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*\[Riley 11.3(c)]* latex0 is a vector field latex1 and latex2 is a path parameterised by latex3 , latex4 , latex5 for the range latex6 . | 0 |
Similarly, find the curves where latex12 , consider what is latex13 there and work out how the flow crosses those lines. | 1 |
After some transient, the fluid in the tank undergoes a rigid-body rotation, and is stationary with respect to the tank. | 0 |
If latex9 is constant, this equation becomes the equation of a plane. | 0 |
However, the percentage of colonies surviving a given irradiance of UV decreases exponentially with time of exposure. | 0 |
An aircraft is flying at latex0 in the standard atmosphere ( latex1 , latex2 ). | 0 |
(Based on P4.13, White) A two-dimensional velocity field is given by latex0 where latex1 is constant. | 0 |
This device is to heat blood taken from the blood bank at latex0 to latex1 at a flow rate of latex2 . | 0 |
Consider the 1-D diffusion equation latex0 where latex1 is the concentration of a contaminant. | 0 |
In the limit where latex27 , we obtain a continuous line of sources spanning the width latex25 , which is a good model for a single open slit of width latex25 . | 0 |
If necessary, write your answer as a surd. | 1 |
At the trailing edge the boundary-layer thickness is latex4 . | 0 |
When latex7 and latex8 are similar, latex9 has the form of a high frequency wave at latex5 whose amplitude is modulated by an envelope at latex6 . | 1 |
The use of a PD control introduces an latex0 on the numerator of the closed loop transfer functions. | 0 |
The velocity distribution in a pipe with diameter latex0 cm is given to be latex1 m/s, where latex2 is the radius of the pipe. | 0 |
Determine the normalised eigenvectors corresponding to the eigenvalues. | 1 |
Show that the following functions satisfy the 2-dimensional Laplace's equation in plane polar coordinates (lectures): where latex0 are constants and latex1 is a positive integer. | 1 |
Which answer best describes the velocity of the air after the throat? | 1 |
Based on your analysis for the horizontal wall, explain why you expect the wave front to steepen. | 1 |
Compute the coefficient of friction, latex4 . | 1 |
What distance does the light pulse travel in terms of latex11 , latex6 , and latex8 ? | 1 |
An ecologist is using a clinometer to estimate the height (and therefore the biomass) of a tree. | 0 |
The Lagrangian positions of the persons are denoted latex3 and latex4 . | 0 |
Calculate the pressure and temperature at that point using the isentropic relation equations. | 1 |
latex1 , latex2 . | 0 |
Estimate the Mach number at section 3, latex5 . | 1 |
The output of the system H is affected by an external disturbance latex0 , as depicted below. | 0 |
Wind with speed latex0 blows perpendicularly to a suspension bridge of length latex1 . | 0 |
We have approximated the equation far from the wall to get the 'outer' solution, latex26 , and near the wall to get the \`inner' solution, latex27 . | 0 |
* **\[Boas 6.12.29]** latex3 and latex4 is the boundary of the square with vertices latex5 , latex6 , latex7 , latex8 . | 0 |
Show that, if the cylinder is closed-ended, it will be predicted to fail at the same pressure latex2 , if the Tresca criterion is used. | 1 |
The annulus height (i.e tip radius minus hub radius) at an axial station where the static pressure is latex6 bar absolute and the dryness fraction is latex7 . | 0 |
Find the angle latex9 the two vectors latex2 and latex3 . | 1 |
Determine the velocity latex2 of the centre of the ball as it starts to roll up the incline in terms of its initial velocity latex3 , and the angle of the incline latex4 . | 1 |
Calculate the phosphorous concentration at latex4 at latex5 . | 1 |
Calculate: The blade velocity (via the Euler turbomachine equation) and hence the mean diameter of the annulus. | 0 |
*\[Riley 11.19]* Evaluate the surface integral latex0 , where latex1 is the position vector, over the part of the open surface latex2 for which latex3 , by each of the following methods: Parameterise the surface as latex4 , latex5 , latex6 and show that: latex7 Then, evaluate this over the limits of the surface. | 1 |
Give an expression for the angle latex4 as a function of the hour latex6 assuming the sun starts at dawn pointing along the latex7 -axis. | 1 |
Find the Mach number latex3 behind the shock wave. | 1 |
Plot the speeds of Persons (1) and (2) as they vary in time, i.e plot the latex5 components of: latex6 latex7 against latex8 . | 1 |
Select all the assumptions needed for Bernoulli’s equation to be valid. | 1 |
Each molecule is modelled as a hard sphere of diameter latex3 . | 0 |
(The error is *not* in these equations.) | 0 |
Derive an expression for the height latex4 to which the masses rise after the collision. | 1 |
A gun fires shells with a muzzle velocity latex0 at an angle latex1 to the horizontal. | 0 |
Using the Blasius solution, estimate the total drag on the fin. | 1 |
Calculate the concentrations at latex3 for latex4 . | 1 |
Assuming that your car can only operate at its maximum motor speed, determine its instanteous acceleration at the beginning of a race (from a standing start). | 1 |
The bungee jumper from lectures steps off a platform latex0 metres above the ground, attached to a cord of natural (unstretched) length latex1 . | 0 |
Calculate the Mach number latex3 if the aircraft is flying at an altitude of latex6 . | 1 |
The surface temperature is latex3 .Derive an equation relating the pressure ( latex4 ) gradient latex5 of the atmosphere to its density and the gravitational acceleration ( latex6 ). | 0 |
