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The driving force then causes the amplitude of the oscillations to grow from zero.

Consider the flow between two infinite parallel plates, separated by a distance latex0 with the top one moving from left to right with constant speed latex1 .

Its centre is at the point latex3 .

How much data is required to describe the flow in one cell?

Note that the values for torque given in the table below are values at the output shaft.

When does the pulse arrive at Rick, and when at Lucy (give your answer in terms of latex4 )?

Express all of your results in terms of the unit vectors latex16 , latex17 , latex18 shown in the diagram: latex18 points along the axle, which is also the latex20 axis; latex16 lies in the latex22 plane and points from the axle to the position of the mass; and latex17 points in the direction of motion of the mass.

Watch the video below, where dye is dropped into the rotating tank, to help make your conclusion.

Consider the alga below.

Assume the driver weighs

A chimney, similar to the one shown in the figure, has a 2 m diameter and is 40 m high.

If a Linde process is operated so that helium leaves the regenerator 'hot' side at latex2 , will there be any liquid helium present at the throttle exit?

In a field campaign on a river of water depth latex0 , measurements of the flow velocity were taken at different vertical elevations from the bed.

It is common practice to scale velocities by the speed of light, so we define latex0 and latex1 .

Describe a method to find latex9 satisfying the criteria for an orthonormal set given that all latex10 with latex11 are already known.

With one further assumption, namely if the flow is irrotational i.e latex2 , the same Bernoulli constant can be used anywhere in the flow (not just on a given streamline; proof of this will follow in the next question).

Three strain gauges latex0 , latex1 , and latex2 are fixed to a point on the surface of a test plate at latex3 intervals and the strains recorded are latex4 and latex5 .

They turn on at times latex1 , latex2 , latex3 , latex4 , and latex5 respectively, in the frame at rest relative to the ground.

What is the normal stress on the bottom plate?

In the left-hand column give a brief description of what happens in the cylinders of a real CI engine.

Write down an expression (as algebra) for the speed of the carriage when it has dropped a height latex1 from point B.

The product mixture is at a temperature of latex2 and contains no excess steam or carbon (i.e complete reaction).

What is the final orientation of the sphere?

The magnitude of the work done on the steam is latex4 and the magnitude of the heat transfer from the steam is latex5 .

The shape of the upper surface is given by: \ latex1 Use supersonic thin aerofoil theory to evaluate the lift coefficient.

The mRNAs for most proteins possess a ‘life-preserving’ poly-A tail, but mRNAs for the proteins called histones lack this tail and are consequently much shorter-lived than most mRNAs.

Convert the Michaelis-Menten equation into the Lineweaver-Burk equation by taking reciprocal of both sides, so that the latex20 -variable becomes latex21 and the latex22 -variable becomes latex23 .

The sediment of the bed has a typical sediment size of latex2 .

latex0 For an input step of amplitude latex1 , determine the steady error for the control system depicted in the figure above, when: latex2 is a proportional and derivative control.

Calculate the drop in voltage across the battery’s internal resistance when the electrical circuit is used to power the interior car lights, which can be assumed to be simply resistive and which dissipate latex2 at latex3 .

What is its average power consumption over 24 hours?

**Counting in decimal and binary systems** In the decimal system (i.e base- latex13 system) we are all very familiar with, any number is represented by a string of figures taken from the following list: latex14 , latex3 , latex16 , latex17 , latex18 , latex19 , latex20 , latex21 , latex22 , latex23 (note that these are symbols, and we could have used any list of nine symbols -- e.g Roman numerals, Egyptian numerals, Chinese numerals).

Sketch the problem in a way that relates to the lubrication theory in Lecture 13, so that you can apply that theory.

This binds an anti-SDS on the rRNA.

Use the energy equation to determine the angular velocity, latex2 , of the rod as a function of latex3 , the angle between the rod and the horizontal plane.

Which of the following integrals are convergent?

A uniform flux latex0 is incident on a sphere of radius latex1 centred at the origin, and thus illuminates the hemisphere latex2 .

* Note how the irreversibility of the compressor and turbine processes causes an increase in the fraction of the turbine gross power absorbed by the compressor, a reduction in the plant efficiency and an increase in the air mass flow rate required to produce the design power output.

According to the work-energy theorem (which states that the work done equals the change in KE): latex7 Suppose now that the train is travelling with an initial speed latex8 m latex2 s latex3 .

Please can you give us some feedback.

Show that the half-power frequencies are solutions of the equations latex9 and latex10 .

Assuming that it is not possible to find a transistor with this specification and that two transistors with latex5 gains of latex7 and latex8 arranged as a Darlington pair are used instead, calculate a suitable value for an additional base resistor.

Show that the error in applying the Bernoulli equation is of the order latex0 , where latex1 is the Mach number.

Find the general solution to the system of linear equations (in terms of latex3 ): Obtain the solutions of the equations for the following values of latex4 : (i) latex5 (ii) latex6

The BHP Iron Ore train broke the world record for the heaviest train in its May 28, 1996 run between Newman and Port Hedland in Australia.

You are required to use a small motor with a speed vs torque curve shown below.

Describe the motion.

For the idealised case of a uniform medium at rest ( latex0 constant), the solution to the 1D diffusion equation is given by latex1 Verify that that the above formula is the time-dependent concentration profile for the idealised case of a uniform medium at rest.

