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With the surface of your hand at a temperature of latex0 , determine the convection heat flux for: A vehicle speed of latex1 in air at latex2 with a convection coefficient of latex3 .
1
Find the change in exergy flow rate in units of latex4 by two different methods: Via the flow stream exergy change: latex5 Via the differential version of the expression for thermal exergy (or work potential of heat transferred), latex6 .
1
(Give 3 decimal places) What will be the pressure at entry to the diffuser, assuming a normal shock wave at the end of the test section?
1
Using the answer to part g, determine the thermal efficiency of the cycle, the Carnot efficiency, and the effective efficiency of the engine as a percentage of the Carnot.
1
Does latex0 exist ?
1
Let latex0 be a Eulerian position in space.
0
The flow is uniform in latex5 , and uniform in the azimuthal direction with no swirl component ( latex6 ).
0
The function latex0 is increasing, i.e latex5 if latex6 .
0
The flow speed upstream of the fin is 40 cm/s and the upstream velocity profile is approximately uniform.
0
A travelator is a moving walkway often found in airports.
0
(ii) Sketch the cycle on a latex6 diagram.
1
Find the real and imaginary parts of the following complex numbers: (**Note** that latex0 denotes the *real part* and latex1 denotes the *imaginary part*) latex2 latex3 latex4 latex5 latex6 latex7
1
In this position the spring, which has a stiffness of latex1 and a negligible mass, is compressed by latex2 .
0
(*Challenge*) Consider an infinitely long metal rod and use the one-dimensional heat wave equation with heat transfer coefficient latex0 : latex1 Let the initial temperature at latex2 be described by the delta function.
1
Estimate the speed of the truck in the picture (state your assumptions).
1
The vehicle has a total mass latex1 and its centre of mass is at a height latex2 above the road surface.
0
We choose latex2 - and latex3 -axes as shown, so that the plates are at latex4 m and at latex5 m. What is the appropriate velocity at the top and bottom plates?
1
The plane strain fracture toughness of an aluminium alloy is latex0 .
0
Either answer the following questions by drawing out a space-time diagram, or solve algebraically using the Lorentz transformations.Two events are separated by latex0 in frame latex1 .
1
You may assume any radius at the throat, i.e 1.
0
A plane solid boundary at latex4 acts as a perfect reflector.
0
We wish to calculate the intensity at a point latex5 on the screen.
1
At what speed does the observer on the spaceship see the centre of the Milky Way coming towards the spaceship?
1
The variation of the water pressure with depth may be assumed to be unaffected by the presence of the submarine.
0
Air with kinematic viscosity, latex0 , flows in a wind tunnel, illustrated in the Figure.
0
On the latex2 *vs.* latex1 plot, there is a point of inflection (momentary steepest gradient) at around latex10 : this is where the buffer is most resistant to change in latex1 .
0
If not, what could you do to make it realistic?
1
Call this matrix latex8 .
0
Manometers are instruments used to measure pressure based on columns of liquid.
0
Use latex6 m/s latex7 .
1
[table] After messing about with all this radioactivity, you need to dispose of the radioactive waste.
0
Hence find the *flux* of solar energy falling on the solar panel as a function of the hour since sunrise given that at midday (i.e , sun directly overhead) the sun provides an intensity of latex8 .
1
Does this field satisfy the incompressible continuity relation?
1
Steam exits as saturated vapour at latex2 with a velocity of latex3 .
0
Are the following velocity fields steady or unsteady?
1
Using energy conservation and the concept of centripetal acceleration, find a formula for the minimum angle of release required for a smaller mass latex5 to lift a larger mass latex6 .
1
A woman of mass 60 kg stands at one end of a 10 m plank of mass 20 kg, which itself lies on a (frictionless) frozen lake.
0
Discuss, using the Exner equation, the expected migration of the antidune after an appropriate time interval.
1
Write the equation of motion relating latex1 and latex0 .
1
, In the image below, the added blue lines show the positions of the metal plates on the inner surface of the central fibreboard cylinder - these extend all the way through the width (i.e into the screen direction).
0
Calculate the required flow cross-sectional area at the turbine exhaust.
1
Find the values of latex5 for both the Von Mises and Tresca yield criteria when the cylinder has **closed ends.
1
A population is said to be at Hardy-Weinberg equilibrium if there is no deviation in the frequencies of the three possible diploid genotypes predicted by the overall frequency of the alleles.
0
Let latex1 denote a polynomial of order latex2 .
0
The mass of release is latex3 .
0
The refrigerant leaving the condenser is throttled to a flash chamber operating at a pressure of latex14 bar.
0
How much time do you need to simulate for?
1
The options available to you are as follows: [table] If the positioning of the shafts for the pulleys is as shown in the diagram below, find the required belt length.
1
Assuming the drag coefficients are constant, and given the drag coefficient data in Figure 16.4, suggest values for the drag coefficients latex17 , latex18 .
