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Show that: latex9 Find latex1 for any positive value of latex3 . | 1 |
Figures 1 and 2 are two views of a Formula 1 race. | 0 |
Air, supplied by a reservoir at latex0 flows through a converging-diverging nozzle whose throat area is latex1 . | 0 |
Figure 1 Figure 2 Figure 1 is consistent with: Figure 2 is consistent with: | 0 |
Using experimental data given in the table, find the thrust generated by a geometrically similar propeller of diameter latex4 , spinning at latex5 at a forward velocity of latex6 , while operating at an altitude where the density is half that at sea level. | 1 |
The following statements are true at *both* plates (1) and (2): o Plate area is latex0 . | 0 |
Note that latex24 is the relative speed experienced by the cups, assumed constant for each half rotation of the anemometer. | 0 |
Challenge yourself to answer this question with no further information. | 0 |
Draw a circuit diagram of the system and select a suitable resistor value. | 1 |
A square plate fixed along all four edges has a set of normal modes characterized by two integers latex0 and latex1 . | 0 |
the latex5 component of latex23 . | 0 |
By how much must the fracture toughness of the material be improved in order to tolerate a longer crack latex11 at the same fracture load? | 1 |
In the lectures we looked at the interference pattern due to a pair of point sources with separation latex0 . | 0 |
In this part of the question you will *begin* to find the latex22 component, latex11 , of the flow Given that the flow does not depend on latex12 or latex13 , simplify the continuity equation and solve it to find the dependency of latex11 upon latex12 , latex13 , latex29 and latex30 . | 1 |
Use the cross product to find the angle between latex5 and latex6 . | 1 |
The card can sample at latex3 . | 0 |
Use a frame of reference fixed to the tank and assume no relative motion between the fluid particles in that frame of reference. | 1 |
Find the values of latex2 and latex3 at latex4 . | 1 |
Make use of Green's Theorem. | 1 |
Consider the function latex0 , where latex1 , is analytic. | 0 |
Using this figure, estimate the maximum operating temperature of a gas turbine blade made out of this material which is to withstand a stress of latex0 for a duration of latex1 hours. | 1 |
The mass flow rate latex4 is the same on each side, so that the temperature difference latex5 between the hot and cold sides is constant throughout the heat exchanger. | 0 |
The ratio of latex7 with latex1 is known as the Froude number (noted latex10 ). | 0 |
It is often easier to understand where they come from and rederive them when needed. | 0 |
Is the discrepancy in air-speed computations significant in this case? | 1 |
There is damping in the system because the accelerating electron dissipates energy by radiation. | 0 |
Show that the maximum value of latex2 is 	 latex3 , and that 	 latex4 The half-power frequencies are defined as the values of latex5 at which latex2 is half the maximum value. | 1 |
Draw an element of material at the point of interest, and indicate the stresses acting on its faces. | 1 |
In the channel flow pictured below, with water entering from the left, in which region (labelled A to F) is the flow field approximately the same as the 'straining flow' field described above? | 1 |
An 'integrated' risk assessment, for simple risks such as everyday activities. | 0 |
This problem leads you through an alternate derivation based on the invariance of the speed of light. | 0 |
Force fields without potentials are called non-conservative. | 0 |
The geometry is illustrated in the figure below, where we鈥檝e assumed latex1 is odd (though the results will not depend on that). | 0 |
** Calculate the safety factor against **buckling in the plane of the diagram**. | 1 |
The general solution of the driven oscillator with light damping, where the driving force is latex0 , is the sum of the steady solution 	 latex1 and the transient solution 	 latex2 . | 0 |
The combustion process in the real engine is to be modelled by a heat transfer latex6 to the air of latex7 . | 0 |
Calculate the latex15 in a heat pump application. | 1 |
A wide freshwater stream has a stream flow of latex0 at a uniform depth of latex1 . | 0 |
Define a control volume in the reference frame moving with the compression front. | 1 |
In the quantum picture, the power is dissipated by emitting photons, each one having energy latex11 . | 0 |
The Reynolds number describes the ratio of inertial to viscous effects. | 0 |
(You may assume throughout this question that all physical quantities are given in dimensionless units, and there are no external forces acting on the particle.) | 0 |
The pressure is latex7 Pa, where latex8 is the distance parallel to the flow (measured in metres). | 0 |
What is the maximum deflection angle for which a flow at latex2 will remain attached? | 1 |
*** The centroid is the Cartesian point latex1 such that latex2 and latex3 where latex4 is the region of integration and latex5 is the area of that region. | 0 |
By recognising: latex8 as a Fourier transform of a function from *Question 3*, evaluate the integral: latex9 through the use of Parseval鈥檚 theorem. | 0 |
