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What is this expressed in latex20 ?
1
The air above the oil is at rest and considered to be inviscid.
0
Sketch the behaviour of latex4 with respect to latex7 , labelling the value of latex7 for which latex9 , and state how the value of latex7 for which latex9 relates to your answer to the previous question?
1
The collector is fed by an ideal latex4 source.
0
At what time did it start snowing (i.e find latex5 )?
1
Steam enters a turbine at latex0 and latex1 bar, and leaves at latex2 bar (all total conditions).
0
Calculate and describe in words the operations given by: (i) latex2 (ii) latex3 (iii) latex4 For the matrix, latex5 show that there is a combination of elementary operations such that: latex6 where latex7 are elementary matrices adapted from part (a).
1
Based on your results from part d), is linear theory appropriate for this problem?
1
Calculate the matrix product for those combinations that *can* be computed.
1
A Newtonian fluid with density latex9 and viscosity latex10 is contained in the gap between the cylinders.
0
Find the angles latex4 and latex5 that the forward and rearward Mach lines form with respect to their local flow.
1
The plate is latex2 wide and latex3 thick.
0
Muons decay quickly to electrons, with a lifetime of latex0 when they are at rest.
0
Which reference frame measures proper time for the light clock?
1
In such cases, we can assume that latex3 .
0
Evaluate the coefficient of performance latex19 , given that latex20 .
1
A data acquisition card has an input range of latex0 to latex1 with a resolution of latex2 bits.
0
What do you notice about latex14 , and what does that tell you about latex16 ?
1
A fluid flows under shear force A fluid fills its container A fluid deforms indefinitely under shear force A fluid is one of the three states of matter
0
Investigate and discuss with your peers and tutors: What is the standard rate and resolution used to store music digitally on a CD?
1
The wind flows at a speed, latex3 , and the air has density, latex4 , and dynamic viscosity, latex5 .
0
You may interpolate from tabulated values.
0
**Figure (b)**: A snooker cue balancing on its base.
0
Try to identify the relationship between latex4 and which derivative of the function is discontinuous.
1
(Use the Data & Formulae Booklet to find material constants.)
0
When sketching the elliptical orbit, think carefully about the locations of the periapsis (point of closest approach to the focus) and apoapsis (furthest point from the focus) relative to Biff.
1
Critical damping is defined by latex18 .
0
Calculate the bending moment acting at this cross-section.
1
For an input step of amplitude latex0 , determine the steady error for the control system above, when: latex1 is a proportional control.
1
Note that the solution to the homogeneous differential equation (derived in the lectures) decays away as latex7 , so this part is often ignored.
0
In the life sciences we use a spectrophotometer to measure the absorbance of a solution of a coloured solute at a particular wavelength of light.
0
What is the input impedance of this circuit at point "A”?
1
Why is a maximum temperature as large as this acceptable in a reciprocating engine but not in a gas turbine engine?
1
Find the magnitude of latex4 (express your answer as a surd).
1
Is it padded with latex14 or latex3 ?
1
You should therefore find that latex16 Using the same logic, find the time latex17 for the light pulse to return from the mirror to the detector in frame M in terms of latex8 , latex19 , and latex6 .
1
Calculate latex3 and give an interpretation of this quantity.
1
The half-life of a radioisotope, latex30 has a relationship with the decay constant latex19 from above.
0
Sketch the output voltage waveform, latex2 , showing maximum and minimum values, and indicate the approximate DC voltmeter reading, when the component under test is: An open circuit.
1
It is believed that on 07-11-1940, the vortex shedding frequency produced by the Tacoma Narrows bridge (USA) matched one the natural frequency of the bridge and led to its dramatic collapse.
0
If the fluid originates from a large tank with nearly zero velocity and flows vertically downward for its latex3 length, estimate the magnitudes of kinetic and potential energy changes.
0
Now use the fact that the edges of the top plate (the plate at latex2 ) are open to the atmosphere to justify the fact that latex50 should be constant.
1
The substitution latex15 yields an integral of the form: latex16 You may also choose to make the subsitution latex17 in the final integration which leads to the latex18 form of the answer.
0
For the triangle with vertices latex0 , latex1 , and latex2 , and the vector field latex3 , evaluate: latex4 around the triangle, proceeding clockwise as seen from latex5 .
1
Give numerical values for latex10 using latex9 .
1
latex7 , latex8 latex9 , latex10
0
Using the Blasius solution, estimate the bending moment at the root of the cantilever.
