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These discs were latex5 diameter and the centers of the holes were latex6 apart. | 0 |
The change in specific exergy flow rate of the steam flowing into and out of the turbine. | 0 |
Define latex0 : If latex1 and latex2 are both real, find latex1 . | 1 |
Now suppose that the boiler is able to superheat the steam, to a boiler exit / turbine inlet temperature latex7 of latex8 . | 0 |
When the rod rotates fast enough, the bearing breaks. | 1 |
Its binary representation is latex105 , wherein the sequence latex48 is repeated \_ad infinitum}. | 0 |
State whether the the bed shear stresses computed in Part (a) and Part (b) should be the same or not. | 1 |
Calculate the exit velocity latex0 . | 1 |
Using dimensional analysis find the non-dimensional parameters which govern this observed behavior. | 1 |
The chain is required because the engine's output shaft is connected to a sprocket and the belt is required to allow for slip. | 0 |
How long does a pendulum need to be to have a frequency of latex7 ? | 1 |
Show that the latex10 -component of the velocity is zero everywhere in the gap. | 1 |
The functions are referred to as (**Square**), (**Triangle**) and (**Parabola**) in the solutions. | 0 |
All this implies, for the real plant, an increase in fuel consumption and an increase in size and cost. | 0 |
Show that: latex3 Use your result to part (a) to find an expression for latex4 for an initial Gaussian temperature distribution: latex5 | 1 |
Consider the direction of the flow (to the right) as positive. | 1 |
The wheel is a uniform disc of diameter latex1 and mass latex2 . | 0 |
With the system at rest. | 0 |
**(L8)**: Use Gaussian elimination to find the intersection between the line latex0 and the plane latex1 . | 1 |
The enzyme lactate dehydrogenase catalyses the reaction: latex0 The progress of the reaction can be monitored by measuring the rate at which latex1 is produced spectrophotometrically, using the Beer-Lambert law: latex2 * latex3 Absorbance (dimensionless) * latex4 Molar absorption coefficient. | 0 |
Find the height latex7 reached by the ball after its first bounce and the corresponding drop time latex8 . | 1 |
If latex0 and latex1 and latex2 are related to two new independent variables latex3 and latex4 by latex5 so that latex6 , Use the chain rule to find latex7 and latex8 in terms of latex9 and latex10 . | 1 |
The wall is of thickness latex1 and of thermal conductivity latex2 . | 0 |
(**Hint:** Find the new normal vector of the solar panel.) | 1 |
The internal forces cancel out. | 0 |
The clinometer is held exactly latex1 above the ground. | 0 |
That one regenerated latex0 molecule can then re-enter the Q cycle again (note the halving of all the terms): latex17 And the ‘half a molecule of latex0 regenerated by this can re-re-enter the Q-cycle too: latex19 And so on. | 0 |
Sketch the output waveform at point "P", showing voltage and time scales, whilst this voltage is applied. | 1 |
How many units of enzyme were present per millilitre of the lactate dehydrogenase solution? | 1 |
In this problem, we will consider some practical applications of the Fourier transform in optics. | 0 |
Consider a solar power plant. | 0 |
* The distance between points latex0 and latex5 is latex9 * The distance between points latex0 and latex3 is latex12 Find the time, latex13 , required for the axle to complete a revolution about latex0 and the direction of this rotation. | 1 |
(lamina = thin sheet) Find the area the ellipse encloses. | 1 |
Give your answer to 1 decimal place. | 1 |
**(L9)**: Consider the matrices: latex0 Calculate the following, and state in words the property being demonstrated in each part, e.g "associative" or "non- associative". | 1 |
The other end may be supported by one of the following methods (see parts (a)-(e)). | 0 |
latex8 [table] Using the life fraction rule, calculate the creep damage fraction accumulated in a week. | 1 |
Assuming that the height difference latex4 is initially zero, how long will it take for the mass to be dislodged? | 1 |
You are now tasked with building a go-kart capable of travelling at a max speed of between 12 and 14 m/s. | 0 |
Show that latex0 where latex1 is a constant and latex2 . | 1 |
We are going to test a latex8 scale model of a latex9 long ship. | 0 |
iii) latex8 ? | 1 |
