0 stringlengths 10 969 | label int64 0 1 |
|---|---|
*\[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 sur... | 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 latex... | 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 g... | 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 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.