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a) latex0 b) latex1 c) latex2 | 0 |
(i) Draw a block diagram showing the components of the plant as modelled by the reversible open cycle. | 1 |
Determine the order of magnitude of the rate of dissipation of turbulence kinetic energy. | 1 |
The specific volume of steam at latex8 bar and latex9 . | 0 |
OPTIONAL: plot (manually or using MATLAB) the variation of area and Mach number along the nozzle. | 1 |
It was radiocarbon dated at 32 000 years old and an embryo from one of the frozen seeds was successfully dissected out, germinated in tissue culture, and grown into a mature plant. | 0 |
Let latex5 be a non-dimensional form of the stream function: latex6 where latex7 is the kinematic viscosity (assumed constant) and latex8 is the latex1 -component of the freestream velocity, which is also a constant. | 0 |
Derive the expression relating latex3 to the state of the 4 digital lines. | 1 |
If the steam cycle efficiency is latex2 , what is the overall efficiency of the combined cycle? | 1 |
The engine power output is latex4 and the rotor speed latex5 . | 0 |
Add the concentration profile latex4 resulting from the image source to your sketch (the diffusion from the image source also develops as on an unbounded domain). | 1 |
(L2): For vectors latex0 with: latex1 Find the magnitude of latex2 and latex3 . | 1 |
For a specific design Mach number latex0 , the geometry of an inlet can make the reflected shock wave cancel. | 0 |
**(L7)**: Use Cramer's rule to find the intersection of the lines latex0 | 1 |
Prove that: latex11 Using a similar approach to (a), show that the reference voltage latex12 around which the op-amp stage will "switch states" occurs at: \ latex13 If latex14 , latex15 and latex16 , find the values for latex17 and latex18 which are needed to ensure that the compressor is switched on (i.e latex1 are applied across its two ports) when the pressure sensor voltage drops below latex2 , while being turned off otherwise. | 1 |
What is the probability that the Cs in positions 3 and 4 of the DNA sequence mentioned above will both mutate to any other base (assume that mutations are independent of one another)? | 1 |
A cup anemometer, illustrated here, is a particular design that rotates due to the difference in drag coefficient experienced by a cup shape when facing opposite directions. | 0 |
For each of the following flows, perform a very rough estimate of the Reynolds number and describe whether this is high-Reynolds-number or low-Reynolds number flow: (Note: that we are analysing the fluid flow, so if an object is moving through a fluid, we will be analysing the fluid surround the object not the object itself. | 1 |
We measure the positions of the two ends at latex17 in its rest frame. | 0 |
The reduction from latex3 Bit to latex4 Bit resolution III. | 0 |
By defining a complex displacement latex16 , show that the above equations can be written as the single complex equation: latex17 Show that the roots of the characteristic equation are latex18 and that the general solution is therefore latex19 where latex20 are complex constants determined by the initial conditions. | 1 |
Using the definition of 'speed' to mean a component of the velocity vector --- which means that a speed can be negative or positive --- solve the following problems. | 1 |
Check your answer before proceeding to the next steps. | 0 |
Give the physically meaningful solution for latex3 . | 1 |
Write latex5 as 'log(x)'. | 1 |
While he did not state it explicitly, it appears that he considered such a process to be isothermal.Rederive the speed of sound for an ideal gas, but assume the successive compression/expansion of the fluid particle to be isothermal. | 1 |
Compare the transport equations for laminar and turbulent flows. | 1 |
Reconsider the sea-river system below. | 1 |
\[Lectures] Show that the mean distance over **angle** of the planet from the Sun is given by latex3 | 1 |
What is the minimum upstream Mach number for which the flow deflection can be achieved with a straight oblique shock? | 1 |
For the following systems, consider whether the first and/or second laws of thermodynamics are violated. | 0 |
Note: error is defined as latex0 | 0 |
An open-cycle gas turbine engine is used to drive an electrical generator. | 0 |
Is this consistent your answer to (a) given time dilation? | 1 |
Calculate the power transmitted. | 1 |
Use shock-expansion theory to find the pressure on every surface of the following cranked aerofoil in a Mach 2.5 flow (relative to latex0 ). | 1 |
Density and viscosity of both the oil and the water can be considered uniform and constant. | 0 |
Create a plot of the concentration at latex5 , as a function of latex6 . | 1 |
The potential energy latex0 shared between two water molecules is found empirically to be given by the formula latex1 where latex2 is the distance between the centres of the molecules in metres. | 0 |
Standing acoustic waves are formed in a tube of length latex0 whose axis is along latex1 . | 0 |
**\[Boas 6.7.19]** For latex0 evaluate latex1 . | 1 |
Repeat (a) for a stoichiometric reactant mixture. | 1 |
The effectiveness of the recuperator may be taken as latex6 , so that latex7 = latex8 . | 0 |
First, given that the lawnmower is rated for speeds between 1 and 5 m/s, you need to determine the range of the engine rpm if the lawn mower wheels are 0.4m in diameter and the following drive transmission is used: (you may assume no change in rotational speed other than from the drive transmission below) [table] Determine the minimum required cylinder capacity to ensure a minimum of 3kW is supplied at all engine speeds. | 1 |
