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One of these holes was at the mid-point of the span. | 0 |
The horizontal range latex0 of a projectile is given by latex1 , where latex2 is the projection speed, latex3 is the angle of elevation and latex4 is the gravitational acceleration. | 0 |
How much total memory is required? | 1 |
She walks to the other end of the plank. | 0 |
What would be the total change in length of a bar of latex8 initial length at latex9 , which is held at a stress of latex10 when immediately on heating to latex0 and loading (i.e thermal expansion). | 1 |
A DNA sequence is 1 million bases long and the rate at which a base mutates per generation, latex0 , is latex1 . | 0 |
Is there a reference frame latex2 in which the events are simultaneous, or at the same position? | 1 |
An instantaneous release into a water pipe. | 0 |
How much kinetic energy has the block gained? | 1 |
Can you also evaluate the highest transmission ratio that could be sufficient for this use case (using the 5% lower bound)? | 1 |
The inlet pressure latex0 is measured as latex1 bar gauge and the sample is throttled to atmospheric pressure latex2 , measured as latex3 mbar. | 0 |
Derive an expression for the period of small oscillations about the position of stable equilibrium. | 1 |
The specific internal energy of saturated steam at latex5 bar. | 0 |
Choose Fick's Law, stating the meaning of the variables on paper. | 1 |
\[Note: to enter numbers in scientific notation, use format 1.5e6, for instance] Determine the pressure coefficient at the nose of the aerofoil. | 1 |
In particular on (2) latex6 . | 0 |
The mean resistance of the earth to penetration, latex4 , if the pile is driven latex5 into the ground by the blow. | 0 |
Take latex3 . | 0 |
When a medium is dispersive the phase velocity in the medium varies with the frequency of the wave. | 1 |
Sketch the processes in the valve and turbine on an enthalpy - entropy ( latex7 ) diagram, including the relevant isobars. | 1 |
Confirm the above for latex6 , latex7 by calculating latex8 , latex9 , latex10 , latex11 . | 1 |
Let latex0 and latex1 be two spatio-temporal functions (i.e they both depend on latex2 , latex3 , latex4 and latex5 ). | 0 |
Use the above result to find expressions for latex2 and latex3 in terms of latex4 and latex5 . | 1 |
What buckling mode do you now expect, and what failure load? | 1 |
Find the velocities latex5 and latex6 (assumed uniform). | 1 |
Solve this problem again, this time using the concept of the centre of mass. | 1 |
Assuming the density of air to be constant at latex0 kg/m latex1 what is the pressure change from the top of a mountain to its base if the elevation change is 3500 m? | 1 |
**(L13)**: Find transformation matrices for the following operations in three dimensions: A reflection in the latex0 -plane A reflection in the latex0 -plane followed by a reflection in the latex2 -plane. | 1 |
Inviscid fluid, steady flow 2. | 0 |
An orthonormal basis set can be found based on latex2 by first normalising latex2 to find the first vector latex4 . | 0 |
Calculate the transmitted torque. | 1 |
latex1 latex2 latex3 | 0 |
Which of these effects is more important in a laminar flow? | 1 |
Calculate its value on Mars ( latex13 , latex14 ). | 1 |
You may assume the flow is steady and symmetric. | 0 |
Select the engine which is the appropriate choice to meet the criteria set out for this mock design task. | 1 |
What does latex8 equal in terms of latex0 , latex10 and latex6 ? | 1 |
Based on reading the graph, estimate (roughly!) | 1 |
In a simple vapour-compression refrigerator using R134a, the pressure of the refrigerant in the evaporator is latex0 bar. | 0 |
By using the principle of conservation of momentum, work out how far she has travelled relative to the lake. | 1 |
Given that latex2 , find latex3 up to a constant (use latex4 for the constant). | 1 |
Now use the boundary conditions at latex1 and latex2 to simplify the expression you got in Question 8.15a) to get an exact expression for latex11 (with no undefined constants or functions of integration). | 1 |
The compressor has a pressure ratio ( latex1 ) of latex2 and an isentropic efficiency of latex3 . | 0 |
Discuss why this is not the case and see of you can come up with some ideas for how to achieve this anyway. | 1 |
Calculate the stagnation pressure ratio across the stage when the inlet stagnation temperature is latex5 . | 1 |
This question is quite difficult - if you do get stuck, try looking at the answer and work backwards from that. | 0 |
(Notice that latex4 is negative, so the block is initially moving in the latex5 direction.) | 0 |
Find expressions for the latex3 and latex4 component of the particle accelerations. | 1 |
* Temperature latex0 of water entering tower: latex1 latex2 [embedded] * Temperature latex3 of water leaving tower: latex4 latex5 [embedded] * Mass flow rate latex6 of water leaving tower: latex7 latex8 [embedded] * Temperature latex9 of moist air entering tower: latex10 latex11 [embedded] * Relative humidity, latex12 of moist air entering tower: latex13 latex14 [embedded] * Temperature latex15 of moist air leaving tower: latex16 latex17 [embedded] * Relative humidity latex18 of moist air leaving tower: latex19 latex20 [embedded] * Temperature latex21 of make-up water: latex22 latex23 [embedded] * Atmospheric pressure latex24 , latex25 : latex26 latex27 bar All processes are assumed to be adiabatic. | 0 |
Compute the shear stress on the top plate. | 1 |
*The following question is broken down to encourage discussion as a group and/or as an exercise during tutorials. | 0 |
A transversion is defined as a mutation that converts a purine (A or G) to a pyrimidine (T or C) or *vice versa*. | 0 |
( i ) Express latex6 in terms of latex9 , latex14 and latex0 . | 1 |