1
if, in addition, the flow is irrotational, i.e latex0 .
0
Consider a long, horizontal, shallow, open channel containing a stationary liquid.
0
Calculate the tangential component of absolute velocity at inlet to the rotor blade row.
1
*** *Hint*: When finding the Jacobian, you might find it useful to remember that: latex10
1
The wheel spins as shown at latex6 with its axle in the horizontal plane.
0
Immediately the automated defence system yaws the aircraft away from its original direction.
0
From this linearised equation identify the gradient latex21 : From this linearised equation identify the y-intercept latex22 : The rate constant for the decomposition of hydrogen peroxide increases with temperature, as shown in the table below.
1
We're going to build up a graph showing the changes in density, latex0 , of a fluid as the size of the element volume, latex1 increases.
1
You might then also attempt the hard way.]
1
A species of bacterium may be modelled as a point like cell body attached to the end of a cylindrical tail of length latex0 m and diameter latex1 m (note: this isn’t very realistic since the tail is usually quite light, but it gives you a chance to practise the calculation).
0
Again, you have determined that the conditions at the start of the compression process are a temperature of 25°C and a pressure of 1 atm.
0
A steam boiler burns natural gas with the properties given in Table 8.4 of the lecture notes.
1
*For* latex8 , *you will first need* latex9 , *from an isentropic process relationship, and for* latex10 *you will need* latex11 ) (iv) Verify that the thermal efficiency found in (iii) is the same as that given in the lecture notes (Equation 3.9), and compare it with the efficiency of a Carnot cycle having the same maximum and minimum temperatures.
1
What is the critical bed shear stress, latex4 , for this channel?
1
latex0 Put latex1 into partial fractions.
1
The boundary at latex3 is a perfect absorber.
0
What other force is acting on the diagonal block?
1
**(L4):** Find whether latex0 points into or out of the page for the following pairs of vectors:
1
Can latex1 vanish?
1
What is the minimum latex5 of the required transistor for the load to operate at the rated voltage and power?
1
What was the speed of the bullet?
1
There is a relationship between the size of an island (or other defined area) and the number of species it contains.
0
Calculate the magnitudes ( latex2 ) and directions ( latex3 ) of the principal stresses.
1
Calculate the required series resistor and the maximum regulated output current for this series combination of Zener diodes.
1
The Michaelis-Menten equation describes enzyme kinetics.
0
From the absorbance value, we can calculate the concentration of the coloured solute in that solution.
1
Consider the Joule Cycle.
0
Consider the spread of an instantaneous point release of contaminant in a shallow lake.
0
Show that the solution indeed satisfies this boundary condition.
1
Consider a river stream with the specific flow rate latex0 , and a water depth of latex1 .
0
problem sheet 4!
0
Assuming that the weight and the pile move together after the impact, find: The velocity, latex3 , with which they begin to move.
1
Calculate the length of the pendulum needed to make a clock that ticks once every second.
1
latex4 is the frequency of *AA* homozygotes, latex5 is the frequency of the *Aa* heterozygotes, and latex6 is the frequency of the *aa* homozygotes.
0
You may neglect any changes in potential energy but you may not neglect the change in kinetic energy of the steam in this case.
0
Assuming the velocity profile depends linearly on the depth (which it will do as long as the Reynolds number is small), write down the water velocity latex5 as a function of height latex6 above the bottom surface.
1
[table] Consider factors that may influence the component selection other than the achieved transmission ratio.
0
The masses can only move perpendicular to the walls.
0
Why can’t the Bernoulli equation be used to equate the two heads?
1
The key calculation (for which you should work out the probability below) is how likely is the sequence 'AGGAGG...AUG' to arise by chance in a typical bacterial citron, which is latex3 bases long?
1
It accelerates from rest until latex1 of the fuel is burnt.
0
The parameters of the D.C. motor are: latex4 latex5 latex6 latex7 latex8 (No frictional losses)
0
In a gasifier, solid carbon and steam (as oxidant) form gaseous carbon monoxide and hydrogen.
0
Given that latex10 km and latex11 kg latex12 m latex13 , how long did the orbit take and how fast did Biff throw the rock?
1
Point “C” is now disconnected from its DC input.
0
*Do not use results from part (a).
0
Calculate the shear force acting across this section, assuming that it is uniform across the whole cross-section.
1
The carriage then returns to the starting point A along a flat track (not shown on diagram), where it is stopped for the passengers to alight.
0
Write each of the following expressions as a complex number in the form latex0 : latex1 latex2 latex3 latex4 latex5 latex6
1
Show that writing down the Fourier series in the form: latex3 latex4 is equivalent to the trigonometric Fourier series if: latex5 Show that the form of latex6 is unchanged by a phase shift in latex7 .
1
Apply the divergence theorem to this integral and show that latex4 gives the same answer.
1