0 stringlengths 10 969 | label int64 0 1 |
|---|---|
Use Ackeret's theory to estimate the pressure coefficient on each side of a flat plate in a flow at latex0 at an incidence angle of latex1 . | 0 |
A steel is used in a steam turbine pipe which operates at latex0 . | 0 |
Show that for very light damping ( latex6 ) the initial state of the transient solution satisfies latex7 , latex8 . | 1 |
A partition in the tank ensures that the oil stays on the left. | 0 |
After analysing the readings from a strain gauge rosette mounted on a latex0 diameter shaft which was subjected to bending and torsion, it was found that the principal strains latex1 and latex2 were latex3 , latex4 and that latex1 was inclined at latex6 to the axis of the shaft. | 0 |
Show that, if the cylinder is closed-ended, it will be predicted to fail at latex6 if the Von Mises criterion is used. | 1 |
Explain the *differences between bed-loa*d and suspended-load sediment transport. | 1 |
Its rate of climb is latex1 . | 0 |
**Figure (a)**: A snooker cue balancing on its tip. | 0 |
What is the value of latex4 at the bottom surface and the top surface of the water? | 1 |
The Bernoulli equation says that the total head, latex0 on a streamline is constant and can be defined as: latex1 Show what the three terms on the right-hand side represent. | 1 |
Calculate the separation of the bright fringes on a screen 2 m from the slits. | 1 |
**\[Boas 4.53]** Given latex0 , latex1 , latex2 , find latex3 (using the chain rule). | 1 |
Of the two solutions in part (a), consider the one closest to latex7 . | 1 |
An entire, real reciprocating engine, accounting for the air and fuel entering and the exhaust gas mixture leaving? | 1 |
For a first order process with gain latex0 and time constant latex1 , determine a control gain latex2 in a unity feedback control system, necessary to speed up the step response to latex3 . | 1 |
Explicitly calculate when the points latex2 , latex3 , and latex4 pass a station latex12 downstream of the origin. | 1 |
Determine an expression for the length latex4 of the region in which latex5 . | 1 |
Considering for now only the line latex4 , show that your answer to (b) simplifies to an ODE for latex9 . | 1 |
Calculate the product latex8 . | 1 |
Calculate the values of latex3 and latex4 from this data set using linear regression (use Excel if you want). | 1 |
It must withstand an axial compressive load of latex0 . | 0 |
An infinity of solutions latex0 latex1 latex2 latex3 | 0 |
Explain the method and state the underlying assumptions you consider to be of importance. | 1 |
What would be the concentration of caffeine in the coffee drinker's blood after latex13 , given that the elimination constant latex3 is latex15 ? | 1 |
For large (but not infinite) latex1 , this is a good model of a diffraction grating. | 0 |
Consider the following equation: latex0 where latex1 is a variable and latex2 is a parameter (i.e it doesn't depend on latex1 ).Write an expression for the solution to this equation. | 1 |
The real part is latex1 and has units of length. | 0 |
**(L8)**: Use Gaussian elimination to solve the system of equations below (**Note**: these are the same equations as Q1, so you know the type of solution to expect). | 1 |
When gas and latex0 excess air are supplied at latex1 , the temperature of the flue gases leaving the boiler is latex2 . | 1 |
% display the two initial values and print their difference fprintf(' '); fprintf('Initial values for X1 and X2: '); fprintf('X1 = %+18.16f ',X1); fprintf('X2 = %+18.16f ',X2); fprintf('----------------------------- '); fprintf('diff = %+20.14e ',X2-X1); % .................................................................. | 1 |
A pulley, latex0 , of diameter latex1 and moment of inertia latex2 is connected by a belt to a pulley, latex3 , of diameter, latex4 . | 0 |
One end of a light string of length latex0 is attached to a fixed point at latex1 . | 0 |
Why are both sets of lines parallel to the dry-bulb axis? | 1 |
Determine the transfer function latex0 of the two following circuits, with latex1 , latex2 , latex3 and latex4 : | 1 |
Use these expressions to find latex12 and latex13 in terms of latex4 and latex18 . | 1 |
It is essential that the robot, when approaching the eye, does not exceed the target position, otherwise it will perforate the eye irreversibly. | 0 |
Carbon dioxide, which can be treated as a perfect gas, flows steadily at a rate of latex0 through a heat exchanger where it is cooled at constant pressure (i.e with negligible friction) from latex1 to latex2 . | 0 |
A wide river is dredged to make it more navigable. | 0 |
What is the order in which the lamps turn on in the car's rest frame? | 1 |
Find the transformation matrix that transforms the resulting shape into a rectangle latex7 . | 1 |
Given that the tower is 60 m high, what is the separation of the two balls when the first hits the ground? | 1 |
Select a resistor which, in combination with a latex5 capacitor, will reduce the ripple by latex8 . | 1 |
Recalculate the energy falling on the panel if it is now placed flat on the ground at a location with latitude latex9 . | 1 |
If not, what was wrong with the approach taken in this question? | 1 |
If the blade speed is latex2 , calculate the velocity and flow angle relative to the rotor blades. | 1 |
A scale model of an aeroplane is to be tested in a wind tunnel at latex0 . | 0 |
Find latex2 for latex4 . | 1 |
