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Diffusion only and in latex0 -direction. | 0 |
Note that this means that if 1000 muons are created simultaneously, after latex5 on average latex6 muons will remain, while the rest will have decayed into electrons.The muons move at a speed close to the speed of light: latex7 = 0.995. | 0 |
How does the pressure in the meniscus relate to atmospheric pressure latex2 (i.e is it bigger or smaller than latex3 )? | 1 |
You need to simulate the wind, the wake of the chimney, and the dispersion of exhaust in the immediate vicinity. | 1 |
What is the speed of the high frequency wave and what is the speed of the envelope? | 1 |
What is the shear stress at the wall if the fluid has a viscosity, latex3 ? | 1 |
The state points are numbered as follows: * Evaporator exit: latex0 [embedded] * Low-pressure compressor exit: latex1 * High-pressure compressor exit: latex2 * Condenser exit: latex3 * Flash chamber inlet: latex4 * Flash chamber liquid exit: latex5 * Evaporator inlet: latex6 * Flash chamber vapour exit: latex7 * High-pressure compressor inlet : latex8 ( latex8 is the state after mixing of vapour in states latex1 and latex7 ). | 0 |
The following complex solutions, latex0 , of the simple harmonic motion equation are written in SI units. | 0 |
Starting from the equation derived in part (b) and by applying proper boundary conditions at latex3 and latex0 show that the velocity of the flow in the water layer is given by the expression: latex10 where latex11 and latex12 are the density and viscosity of the water, respectively. | 1 |
What would be the most suitable Reynolds' Number for B? | 1 |
This distance must equal latex15 . | 0 |
[table] Compute the eddy viscosity, latex1 , filling the missing values in the table of measurements above. | 1 |
The spin tensor is symmetric. | 0 |
If you find it is greater than latex4 , does this violate the principles of Relativity? | 1 |
Determine the rotation axes of latex11 and latex12 (represent these as normalised eigenvectors latex15 ), and comment on your results in light of the result in part (b). | 1 |
This is a bit mystifying. | 0 |
The temperature of the sliding wall can be made colder or warmer than the bottom wall, thus inducing a temperature gradient in the bath. | 0 |
The reduction of the sampling rate from latex1 to latex2 II. | 0 |
Use the notation: latex3 ratio of outer radius to inner radius, latex4 internal pressure, and external pressure latex5 . | 0 |
The record of a risk assessment is a list of hazards and the control measures in place. | 0 |
A perfect gas is expanded isentropically from a reservoir where the pressure is latex0 , the density is latex1 and the absolute temperature is latex2 . | 0 |
Find an expression for the latex5 component of the velocity. | 1 |
The bottom of the loop is filled with mercury (density latex3 kg/m latex1 ), which acts as a manometer, and you may assume is not flowing. | 0 |
Assume that no current can flow into the DA card. | 0 |
A particle at position latex0 metres is moving relative to the origin. | 0 |
Calculate the maximum possible cycle efficiency of the plant if it rejects heat at latex0 , if energy is supplied to the plant: As solar-heated water at latex1 . | 1 |
*This question addresses the following:* Is it easier to balance a snooker cue on its *tip* (**Figure (a)**), or on its *base* (**Figure (b)**)? | 1 |
Consider the three vectors latex0 . | 0 |
Compute the matrix product latex9 , where latex10 indicates the transpose of the matrix. | 1 |
The stock DNA solution has a concentration of latex2 . | 0 |
(Note: there is no response area for this question part) Work out the maximum safe acceleration if the car-car and car-locomotive couplings can support a maximum force of latex8 N. How far would the train have to travel to accelerate from rest to a speed of 20 m latex9 s latex10 ? | 1 |
A sample of a wet steam is passed through a well-insulated throttling calorimeter in order to measure its dryness fraction. | 0 |
In three-dimensional Cartesian coordinates, write the second component of the net force per unit mass on a fluid particle i.e the RHS of the Cauchy equations (this is a very simple but useful question). | 1 |
Consider how the temperature of the house will evolve with time latex3 if energy was provided to the inside by the woodburner as a delta function. | 0 |
At the later time latex3 , this energy has been exchanged - the second pendulum becomes stationary at equilibrium, and the first is moving. | 0 |
Sketch the wave pattern for latex11 . | 1 |
Couette flows are the archetype of lubrication-related issues. | 0 |
Make a graph of the pattern that the solutions to this equation traces out in the complex plane. | 1 |
Consider an infinitely wide river section under steady and horizontally uniform flow (see the figure below). | 0 |
A uniform spherical ball rolls without slipping along a horizontal plane towards an incline. | 0 |
What can we conclude? | 1 |
Is exergy a property of a fluid in the same sense as enthalpy, entropy etc.? | 1 |
An air-standard Joule cycle, modelling the processes in a closed-cycle gas turbine engine? | 1 |
Let the temperature at time latex4 be distributed according to a Gaussian with zero mean, width latex5 and latex6 . | 0 |
The shafts are labelled 1st, 2nd and 3rd in order so you can determine which refer to the pulleys and which for the sprockets. | 0 |
