0
stringlengths
10
969
label
int64
0
1
Evaluate latex7 .
1
You may use a diagram to explain your answer.
0
Obtain the (mean) bed shear stress, latex4 , using the momentum balance approach.
1
The Q-cycle is a part of the electron transport chain in mitochondria, plastids, and many prokaryotes.
0
At point D the passengers should be weightless.
0
Use 'sqrt()' for the square-root function, *i.e * write latex12 as 'sqrt(x)', and use '\*\*' for the power function, *i.e * write latex13 as 'x\*\*2'.
1
How far from its initial position was the block after 5 s?
1
The angular frequency of the light is changed to latex12 rad s latex5 .
0
The stator exit flow angle of an axial-flow turbine is latex0 .
0
Constant, uniform density 3.
0
If latex0 where latex1 is an integer, Show that latex2 for latex3 .
1
Calculate the decay constant for latex3 from its half-life.
1
A closed rectangular box has sides latex0 .
0
Decide the "easy'' way to do this.
1
What does this tell you about latex12 ?
1
Each cup experiences a force due to the wind, of which the component latex6 contributes to the torque.
0
The legs are attached rigidly to the underside of the bench top, which is free-standing.
0
Sketch the pressure distribution in the tunnel.
1
In use, the cylinder is clamped in place by an axial force of latex3 .
0
What was the (absolute) rate of absorbance change in the cuvette per minute?
1
Calculate the Mach number latex6 behind the resulting oblique shock wave.
1
Feel free to use early steps of the worked solutions to get you going in some parts.
0
If latex0 , Find latex1 Find latex2 Find latex3 For what values of latex4 does latex5 ?
1
in a cylindrical frame of reference (consider latex2 ).
0
Plot the results.
1
What is the value of the difference between the stagnation and static pressures?
1
Starting from the Euler equation, show that the governing equations applicable to the water in the tank simplify to: latex3 *Hint: given that the reference system is rotating, non-inertial effects should be accounted for: the Coriolis acceleration ( latex4 ) and the centrifugal acceleration ( latex5 ).
1
The torus is filled with a fluid, the mass density (mass per unit volume) of which is given by latex2 .
0
You may wish to use .
0
The density of water is latex8 and that of oil is latex9 .
0
There is a sharp crack of depth latex3 in the tensile face opposite the central loading point.
0
A second trapping session, one day later, caught latex1 rabbits, of which latex2 had been marked in the previous trapping session.
0
The following data apply to extruded and cold rolled Nimonic 80A at latex0 .
0
Note that no Euler force applies after the initial transient since latex2 is a constant.
0
You may also assume that the flow and pressure are steady (independent of time).
0
Steady flow, i.e latex1 One-dimensional flow such that latex2 .
0
Which one of the following is true?
1
What would be the total change in length of a bar of latex8 initial length at latex9 , which is held at a stress of latex10 after remaining at latex10 for latex16 hours.
1
The static temperature and pressure of air at inlet to a compressor are latex0 and latex1 bar respectively.
0
Evaluate the surface integral latex0 where latex1 in spherical polar coordinates and latex2 is a sphere of radius latex3 centred at the origin.
1
Conversely, if latex1 , latex2 and latex3 are all real, and latex5 is a solution of latex7 , deduce that latex6 is also a solution.
1
Neglecting the feed pump work latex3 (i.e taking states 2 and 1 to coincide) and all kinetic energies, calculate: (i) The heat transfer per unit mass, latex4 , to the water /steam in the boiler; (ii) The heat transfer per unit mass latex5 from the water/steam in the condenser.
1
Ky "Rocketman" Michaelson battled against gravity and dyslexia to become the first civilian to launch a rocket into space.
0
This relationship is known as the dispersion relation.
0
Show that the surface element latex4 on the plane is given by: latex5 Hence show that: latex6 Show that the direction of latex4 agrees (to within a latex8 sign) with that extracted directly from the equation of the plane in standard form, i.e , latex9 Find latex10 and hence calculate the area of the portion of the planar surface with latex2 and latex3 .
1
See *Problem Sheet 4, Question 3* for the centre of mass approach.]
0
The figure below shows a record turntable.
0
Note that latex5 bar latex6 Pa.
0
Start here: latex42 Remember that latex1 is defined as: latex44
0
The analogy to fluid flow is that each person represents a fluid particle.
0
What is the total kinetic energy of the system in the centre-of-mass frame?
1
Calculate the local stress at a distance of latex8 directly ahead of the crack tip and comment on whether this stress is realistic.
1
A steady flow implies a pressure gradient equal to the null vector.
