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Give the equation for the three-dimensional time-evolution of contaminant concentration. | 1 |
Write down latex2 , the matrix of eigenvectors for latex1 . | 1 |
To explain as fully as possible why this is needed, you can use probabilities to back up your argument. | 0 |
ii) latex11 ? | 1 |
Determine the Mach number downstream of the expansion. | 1 |
State the value of the maximum concentration latex6 at time latex7 . | 0 |
Following what was done for latex13 , a latex16 is now placed in front of the latex14 (i.e we get latex35 ), indicating that we went through the list latex16 times. | 0 |
The pipe maybe assumed thin and axial stresses neglected. | 0 |
(*Hint: Use the fact that* latex7 . | 0 |
In the light of your answer to Part 8.15g) & i), simplify your expressions for the velocity components latex9 , latex10 and latex11 . | 1 |
Evidently the system behaves differently near the wall and a different approximation is needed near the wall. | 0 |
Show that the maximum hoop stress is given by: latex6 . | 1 |
Obtain the friction coefficient, latex2 . | 1 |
Sketch the behaviour of latex15 over time for different initial velocities latex16 . | 1 |
The signal is recorded with latex2 -bit ADC card that has a sampling frequency of latex3 samples per second and an input range of latex4 . | 0 |
An aircraft cruises at latex0 at latex1 altitude on a standard day. | 0 |
Determine the maximum concentration latex1 as a function of time. | 1 |
If necessary, write your answer as a surd. | 1 |
Here we will look at how the smoothness of a function affects its Fourier series. | 0 |
(Be careful with units here). | 0 |
You have been told that you should prioritise efficiency whilst ensuring 50kW of power is provided. | 0 |
The maximum incident light intensity is estimated to be latex2 . | 0 |
Find the steady angular speeds of each disc and of the carrier. | 1 |
Find the orthonormal basis set { latex11 } with one axis based on latex2 , and check they are orthogonal to each other. | 1 |
When the number latex23 is reached, we go back to latex14 , and put a latex3 in front of it so as to indicate that we have been through the list latex3 time (i.e we get latex13 ). | 1 |
*** **Note:** In the Response Area, start your matrix from the top left. | 0 |
The surroundings of the turbine are at a pressure latex6 bar and at a temperature latex7 . | 0 |
The absolute velocity at exit from the stage is axial. | 0 |
Given that the Red Bull car can achieve an acceleration of (pick higher than answer to c), but only has a max speed of (lower than b), will you beat them? | 1 |
Show that a single-stage rocket of the same initial mass, burning the same total mass of fuel, would reach a final speed of approximately latex4 . | 1 |
The signal generator provides a latex0 to latex1 square wave. | 0 |
The power required to drive the compressor, corresponding to the mass flow rate from the previous part. | 0 |
*(Take rotation in the anti-clockwise direction to be positive)* | 0 |
Therefore the material undergoing fusion must be hot, so that the individual particles have sufficient kinetic energy. | 0 |
For how long, in hours, can the bacteria be grown and have their growth safely monitored using latex4 measurements without dilution (*i.e * latex11 ), if their initial optical density is latex12 , and the growth rate constant, latex7 is latex14 ? | 1 |
\[Note: for exponentials, use \*\* instead of ^. ] | 0 |
For latex0 Find the Taylor expansion (up to quadratic terms) about latex1 . | 1 |
Calculate the required mass flow rate of make-up water added to the pond at the base of the tower. | 1 |
Rearrange the equation above to allow us to work out the concentration, latex8 , of a compound from its absorbance value. | 1 |
Integrate the expression with respect to time to obtain a solution for the latex1 . | 1 |
Imagine the body is rotating mainly about principal axis 3 (see Figure), so that latex5 where latex6 and latex7 is a constant. | 0 |
Calculate the drop in voltage when all lights (interior and headlights) are on at the point in time when the engine is ignited. | 1 |
Sketch the results of Part (b) and Part (c). | 1 |
The magnitude of the heat transfer. | 0 |
Hence solve the latex22 component of the Navier latex0 Stokes equations to show that latex49 for some function of integration latex50 . | 1 |
The downstream limit (point B) consists of a rocky rigid bed. | 0 |
A few moments sketching the functions and recognising the symmetries can save a great deal of unnecessary integration. | 0 |
Assuming that the material is **perfectly linear elastic. | 0 |
At the inlet to a compressor stage, the absolute flow velocity is measured to be latex0 at an angle of latex1 to the axis. | 0 |
Millennium Dome and that the money at his disposal post-Brexit will only purchase a large uniform paper-clip of mass latex0 and wire length latex1 . | 0 |
The compressor has a constant axial air velocity of latex4 . | 0 |
Carry out a similar analysis for when the drag force is of the form latex2 , where latex3 is a constant, appropriate for turbulent drag (again, you don't need to know the details of the physics of this). | 1 |
*\[Riley 2.10(a)]* Use the chain rule to show that the first derivative of latex0 is latex1 . | 1 |
The legislator requires the flow in the tunnel to never be choked. | 0 |
The change in specific enthalpy of the mixture. | 0 |
When are the dry-bulb and dew-point temperatures identical? | 1 |