The upper half of the rod joining the two masses traces out the curved surface of a cone with its point at the bottom, while the lower half traces out the curved surface of a cone with its point at the top.

latex3 The relationship between concentration and absorbance is described by the Beer-Lambert law: latex4 Where: * latex0 Absorbance (no units) * latex6 Molar extinction coefficient ( latex7 ) at a particular wavelength * latex8 Concentration ( latex9 ) * latex10 Path length ( latex11 ) In most spectrophotometers, the path-length is fixed at latex12 , and extinction coefficients can be obtained from books of data for chemicals of interest.

The link is as follows: latex72 (i) If latex73 , show that latex74 *(Hint: first show that latex75 and take the limit as latex6 goes to infinity)* (ii) Show that if latex77 , then latex78 (iii) Show that if latex79 , then latex80 (iv) Show that if latex79 , then latex82 (v) Show that latex83 , where the \`\`overbar'' denotes the bit complement: latex84 and latex85 (i.e bit inversion).

latex9 [table] The load displacement plot from the test is linear up to latex10 , at which point fast fracture occurs.

Subsonic air enters a converging-diverging nozzle, and is choked at the throat (meaning that it is sonic at the region of minimum cross sectional area of the nozzle).

Explain the shape of the curves.

Using Gaussian elimination or otherwise, show that the solution latex5 to the system of equations can be written in the form latex6 and identify possible values for latex7 and latex8 .

The distribution of the values of, latex2 , is called the **power spectrum** of the Fourier series.

If the boundary layer is tripped to become turbulent, will it grow faster or slower than a laminar one at the same Reynolds number?

Calculate latex13 explicitly.

Calculate the stagnation density in the reservoir.

Write your answer in terms of latex4 and latex5 .

By resolving horizontally and vertically, show that latex8 Write down expressions for the position vector latex9 of the bob relative to latex10 , its momentum latex11 , and the force latex12 acting on it.

What are the Kolmogorov length and time scales?

Benzene ( latex0 ) and air react in proportions such that the products contain latex1 , latex2 and latex3 only.

In doing so, assume that the flow discharge and water surface elevation remain constant over that period of time.

From this, retrieve the velocity addition formula: latex5

The frame of the gyroscope shown below is supported at latex0 so that it can turn freely in all directions.

3 operating points for the engine are being considered, for which torque is known but not the associated rpms.

Show that for each point latex4 on the ellipse the lines latex5 make equal angles with the normal latex6 to the ellipse at latex7 .

Then, calculate the corresponding intensity that would be recorded by a detector.

Select all of the features that describe a turbulent flow.

How is it related to the enthalpy of reaction?

These appear to be made of steel and to be about latex4 mm thick.

Find the third derivative of latex0 ...directly ...using the Leibniz formula (lectures).

An experimental vehicle is fitted with a gyroscope to counteract completely the tendency of the vehicle to tip when rounding a bend.

A permanent magnet D.C. motor has the following characteristics: Moment of inertia: latex0 Armature resistance: latex1 Back e.m.f.

In Lecture 3 we looked at the relativity of simultaneity by analysing a situation whereby Lucy, Matt, and Rick synchronise their clocks in their reference frame.

Given (b) and (c), what length of time does the observer on the spaceship measure for the trip?

You may assume the density is such that the cube in this question will be fully submerged in a fluid.

Then follow the method used in Lecture 14 when analysing the latex4 -momentum equation.)

At a point in a stressed material, the stresses on a certain plane are a direct compressive stress of latex0 and a shear stress of latex1 .

The College is aiming to operate one carriage every 5 minutes for twelve hours a day.

The operating parameters of the gas turbine are: * Compressor air inlet temperature: latex1 * Compressor air inlet pressure: latex2 bar (absolute) * Compressor pressure ratio: latex3 * Combustor gas exit temperature: latex4 * Turbine pressure ratio: latex5 Kinetic energy changes of the gas and the pressure drop in the combustor are negligible.

Rewrite this equation in terms of latex8 , latex2 , latex6 , and latex19 .

The diagram below shows the Earth at the March equinox.

Write down the boundary conditions at the top and bottom of the channel.

Explain your answer.

Find the pressure field, latex3 if the pressure at the point latex4 is equal to latex5 Convert the flow into polar coordinates, and show that latex6 and latex7 .

A pump is situated 4 m above sea level to move the water up the hill.

A Couette flow between two parallel plates is irrotational.

A particle of mass 2 kg follows the path latex0 .

(*Hint: sketch both processes on the same latex0 diagram*)

Starting from an appropriate base solution, construct the solution for this particular problem.

How long does it take for the astronauts to meet?

Are the following flows steady?

A spaceship travelling at constant latex0 travels from the Earth to the centre of the Milky Way, which in the Earth's inertial frame is a distance of latex1 light-years away.

Sketch the enthalpy-entropy diagram for a single stage impulse turbine, assuming: Adiabatic, isentropic expansion.

The amplitude decay time, latex4 , is the time taken for the amplitude of the oscillations to reduce by a factor of latex5 .

Go and read Wikipedia to learn more about the power of a procedure as simple as that of *counting*.

A potential exists in 3D space - latex2 .

What would happen if the larger and stronger astronaut suddenly decided to start pulling as hard as possible?