0
Determine the typical radius latex2 ( latex3 -folding length) as a function of time.
1
The beam is subjected to a load of latex3 acting vertically downwards latex4 from the built in end.
0
Assume the beam material has a relatively low density and a Modulus of Elasticity of latex5 .
0
For NADH at latex5 , this is latex6 * latex7 Molar concentration ( latex8 ) * latex9 Path-length of the cuvette ( latex10 ) latex11 of lactate dehydrogenase solution, latex11 of lactate solution, latex13 of latex14 solution and latex15 of buffer were mixed together in a latex16 spectrophotometer cuvette.
0
Locate the stationary points of latex0 and deduce their nature (i) from a contour sketch \[Sketch contours of the function and indicate regions where latex1 is respectively zero, positive and negative.]
1
Use this method in future, approximating latex7 as the value at the pump inlet, unless otherwise specified.
1
This mixture is known as "water gas" and is used as fuel for turbines.
0
Calculate the effective crack length latex1 for small scale yield conditions.
1
The specific work transfer to the air.
0
A mass of 0.2 kg is attached to a spring.
0
(ii) Calculate the values of latex2 and latex3 to achieve a damping ratio of latex4 and enforce the system to operate at a natural frequency of latex5 .
1
**(L4)** A plane passes through the three points latex0 in latex1 .
0
Planes A and B are not necessarily at right angles to each other.
0
Is this the same as the original area of the shape?
1
In service, the cylinder fractures locally at an angle of latex3 to the axis.
0
Calculate the speed of a longitudinal wave travelling along an aluminium rod.
1
Integral with latex4 is a gear pinion latex8 which has a pitch circle of radius latex9 and a mass moment of inertia latex10 about its axis of rotation.
0
*The following question is broken down to encourage discussion as a group and/or as an exercise during tutorials.
0
An air cooling system for an aircraft cabin is based on a reversed Joule cycle.
0
How do these results compare with your personal observation as a pedestrian living in London?
1
Compute the bed shear stress, latex3 .
1
If there is a constant force of latex12 resisting the motion of the car along the track, what is the velocity, latex13 , of the car at latex14 when latex15 and latex16 ?
1
The loop has width latex5 cm, and in this question you should assume that latex6 m/s latex7 .
0
The specific enthalpy of wet steam with a pressure of latex6 bar and a dryness fraction of latex7 .
0
Calculate: The temperature of the air leaving the compressor.
0
*(Take rotation in the anti-clockwise direction to be positive)*
0
Find an expression for the area of any section along the nozzle latex6 as a function of the area at the throat latex7 and the non-dimensional distance from the throat latex5 .
1
If you need to look up properties you can use Table E.3 of the Data book or any reliable sourceWhat is the speed of a sound wave in air at latex0 ?
1
* Elastic (Young’s) Modulus latex1 * latex2 Proof Stress latex3 * Elongation to fracture = latex4 (short term tensile test) * Mean Coefficient of Thermal Expansion ( latex5 range) latex6 The stress to cause a creep strain in 3000 hours is: [table] Neglecting primary creep, calculate the secondary (steady state) creep strain rate at each stress level.
0
Under the assumption that buoyancy effects are negligible and that the release can be regarded one-dimensional, plot the concentration profile after one minute under the different conditions that follow.
1
The ambient temperature is latex4 .
0
Let latex5 where latex6 is a constant.
0
Comment on this result, and what would happen if latex11 .
1
Also calculate the flux through the circle latex4 located at latex6 .
1
A spherical interplanetary probe of latex0 diameter contains electronics that dissipate latex1 .
0
Show your working.
1
Is there a better approximation to the equation (i.e should a different term be neglected?)
1
Find expressions for latex6 and latex7 in terms of latex4 and latex5
1
The transport of contaminant when there is no mean flow (i.e the diffusion equation).
0
**(L5)**: A curve is defined by the parametric equation, latex0 Describe the curve Find the derivative and the second derivative of the curve with respect to latex1 .
1
Determine the minimum bottom width, latex5 .
1
Again, check your answer before proceeding.
0
Determine the pressure downstream of the expansion, if upstream the pressure is atmospheric.
1
What is the amplitude of oscillation of the electron in the steady state?
1
The input step has a unity amplitude.
0
Prove this is true by applying the Lorentz transformations to the components used in latex1 and showing that latex3 .
1
The capacity of a buffer ( latex0 ) at a particular latex1 is defined as the infinitesimal number of moles of base ( latex2 ) needed to cause an infinitesimal increase in latex1 : latex4 Above are graphs of latex2 and latex0 vs latex1 for acetic acid.
0