Growth of the bacteria is modelled by the following equation: latex1 * latex2 Absorbance (population size) at time t [embedded] * latex3 Initial absorbance [embedded] * latex4 Specific growth rate in exponential phase. | 0 |
What is the probability that there will be *at least one* mutation at any position? | 1 |
What is the shear stress exerted by the water on the block? | 1 |
Compute the air speed from this actual difference assuming incompressibility. | 1 |
(Optional - at least note the answer!) | 0 |
As density decreases, the mean-free path is expected to increase. | 0 |
Considering the shedding frequency as the main quantity of interested, suggest a list of dimensionless groups to describe the problem. | 1 |
The end just rests on a rigid roller, which is mounted on a rigid foundation. | 0 |
\[Note that plane polar coordinates latex8 latex9 Cartesian coordinates latex10 via latex11 and latex12 .] | 0 |
Consider the cylindrical container shown in the image, below. | 0 |
A cylindrical beaker of radius 5 cm contains a fluid with coefficient of surface tension latex0 N/m. | 0 |
Assume that all the forces and moments are steady, i.e they do not vary during each rotation of the shaft. | 0 |
Write the following complex numbers in Cartesian coordinates (rectangular form, latex0 ): latex1 latex2 latex3 latex4 | 1 |
**\[Boas 6.11.16]** What is wrong with the following \`\`proof'' that there are no magnetic fields? | 1 |
Which shock wave arrangement is more efficient in decelerating supersonic flow (fewer losses, that is, smaller drop in stagnation pressure)? | 1 |
The temperature of the environment is latex4 . | 0 |
What is the air pressure at the lake (taking the density of air to be constant)? | 1 |
Leave your answer in terms of latex2 . | 1 |
In this question you should take the density of water to be 1000 kg/m latex1 and the acceleration due to gravity to be 10 m/s latex3 .. Find the velocity latex13 at Point 3, naming the physical principle you are using. | 1 |
The thickness of the fibreboard is latex3 mm. | 0 |
Use the boundary condition and compare to the general equation in part (b). | 1 |
Which sketch best represents the streamlines? | 1 |
In this question we are looking at the power spectrum of a Fourier series and why that is a useful quantity. | 0 |
The change in sensible enthalpy when latex6 is heated from latex9 to latex10 . | 0 |
Assume that latex4 and ignore all forces other than gravity. | 0 |
What are the gain and the time constant of the following first order systems: latex0 latex1 | 1 |
Ignore air resistance and the weight of the bungee cord. | 0 |
Use supersonic thin aerofoil theory to evaluate the wave drag coefficient. | 1 |
What is the approximate value of latex0 ? | 1 |
The collar is held at the position where latex0 . | 0 |
Under certain conditions, the dispersion relation for deep-water waves is latex21 , where latex22 is the acceleration due to gravity. | 0 |
If a computer is to be used to count the **number of complete rotations** made by the encoder for a total linear range of 500 mm, what is the minimum number of bits required to store the information content for this task? | 1 |
Consider a Rankine Cycle where the boiler pressure is latex0 bar and the condenser pressure is latex1 bar. | 0 |
Write the streamwise evolution of the boundary-layer, displacement and momentum thicknesses in terms of the Reynolds number based on the distance from the leading edge ( latex9 ). | 1 |
Describe how the vector describing the first derivative varies with latex1 . | 1 |
A unique solution 2. | 0 |
Consider a steady flow of an inviscid fluid with constant density. | 0 |
Show by comparing the units of the variables involved that the only possible expression for the spread is latex4 . | 0 |
Calculate heights latex2 and latex3 of the columns of oil and water, respectively. | 1 |
**Note:** The last function is constructed from two parabolas stuck together. | 0 |
A ship, the MS Beluga SkySails, is 132 m long, with a beam (width) of 15.8 m, and draft (depth into the water) of 7.7 m. Estimate the surface area of the ship that is in contact with the water. | 0 |
Show that what you know already about the dependence of latex9 on latex12 , latex13 , latex29 and latex30 means that latex66 for some constant latex67 and function latex13 ? | 1 |
Revert to just two slits now, but make the slits have a Gaussian absorption profile with width latex15 . | 0 |
Indicate any position(s) of stable equilibrium. | 1 |
An "enzyme unit" latex21 is defined as the amount of product an enzyme can produce in a given time, and has units of latex22 . | 0 |
(*Challenge*) Consider a house that is heated by a woodburner. | 0 |
The calorimeter exit temperature latex4 is measured as latex5 . | 0 |
They mesh with a fixed gear wheel latex3 . | 0 |
Assuming latex9 then we are interested in the limit latex10 where we recognise the Reynolds number (more on that later!). | 0 |
Hint: the nose of the aerofoil is a stagnation point. | 0 |
Calculate the value of the valve setting to achieve the desired steady state outflow. | 1 |
A real open-cycle gas turbine engine? | 1 |
Now add a wall at the origin latex3 which acts as a perfect reflector. | 1 |
The figure below shows a conical pendulum. | 0 |
Calculate the safety factor against **buckling** in the **perpendicular direction to the plane of the diagram**. | 1 |
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