Compute the spin tensor at any location in the flow field. | 1 |
If latex1 , one can approximate latex2 by expanding it as a series in powers of latex3 and keeping only the first few terms. | 0 |
The Arrhenius equation describes the exponential relationship between the rate constant ( latex0 ) for a reaction and the temperature ( latex1 ) of the reactants: latex2 o latex3 Activation energy of the reaction ( latex4 ): (same thing as latex5 if you used this terminology at A-level.) | 0 |
See if you can see both paths to the solution. | 1 |
We can do this by rewriting the solution from part (a) as a Taylor series for the limiting case latex6 . | 0 |
Write down an expression for the complete solution latex11 , and sketch a graph of latex12 as a function of latex13 . | 1 |
Air may be assumed to behave as a perfect gas, with the same specific heat values for all processes. | 0 |
Substitute what you now know about the dependent variables latex9 , latex10 and latex11 to simplify all three of the equations (considerably). | 1 |
Use exp( ) to express exponential functions. | 0 |
Derive an expression for the output of a difference amplifier with inverting input resistor latex0 , negative feedback resistor latex1 , non-inverting resistor latex2 and ground resistor latex3 . | 1 |
**\[Boas 6.7.7]** Compute the divergence of the vector field latex0 | 1 |
From the appropriate table in the Data & Formulae book, identify two gases such that any mixture of the two will have a mass fraction identical to the mole fraction. | 0 |
A latex0 wheel rolls without slipping on a level surface, and is subjected to a horizontal force latex1 at a radius of latex2 as shown in the diagram below. | 0 |
(*Hint: Find the mass of air to be taken in per cycle, using the specific work from (c))*. | 0 |
Using your answer to part a, determine this maximum speed you will need to limit the motor to. | 1 |
The refrigerant mass flow rate if heat is to be removed from the cold space at a rate of latex3 . | 0 |
A cast iron hydraulic cylinder had a bore of latex0 and a wall thickness of latex1 . | 0 |
\ Leave your answer as a fraction. | 0 |
These energy supplies are to be replaced by an on-site combined heat and power (CHP) plant where the prime mover has an efficiency (for electricity) of latex5 and a heat-to-power ratio of latex6 (matching the site requirements). | 0 |
You and a friend each acquire 1 C of charge. | 0 |
(Based on P2.35 in White) What would be the pressure drop latex8 if the fluid were stationary? | 1 |
Calculate the stagnation temperature in the reservoir. | 1 |
**(L15)**: Consider the matrix latex0 Find the eigenvalues and normalised eigenvectors of latex1 . | 1 |
20 latex0 of a stock DNA solution are pipetted into 85 latex0 of buffer. | 0 |
**(L9)**: For matrices latex0 , latex1 , and latex2 , latex3 Select the matrix combinations for which the product is possible to calculate. | 1 |
Eliminate latex14 from the expression for latex19 . | 1 |
A steel beam supported a point load of latex0 at the mid-point of a latex1 simply supported span. | 0 |
Helium, at latex0 , enters a nozzle isentropically. | 0 |
The toxicity of a chemical to a bacterium can be modelled by the equation: latex0 where: * latex1 is the bacterium's growth rate * latex2 is the concentration of the toxic chemical * latex3 and latex4 are both positive constants Consider a plot of latex1 ( latex6 -axis) against latex2 ( latex8 -axis). | 0 |
Consider a fluid with the following quantities of interest:* velocity field latex0 * temperature field latex1 * pressure field latex2 * density field latex3 * the location, latex4 of a vertex of the surface of an object immersed in the fluid where latex5 , latex6 and latex7 are Cartesian coordinates and latex8 is time. | 0 |
The rope is very light so it's a good approximation to ignore its contribution to the mass and the moment of inertia of the spool. | 0 |
If the fluid were not flowing, what would the height difference latex12 be? | 1 |
Does the light pulse still arrive at Rick simultaneously in this frame? | 1 |
Calculate the work he performs after pulling the child for latex2 . | 1 |
Design a proportional control system, with unity feedback, to ensure a prompt response within latex2 with an error less than latex3 . | 1 |
How can you achieve an arbitrary rotation? | 1 |
**\[Boas 5.4.20]** In the integral: latex0 make the change of variables latex1 , latex2 and evaluate latex3 . | 1 |
Find the projection of latex10 onto latex11 , and hence write latex10 in terms of components parallel ( latex13 ) and perpendicular ( latex14 ) to latex11 . | 1 |
Write the total fluid stress on the top plate as a vector. | 1 |
The vertical temperature gradient is latex2 per km of altitude. | 0 |
We actually observe a much higher fraction of the muons make it all the way to the Earth's surface and this is due to relativistic effects. | 0 |
**(L14)**: The matrices below represent rotations in latex0 about the latex1 -axis ( latex2 ) and about the latex3 -axis ( latex4 ), each by 90 latex5 in the counter-clockwise direction: latex6 Find the real eigenvalues of latex2 and latex4 (denoted latex9 , latex10 respectively). | 1 |
A river stream has a flow rate of latex0 and a river depth of latex1 . | 0 |
Find the emitter voltage and current in each transistor shown below, for which latex0 is 100 and can be considered to be very high (i.e latex1 \~ latex2 ). | 1 |
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