1
Derive the following properties for Fourier transforms.
1
Additional details about the spool are given below: The outer discs forming the spool have diameter latex0 cm.
0
Select all that apply.
1
Evaluate the following limits: latex0 latex1
1
*(Take the rotation of the motor to be in the positive direction)*
0
The dynamic viscosity latex10 of the liquid depends on the temperature and is assumed to vary linearly across the bath: latex11 where latex12 is a constant parameter.
0
Plot the velocity field (by hand or computer).
1
Design a low pass filter that will reduce the possible aliasing to latex5 of the ADC range.
1
Advection only and in latex0 -direction.
0
Make sure you put a "\*" between items that need to be multiplied together.
0
Parts (a-b) of the question below start with the description of the collision in the centre-of-mass frame and converts everything to the lab frame.
0
Same as (b) but the roller is lowered by latex6 .
0
(ii) the percentage saving in fuel energy (considering fuel consumed on site and in power stations)?
1
What is the relationship between the pressures latex0 and latex1 ?
1
latex10 if and only if latex11 .
0
The Foucault pendulum is a simple experiment to demonstrate Earth's rotation.
0
After a transient period the water in the tank settles into a solid-body rotation, i.e stationary with respect to the tank.
0
The secondary creep rate is latex10 at stresses of latex11 and latex12 and temperatures of latex13 and latex14 , respectively.
0
If you want to store information about all of the motion, how much computer memory would be required?
1
The ambient temperature of the environment surrounding the heat exchanger is latex3 .
0
Sketch this curve.
1
A robot arm with transfer function latex0 is used to perform vision medical check-up of the cornea in the eye.
0
If latex6 and latex7 , determine the natural frequency latex8 and the damping constant latex9 that will result in damping ratio latex10 .
1
Is it consistent with your answer to Q2.1(d)?
1
**Separating controls into prevention and mitigation** In the example of crossing the road, the control measure was to take care, i.e to stop, look and listen.
0
For each of the npn transistors shown below, for which latex0 : 1.
1
What is the probability that the C at position 3 will mutate (to any other base) but that *none* of the other bases in the sequence will mutate?
1
What is the probability of a transversion of any one specific adenine residue in the DNA?
1
Solve the differential equation with the initial condition latex1 .
1
Introduce a complex variable latex8 , where latex9 .
1
In a development plan, a mall is planed to be built extending latex4 perpendicular to the river and latex5 parallel to the river.
0
What is the resolution (mm) of the linear position measurement?
1
How large is the error if you follow the above procedure to calculate the distance to the lightning?
1
Compare you sketch to the answers in the next part.
1
For each of the cases, determine the *deflection of the beam* at the point of application of the load and find the *maximum stress* in the beam after the load has been applied.
1
Give a numerical value in the case of air.
1
Which ones can it depend on?]
1
No pressure gradient is applied in the latex5 direction.
0
Explain your reasoning in detail.
1
Oil flows in the central part of the pipe.
0
Show that the dryness fraction of the steam at the turbine exhaust is latex8 .
1
In order to adjust the buckling temperature, one end mounting can be screwed-in to compress the strip axially.
0
It accelerated until the ammonium perchlorate-based fuel, which burned at a constant rate of latex1 , was exhausted.
0
It is pressurised to latex3 Calculate the safety factor for the hemispherical ends, using both Tresca and Von Mises criteria.
1
The acceleration of an object moving around a circle of radius latex2 at speed latex3 is latex4 .
0
The mole fraction of each component.
0
The velocity latex2 of the plough is given by latex3 where latex4 is a constant.
0
Show that the complex Fourier series of latex2 is given by: latex3 Rewrite the above to a sum from latex4 to latex5 .
1
Determine the following quantities downstream of the continuous latex0 convex corner shown below, with the flow upstream of the corner being at Mach 2: The Mach number, latex1 .
1
(Based on P2.12, White) Give all of your answers as fractions.
0
What is the probability that the C in position 3 of the DNA sequence mentioned above will mutate during one round of replication (assume all possible mutations are equally likely)?
1
** Use the polar representation of complex numbers, latex3 , to obtain the roots: latex4 for latex5 .
1
Indicate which of the dashed lines are oblique shocks and which are P-M expansion fans Use shock-expansion theory to calculate the pressure in region 3 as a fraction of the upstream pressure ( latex2 ).
1