth sprocket, and then the 22 to the 58mm diameter pulley, you need to confirm the maximum (linear) speed of the go-kart achieved by this combination. | 1 |
A person of mass latex0 kg, standing in a stationary train carriage, starts walking towards the front of the train, accelerating from initial velocity latex1 m latex2 s latex3 to final velocity latex4 m latex2 s latex3 relative to the carriage. | 0 |
The dissociation will also produce an equal concentration of conjugate base, latex4 , and lower the concentration of latex0 by the same amount. | 0 |
Calculate the power dissipated in all components of the circuit below. | 1 |
Hence show that, for elementary matrices, latex12 Hence show that latex13 . | 1 |
Which parts of the spool give the largest contribution to the total moment of inertia? | 1 |
By taking care when crossing the road, what type of control measure are you implementing? | 1 |
Sketch the volt-amp characteristic, latex0 vs. latex1 , for each of the ‘equivalent networks’ shown below, which contain PERFECT diodes. | 1 |
Hint: to solve the differential equation, try seeking a solution of the form latex14 . | 0 |
Having learnt to duck, Biff now throws the rock horizontally at speed latex14 , which is fast enough to place it into an elliptical orbit. | 0 |
Finally, suppose that a single-stage rocket could be built which could carry the same total mass of fuel but where the mass without any fuel on board was the same as that of the second stage of the two-stage rocket without any fuel on board. | 0 |
Heavy rainfall causes a large amount latex1 C_{\min} latex2 \sqrt{(x-Ut)^{2}+y^{2}} latex3 \dot{M}\ \mathrm{[kg/ms)]} latex4 0...T$. | 0 |
Displacement of woman relative to lake, latex0 : | 0 |
In lecture 19 we looked at a spool of thread. | 0 |
Determine the unknown velocity component latex0 or latex1 for the following flows: latex2 latex3 latex4 latex5 | 1 |
Show that the individual terms in the trigonometric Fourier series are orthogonal. | 1 |
And what does what you know about the dependence of latex10 on latex12 , latex13 , latex29 and latex30 then tell you? | 1 |
Three identically sized plates have been positioned at tangents to the earth’s surface at the equator, mid-latitude and high latitude. | 0 |
Evaluate latex0 where latex1 , latex2 is oriented upward, and latex3 is the portion of the plane latex4 in the first octant. | 1 |
Assuming the fracture to have taken place in the plane of maximum shear stress, determine the torsional load on the cylinder and the magnitudes of the principal stresses in the cylinder wall. | 1 |
latex0 latex1 latex2 t \le -T latex3 -T [embedded] T latex4 | 0 |
A single-stage turbine has a blade speed of latex0 and a specific work output of latex1 . | 0 |
The cord exerts no force when she is less than latex1 metres from the platform but acts like a perfect spring with spring constant latex3 when stretched. | 0 |
Again use one step of the worked solutions to get you going if needed. | 0 |
*** *Draw a sketch to convince yourself that this is a torus*. | 1 |
Calculate the pressure and temperature at that point using the compressible flow tables. | 1 |
The four-velocity is given by latex0 , where latex1 is the usual three-velocity of a particle, latex2 and latex3 .What is the squared-length of the four-velocity? | 1 |
What is the probability that *only one* base (at any position) in the DNA sequence will mutate? | 1 |
A buoyant release of contaminant. | 0 |
Compute the pressure just downstream of the shock at section 1. | 1 |
The system represented by the block diagram shown below has transfer function values of latex0 , latex1 and latex2 . | 0 |
Show that if the cue starts at rest with a very small angular deflection latex16 , the solution becomes, latex17 On the same axes sketch latex18 for the two cases. | 1 |
The figure below shows a u-bend manometer, usually used to measure small pressures. | 0 |
In higher dimensions a similar relation holds, but it is important to keep track of which variable is being kept constant. | 0 |
Imperial College lies at a latitude of latex13 North. | 0 |
Determine the overall transfer function of the system. | 1 |
What was the volume of the assay in litres? | 1 |
The disturbance moves with constant velocity latex1 . | 0 |
Show, using conservation of mass, that the streamwise component of the velocity outside the boundary layer can be expressed as latex7 The Blasius solution gives latex8 where latex9 and latex10 is the distance along the wall. | 1 |
latex5 is the transverse component of the velocity (perpendicular to the flat plate) at the edge of the boundary layer. | 0 |
Show that latex4 is normalised and is orthogonal to latex5 . | 1 |
The specific exergy destruction (or irreversibility). | 0 |
The insolation at a particular latitude is trigonometric function of latitude. | 0 |
The total amount of mRNA in a culture of rapidly dividing cells increases exponentially: latex0 * latex1 Mass of mRNA [embedded] * latex2 Initial mass of mRNA [embedded] * latex3 Cell growth rate [embedded] * latex4 time Use (natural) logs to derive an equation of the form latex5 . | 1 |
The gas turbine engine is to be modelled as a closed-cycle plant operating on the air-standard Joule (or Brayton) cycle. | 0 |
What should you do to extend battery life? | 1 |
The mean diameter is latex2 and the mass flow is latex3 . | 0 |
A seed of the narrow-leaved campion *Silene stenophylla* was recently recovered from a ground-squirrel food cache in the Siberian permafrost. | 0 |
He created Civilian Space eXploration Team and on May 17th 2004 they launched they launched an amateur rocket above the surface: space! | 0 |
Let's look at that in more detail. | 0 |
How do the above results compare with your personal observation as a pedestrian living in London? | 1 |
You are required to use a small motor with a speed vs torque curve shown below. | 0 |
Two equal masses (each of mass latex0 ) are connected to each other and to two adjacent walls by identical springs (spring constant latex1 ). | 0 |
Write all necessary conditions on latex10 to determine the coefficients in the polynomial expansion, and show that: latex19 Calculate the displacement ( latex20 ) thicknesses of the velocity profile, as functions of the boundary-layer thickness ( latex4 ). | 1 |
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