What is the insolation in latex14 at Imperial College according to your formula? | 1 |
Consider two vectors in latex0 : latex1 and latex2 . | 1 |
Calculate the thermal efficiency of this cycle, first using only the heat transfers from part (b) then again using the basic definition latex6 . | 1 |
A fast response probe with sampling frequency equal to latex0 kHz has been placed at a given location (fixed in space) in the wake formed by an air flow ( latex1 latex2 ) around a square bluff body with characteristic size latex3 m. The time history of the three components of velocity has been recorded for latex4 minutes. | 0 |
Evaluate the mass ratio of air to fuel. | 1 |
Use this to give an expression for the total head on surface 2 in terms of the geometrical variables latex4 and latex5 , and the upstream variables latex6 , latex7 and latex8 . | 1 |
The bearing is at the centre of mass. | 0 |
Avogadro’s number is latex38 , bulk carbon has a molar mass of latex39 , and in living matter, there is about one latex3 atom per latex6 atoms of carbon at death. | 0 |
Given an overall propulsion efficiency of 50%, estimate the engine shaft power requirement at a cruising speed of 5 m/s. | 1 |
As part of a design project where you have been tasked to build a car, you must select an engine to use. | 0 |
Estimate the total population size, using the Lincoln index: latex3 * latex4 Number marked and released * latex5 Total population size * latex6 Number of marked recaptures * latex7 Total number in the recapture sample By how much does the estimate in part (a) for total population size vary from the estimate given by Bailey’s modification (below) to Lincoln’s index? | 1 |
Calculate the maximum temperature latex10 and maximum pressure latex11 in the cycle. | 1 |
The plot shows the step response of a first order system. | 0 |
(Based on P4.27, White) A frictionless, incompressible steady flow field is given by latex0 , latex1 , latex2 in arbitrary units. | 0 |
The transfer function of the process is latex1 . | 0 |
Apply Bernoulli's equation along the water surface (which is a streamline at constant pressure) to find that latex5 . | 1 |
A second basis vector can be found by taking latex5 and then removing (subtracting) the component of it that lies along latex4 and then normalising the result to make a new vector latex7 . | 0 |
Which one of the following is true? | 1 |
Let the average insolation at the equator ( latex8 ) be latex9 . | 0 |
The figure shows a rotational viscometer, where a rotating shaft is placed within a concentric cylinder attached to the ground. | 0 |
Can you explain why a person who has inhaled helium speaks with a high-pitched voice? | 1 |
The gearbox you have been supplied with did not come with a guide, so you have opened it up and can see the gears inside… \##insert pictures of gears here## What is the step down ratio of the gearbox? | 1 |
What is the speed in helium at the same temperature? | 1 |
Show that the constant in the Bernoulli Equation can be applied anywhere in the flow (not necessarily along streamlines!) | 1 |
Take the differential equation, latex0 Determine the type of differential equation. | 1 |
This satisfies the complex differential equation, latex10 which returns the original differential equation if we take the real part. | 0 |
The flow is driven by the motion of the top plate, which is moving with constant speed latex2 in the latex0 direction (see the image below). | 0 |
A weight of latex0 falls latex1 onto a pile weighing latex2 . | 0 |
Consider a velocity field that in a cylindrical frame of reference is described by latex0 where latex1 is a constant. | 0 |
Are the following exact differentials? | 1 |
How is the enthalpy of formation of latex0 defined? | 1 |
What is the aircraft speed in m/s? | 1 |
How should latex0 be chosen to maximise the profit, and what is latex4 ? | 1 |
Here is one of the most interesting questions they came up with.] | 0 |
**\[Boas, after 6.6.3]** Find the derivative of latex0 at latex1 in the direction of the vector latex2 . | 1 |
Write down an expression for the total head at surface 2, latex1 , if gravitational effects can be neglected. | 1 |
Separate the latex16 and latex21 variables and integrate the result to find a general solution to this ODE for latex16 at any given time latex21 . | 1 |
The system is now driven with a force latex2 (in SI units). | 0 |
Calculate the stoichiometric air requirements and excess air in the products if latex0 of wood is burnt with latex2 excess air. | 1 |
latex3 What is the melting temperature of a sample of DNA that is latex4 adenine? | 1 |
Find the dot products latex7 , latex8 and latex9 . | 1 |
(iii) What was the maximum latex22 -force experienced by the jumper? | 1 |
The boundary at latex3 is a perfect reflector. | 0 |
The fixed z axis at latex4 in the direction shown. | 0 |
Plot the speeds observed at locations latex9 and latex10 as they vary in time, i.e plot: i. the latex5 component of latex12 against latex8 and ii. | 1 |
What is the total acceleration of the water in the tank (in the cylindrical coordinates system)? | 1 |
Show that latex27 and latex28 . | 1 |
Referring to data from the wind tunnel in Figure 14.6, measured velocity profiles, latex0 , are given at different locations, latex1 . | 0 |
**(L3)** For three vectors in latex0 : latex1 , latex2 , and latex3 : Find the lengths latex4 , latex5 , latex6 using the dot product (leave as a surd where relevant). | 1 |
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