Ignore the possibility of buckling failure modes and the weight of the beam. | 0 |
Two point charges of value latex0 are fixed in position at latex1 and latex2 . | 0 |
The circuit shown below is used in an automatic camera to measure light intensity. | 0 |
Compute the coefficient of friction, latex4 . | 1 |
By matching the transfer operators of the op-amp stage and its block diagram representation, derive expressions for A and B. | 1 |
A device to measure the dynamic viscosity of a fluid is called a *viscometer*. | 0 |
The frame has a mass latex4 with centre of gravity latex5 . | 0 |
What is depth of the plate into the water? | 1 |
In this problem we will assume that all three principal moments are distinct latex1 . | 0 |
An isolated air bubble of radius latex0 is in water. | 0 |
Note that Zener diodes can be used in series to achieve non-standard voltages (i.e their Zener voltages can be added, while the same current flows through each one). | 0 |
In lectures, you saw that the total laboratory-frame kinetic energy of two particles is the sum of their kinetic energy in the centre-of-mass frame and the kinetic energy of the centre of mass in the laboratory frame. | 0 |
(This is the mechanics question from the 2020 exam. | 0 |
**Note**: The solutions below should be given in their simplest form. | 0 |
Now, let's repeat this exercise using complex numbers (which should be much easier). | 0 |
The video linked from the image below shows an Imperial College physics student doing a simple experiment with a pendulum. | 0 |
The rotor exit tangential gas velocity component (magnitude and sign). | 0 |
Assume the following: 1. | 0 |
If you're short of time, leave this for another day.Show that: latex10 Verify that the wall-normal velocity component latex11 may be related to the stream function as follows: latex12 Show that: latex13 Based on the above results, show that the momentum equation from the boundary-layer equations eventually redu... | 1 |
Show that: latex11 | 1 |
It accelerates down to the ground at C, rises to D, and descends to E, which is at the same height as A. | 0 |
Again ignoring time dilation, use the exponential function of particle decay to find the average fraction of muons predicted to reach the Earth's surface. | 1 |
Consider steady flow between two stationary, flat plates as illustrated below. | 0 |
Anti-aliasing filters are used to remove signals that could cause aliasing. | 0 |
Using the Blasius solution, estimate the shear stress on the fin at the midpoint. | 1 |
Which of the following properties are scalars? | 1 |
An aircraft flies due North at latex0 ground speed. | 0 |
Consider the fluid contained in a cylindrical container as shown in the figure below. | 0 |
In the chemical reaction latex0 , there is an intermediate step where the latex1 and latex2 molecules combine to form an activated complex latex3 x latex4 \cdot latex5 ^{-1} latex6 \text{NO} + \text{O}_3 latex7 6.022 \times 10^{23} latex8 [\text{NO--O}_3]^{\ast} latex9 m_u \approx 1.66 \times 10^{-27}$). | 0 |
**(L6)** Solve: latex0 | 1 |
If not, when are they closest together and what is their distance of closest approach? | 1 |
(Hint: start from Lecture 13 and non-dimensionalising the equations, but with the appropriate pressure scale. | 0 |
Power lost as a fraction of the initial kinetic power: | 0 |
The container undergoes a rotation around its vertical axis ( latex1 ) at a constant angular velocity, latex2 . | 0 |
Use the shock polar to answer the following questions (estimate to about latex0 ). | 1 |
Suppose that you were lucky enough to take the following picture of a Super Hornet flying slightly above the speed of sound at sea level. | 0 |
Show, by substitution, that in the case of critical damping, the solution is latex19 | 0 |
The specific volume of the fluid with a temperature of latex14 and a pressure of latex15 . | 0 |
Use Mohr's circle *only*. | 0 |
How much energy is dissipated in friction as the record slips on the turntable? | 1 |
Determine the transfer function between the movement of the mass, latex1 , with respect to ground, and the displacement of the cart latex3 . | 1 |
Hence find latex14 in terms of latex0 . | 1 |
Find the velocity field of the flow, assuming that it is a purely circulating motion, that is latex11 , latex12 and latex13 . | 1 |
Calculate the fuel gas volume flow rate required to generate latex7 of dry saturated steam at latex8 bar (absolute) from feed water at latex9 . | 1 |
iii) latex12 ? | 1 |
Determine the Mach number at the nozzle exit ( latex1 ) Determine the pressure at the nozzle exit ( latex2 ). | 1 |
It is falling through a fluid of density latex2 and viscosity latex3 . | 0 |
In the antidune system the water surface is in phase with the bed configuration with a larger water depth at the antidune crest than at the antidune trough. | 0 |
*(Take rotation in the clockwise direction to be positive)* Find the percentage of energy lost in the collision. | 1 |
Analyse the experiment mathematically, assuming for simplicity that the string has been replaced by a light but stiff rod so that the starting angle can range from latex3 to latex4 radians. | 1 |
The gyroscope rotor is mounted on a horizontal shaft fixed across the vehicle frame, parallel with the rear axle and has a mass moment of inertia latex0 about its spin axis. | 0 |
Estimate the thrust capacity. | 1 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.