It branches in two repeatedly, and at each level, the volume of each daughter branch is one quarter that of its parent. | 0 |
Find the acceleration of a disc of mass latex0 and radius latex1 , which has been released from rest, as it rolls (without slipping) down an inclined plane which is at an angle latex2 to the horizontal. | 1 |
The sediment size at the river bed is described by latex2 . | 0 |
If the planes intersect at a point, input the point of intersection. | 1 |
Lubricant viscosity is VG32 (32 mPa.s). | 0 |
Determine the dryness fraction latex6 at the final state of the steam | 1 |
A crack of length latex0 has been found at the center of a large thin plate, with an end load of latex1 . | 1 |
A passive contaminant or tracer. | 0 |
The Navier latex0 Stokes equations describing the flow of an incompressible Newtonian fluid are as follows: latex36 latex37 latex38 In this part you will find the latex12 - and latex13 -components of the flow, latex9 and latex10 , in terms of the pressure field, latex43 . | 1 |
Assume that advection is the only process of importance. | 0 |
(Based on P3.164, White) The nozzle shown below ejects a jet of water into air at atmospheric pressure (101 kPa). | 0 |
Why do these not hold? | 1 |
Is the channel bed stable in terms of initiation of motion for this flow? | 1 |
What is the highest frequency the card can sample without the danger of aliasing? | 1 |
(*Hint: find* latex12 *and* latex13 *from the fact that process* latex14 *is isentropic, then* latex10 *from the 1st Law, then* latex11 *from the equation of state*.) | 0 |
* You may wish to abbreviate that to latex41 for clarity. | 0 |
(iii) Calculate the net specific work and hence the thermal efficiency of the cycle. | 1 |
A constant force latex6 N acts for 5 s. Find the acceleration of the block and hence its final speed and final kinetic energy. | 1 |
However, there is a simple classical model that works surprisingly well. | 0 |
What is the probability of a randomly synthesised 6 nucleotide-long piece of DNA having the sequence AACCGT (assume all bases have equal probabilities of occurrence)? | 1 |
Calculate the total resistance as measured between points **a** and **b** in the network below: | 1 |
*\[Riley 10.11]* The hyperboloid latex0 is parameterised by latex1 , latex2 , latex3 . | 0 |
Use Cramer's rule to find a solution to the following system of linear equations: latex0 | 1 |
Hint: Are there any symmetries that allow reduction of the spatial dimensions? | 1 |
What is the deflection angle that will make the flow behind a shock at latex1 sonic? | 1 |
You should assume that the conditions in the reservoir are steady. | 0 |
Consider two infinitely narrow slits that are separated by a distance latex8 . | 0 |
What is the total resultant force of the water on the dam? | 1 |
Give its numerical value at ground level: Aircraft designers assume air to be a continuum medium. | 1 |
A force of latex1 N acts on the mass for 4 seconds. | 0 |
Assume acceleration is uniform up until the point of reaching maximum speed. | 0 |
Assume the channel to be steady and uniform. | 0 |
What is the pressure at the bottom of a (hypothetical) latex2 mm high column of mercury, latex3 kg/ latex4 ? | 1 |
Find the pressures and temperatures at the end of the expansion process. | 1 |
Hint: You may need to use the latex6 function in Matlab. | 0 |
What is the critical bed shear stress, latex5 , for this channel? | 1 |
Consider a river stream given by the specific flow rate latex0 , where the water depth is latex1 . | 0 |
The water is present in both liquid and vapour phases, and has a total mass of latex3 . | 0 |
Let鈥檚 write the frequencies of these normal modes in the form latex2 . | 0 |
Answer the following questions. | 1 |
If so - of what functions? | 1 |
Find the net specific work of the cycle and then use this to find the power supplied by the engine if it is running at 5000 rev/min and the cylinder capacity is 2 litres ( latex1 ) Using the answer to part c, determine the thermal efficiency of the cycle, the Carnot efficiency, and the effective efficiency of the engine as a percentage of the Carnot. | 1 |
Is the assumption of suspended sediment transport occurring in a small layer close to the bed valid? | 1 |
Repeat this calculation for other time values. | 1 |
Call this number of nuclei latex27 , and use it to obtain a particular solution to the ODE. | 1 |
The phone has an internal resistance of latex2 and requires a latex3 input. | 0 |
A snow plough starts at noon latex1 and moves along a road removing snow at a constant rate. | 0 |
Now consider the burning of the log and describe the temperature latex5 as a convolution of the constant heat provided by the log with the temperature evolution latex6 from part (a). | 1 |
The minus sign in the answer arises because the radial direction points out of the sphere while the flux is into the sphere. | 0 |
**(L13)**: A parallelogram latex0 (in latex1 ) anchored at the origin is defined by the sides with vectors with components latex2 and latex3 . | 0 |
It can be shown that the mean-free path in the hard-sphere model is latex7 . | 0 |
latex0 Which of the following is correct:- Select all that apply Does the function latex1 satisfy Laplace's equation? | 1 |
You must choose your own unit normals --- do this with care regarding the signs. | 1 |
the station. | 0 |