A spherical balloon of latex0 diameter is filled with helium at latex1 and latex2 bar (absolute). | 0 |
You can begin by reading from the graph but later will need the raw data and instructions are provided. | 0 |
Leave your answer as a surd if relevant. | 0 |
Write the generalised expression for electrostatic potential for N charges using latex3 and latex6 | 1 |
Determine: The rate of specific heat transfer to the environment in units of latex7 . | 1 |
If latex4 represents the displacement along a string, say, interpret your sketches. | 0 |
If a refrigerator and a heat pump operate on the same cycle, which has the higher latex0 ? | 1 |
Give an interpretation of this angle. | 1 |
How much longer lived is FBP mRNA than H3 mRNA? | 1 |
The generator requires a shaft power input of latex0 . | 0 |
The oil is a Newtonian fluid with constant and uniform density and viscosity. | 0 |
At what speed are they moving towards each other when they meet? | 1 |
At the instant the rope becomes taut, the velocities (in the same direction) of the two vessels are latex4 and latex5 respectively. | 0 |
The diagram shows a system for pumping water from the sea and from a lake into a reservoir at the top of a small hill. | 0 |
Hydrostatics is the study of static fluids. | 0 |
Determine the overall transfer function latex0 for the following complex systems: | 1 |
Show that this expression reduces to the correct form, as given in Section 5.7.2 of the lecture notes, for a difference amplifier in which: latex4 | 1 |
How long does it take before the correct speed is regained? | 1 |
A hydrostatic fluid is in equilibrium and so the sum of the forces acting must equal zero. | 0 |
Show latex14 . | 0 |
*\[Riley 6.18]* Sketch the domain of integration for the integral: latex0 and characterise its boundaries in terms of new variables latex1 and latex2 . | 1 |
What is the unit of the distance obtained from the above procedure? | 1 |
These are solutions where both masses oscillate at the same constant frequency. | 0 |
In the right-hand column, state the corresponding type of process in the ideal model. | 1 |
(*Hint: first recalculate the compressor exit temperature* latex9 , *the compressor specific work, the turbine exit temperature* latex11 *and the turbine specific work)* (iii) Recalculate the thermal efficiency, the required air mass flow rate and the fraction of the turbine's gross power which is used to drive the compressor. | 0 |
(2)** in terms of exponential functions. | 0 |
(Based on P4.9, White) An incompressible flow has a velocity field of the form latex0 What is latex1 ? | 1 |
A simple diode is used to ensure that no current flows through the driving motor if latex3 becomes negative. | 0 |
Does the axle exert a net force on the rotating rod? | 1 |
The contact angle (see diagram) is latex1 . | 0 |
These five events are indicated in the spacetime diagram below, and a person stands at latex6 to watch them turn on. | 0 |
Using the normal-flow model discussed in class, describe the sediment transport that will lead to the new equilibrium configuration. | 1 |
The *Lorentz Force* acting on a charged particle of charge latex0 and mass latex1 moving in a magnetic field latex2 is given by: latex3 (You will encounter this next term in the VFEM module). | 0 |
The annular gap is filled with the fluid whose viscosity is to be determined. | 0 |
An industrial site requires equal amounts of energy in the form of electricity and heat. | 0 |
An axially-symmetrical wake is formed behind the submarine in which the water velocity may be assumed to vary linearly from latex0 on the axis to zero at a radius of latex2 . | 0 |
Sketch a latex2 diagram of the cycle. | 1 |
For both choices of control volumes (A and B as shown above), derive an expression for: The drag force latex4 of the submarine. | 1 |
Find all the partial derivatives required for a third-order Taylor-Maclaurin expansion of latex1 . | 1 |
The lowest normal mode frequency, latex3 , is obtained when latex4 . | 0 |
How much work is done in lifting it from point A to point B? | 1 |
Calculate the total resistance as measured between points **a** and **b** of the network below. | 1 |
A rectangular box section beam, with outer dimensions latex1 deep, latex2 wide, with wall thickness latex3 . | 0 |
Use the ratio test to determine whether each of these two series is convergent latex0 latex1 | 1 |
**\[Boas 6.8.2]** Evaluate the line integral: latex0 along each of the following closed paths, taken counterclockwise: The circle latex1 . | 1 |
How much average power has to be supplied? | 1 |
This is a good model for the interference of light passing through two very narrow slits. | 0 |
A cylinder is placed in the wind tunnel for testing. | 0 |
The bending moment that will cause plastic behaviour in the flanges but not the central web. | 0 |
The sequence starts AACCGT. | 0 |
in the limit latex17 ? | 1 |
Show (numerically) that latex3 is perpendicular to latex5 and latex6 . | 0 |
The bed is smooth flat and consists of sediment with a mean sediment size latex3 . | 0 |
**\[Boas 5.4.1 (a),(b)]** For the disk latex0 , find by integration using polar coordinates: The area of the disk. | 0 |
Find its velocity vector and total speed. | 1 |
A rotation of latex4 in the latex5 plane, followed by a rotation latex4 in the latex0 plane. | 0 |