Figure: *Square spreading rate as a function of time. | 0 |
At latex1 the engine is turned off and a large garage door is opened. | 0 |
It is of course possible to translate latex70 into latex71 . | 0 |
A wide freshwater stream has a smooth granular bed with a bed slope of latex0 and a uniform flow depth of latex1 . | 0 |
In one-dimensional inelastic collisions, the coefficient of restitution latex0 is defined by the equation latex1 where latex2 and latex3 are the final velocities of the two bodies and latex4 and latex5 are their initial velocities. | 0 |
Let us define a new variable latex8 such that: latex9 Show that: latex10 *Hint: recall trigonometric identities such as latex11 and latex12 *. | 1 |
In a steam power plant, the boiler produces latex0 of steam in the saturated vapour state at a pressure of latex1 bar. | 0 |
The following diagrams show the streamlines of flows of a fluid through an expanding duct: What would be the two most suitable Reynolds' Numbers for A? | 1 |
Firstly, you are offered a selection of only gears to use for your transmission. | 0 |
The readings of the gauges are recorded, and it is found that the maxima or minima values for each gauge occur at latex2 intervals of shaft rotation and are latex3 and latex4 for the two gauges at one instant, and latex5 and latex6 for the same gauges latex2 of rotation later. | 0 |
Solve the ODE you derived in part (c) to give an expression for the pressure along latex4 . | 1 |
Also, assume that the river margins are rigid and any morphological changes occur on the bed. | 0 |
If the frequency of an allele *A* in the gene pool is latex0 , and the frequency of the only alternative allele at that same locus *a* is latex1 , then the following two equations will hold after one generation of mating, assuming the population is large, and the interesting processes mentioned below are not acting: latex2 This assumes only two alleles can be present at the locus latex3 This additionally assumes that there is no selection, drift non-random mating, *etc*. | 0 |
The Ok Tedi river ("Ok" means "river") in Papua New Guinea suffered an important disposal of large amounts of waste sediment from the Ok Tedi Copper Mine. | 0 |
Then, Lorentz transform the events to a moving frame, and find the distance between the events in the moving frame, latex22 . | 1 |
Estimate the bed level changes after 3 months. | 1 |
*The following question is broken down to encourage discussion as a group and/or as an exercise during tutorials. | 0 |
A new high-speed train is proposed between Tokyo and Nagoya. | 0 |
There needs to be a region where they are both valid. | 0 |
The inner cylinder is hollow, but its inside is reinforced with metal plates. | 0 |
For the cantilever as shown in the diagram below. | 0 |
This requires a new dimensionless group, latex17 We can also define a different dimensionless length which is relevant near the wall latex18 Write the dimensionless form of the original ODE using latex19 instead of latex20 and assuming that latex16 is a good lengthscale to use near the wall such that the dimensionless derivatives are indeed latex6 . | 1 |
Determine the steady state response to a step input of amplitude latex3 . | 1 |
* Can you see how it relates to approximating a 3D vector with a vector in a 2D plane? | 1 |
A steel connecting rod in a pump has the dimension shown. | 0 |
Evaluate explicitly both sides of Stokes' Theorem: latex3 (the line integral is defined counter-clockwise), where latex4 is a disk of radius latex5 in the plane latex6 with centre at latex7 . | 1 |
(Based on P4.9, White) An incompressible flow has a velocity field of the form latex0 What is latex1 ? | 1 |
In the decimal system, we write it as latex58 with latex59 , latex60 , latex61 etc. | 0 |
Show that the first and second derivatives are always perpendicular to one another. | 1 |
Its displacement as a function of time, in SI units, is latex0 . | 0 |
For the two diffusivities mentioned in the previous question ( latex0 and latex1 ), plot the distance in the latex2 direction where the concentration exceeds latex3 ( latex4 -axis) as a function of time ( latex2 -axis). | 1 |
The diagram below illustrates the operation of a **4-bit** optical encoder for angular position. | 0 |
Approximately how many atoms of latex3 did this seed contain when it was germinated? | 1 |
latex2 latex3 | 0 |
What final speed could this rocket reach? | 1 |
No body force is applied to this flow (it is simply driven by the motion of the wall). | 0 |
A four-stroke spark-ignition engine with a compression ratio latex0 of latex1 is to be modelled using the air-standard Otto cycle. | 0 |
The system starts with zero displacement and speed. | 0 |
A thick-walled cylinder with an outer to inner diameter ratio latex0 and **closed ends** is subjected to increasing internal pressure until yielding first occurs. | 0 |
where latex7 is a positive number. | 1 |
Let latex11 denote the latex0 matrix of eigenvectors. | 0 |
Verify whether sediment motion will occur. | 1 |
The force field latex17 , where latex18 is a constant with units of N latex19 m latex20 . | 0 |
Why do the horizontal components of the force of the fluid on the beaker cancel? | 1 |
Assuming that the population is well mixed, and that the marking has not affected the survival or trap-wariness of the animals, the proportion of recaptures in the second sample will be the same as the proportion of the total population captured by the first sample. | 0 |
Using the continuity and momentum equation in the radial direction, explain why the pressure varies only in the vertical direction and the velocity of both fluids varies only in the radial direction. | 1 |
We define latex3 as the rate of energy dissipation per unit mass. | 0 |
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