The transistor is of 2N 3055 type, with an latex1 of latex2 , and the motor’s operating voltage is latex3 . | 0 |
However, the equation is actually a linear second order ODE hence analysis is simpler. | 0 |
Calculate the total heads of water at the sea, the lake and at Point 3. | 1 |
Does Matt receive the two light pulses simultaneously? | 1 |
This allows you to calculate the cell growth rate, latex3 , from a graph. | 0 |
A tornado cruising over the ocean suddenly receives an alert signal of being under attack from a missile. | 0 |
Hence convert this into Cartesian form. | 1 |
Given the definitions (in lectures) of the hyperbolic functions latex0 , latex1 and latex2 , show that: latex3 latex4 latex5 latex6 | 1 |
A 5 kg mass moves under the influence of a time-dependent force latex0 N, where latex1 is the time in seconds. | 0 |
Using the average value of latex5 and modelling only the bed boundary condition, give the solution to this problem. | 1 |
Calculate the angular frequencies, latex1 and latex2 , of the two normal modes. | 1 |
Use the transformation matrix to transform all of the points found after the first rotation. | 1 |
Consider the y-momentum equation (13.3) from Lecture 13, applied to a non-parallel channel (illustrated): latex0 and the following dimensionless groups: latex1 Non-dimensionalise the y-momentum equation and identify the order of magnitude of each term. | 1 |
For the network shown below: Calculate the voltage latex0 (remember that, unless otherwise stated, latex0 means the voltage relative to ground). | 1 |
Make sure you take into account the unit quantities. | 0 |
Determine which of the following are exact differentials: latex0 latex1 latex2 latex3 latex4 | 1 |
Assuming that latex3 starts at the negative op-amp source voltage latex5 , the switching point when latex3 becomes latex7 occurs when the voltage at node “a” is equal to latex8 (i.e latex9 ), which we will call latex10 . | 0 |
Show that the torque latex3 exerted on the rod and masses by the axle is given by latex4 It is easiest to work in a coordinate system with the origin at the bearing and the latex5 axis along the axle. | 1 |
The length of the track from latex4 to latex5 is latex6 and the car has a mass of latex7 . | 0 |
One stream has a constant flow latex2 and the outflowing stream should be latex3 . | 0 |
Hence show that latex4 | 1 |
Both scripts are provided in both MATLAB and Python. | 0 |
Square wave inputs of latex1 and latex2 respectively, from sources of very low input impedance, are applied at points A and B as shown: From first principles, derive the expression for a summing amplifier described in Section 5.7.1 of the lecture notes. | 1 |
The shear stress at the interface of the water and oil is latex13 . | 0 |
Hence find the clock period latex21 in this frame. | 1 |
Starting from Navier-Stokes equations in cylindrical coordinates, derive an equation that describes the axial component of the oil/water velocity. | 1 |
The collar shown can slide without friction on a fixed vertical guide. | 0 |
Note that the buffer is also resistant to change below latex14 and above latex15 : this is 'pseudo-buffering', and merely due to the fact that very acidic solutions are resistant to latex1 change purely because they contain very high concentrations of latex17 or latex18 . | 0 |
The fin is a cantilever, i.e it is fixed at one end and free at the other end. | 0 |
(**Note**: there is no response area for this question. | 0 |
latex1 , to obtain an expression for latex0 in terms of latex40 *. | 0 |
What is the maximum range when latex3 ? | 1 |
The strip is latex1 long, with a cross-section latex2 by latex3 , and is pin-jointed at both ends. | 0 |
What is the net wave drag of this configuration at the design Mach number? | 1 |
Sketch the graph of the function in latex4 . | 1 |
Estimate the settling velocity. | 1 |
Air ( latex0 ) is flowing isentropically in a channel. | 0 |
Plot the following numbers in the complex plane (Argand diagram): latex0 latex1 latex2 latex3 | 1 |
Blood flow in the heart is Flow in a river is Water flow from a tap Flow in a vein | 0 |
An acoustic wave in the water, with a wavelength much larger than the bubble, excites the bubble into an oscillating motion (compressing and expanding) at a steady frequency latex1 with an amplitude, latex2 , that is small relative to the bubble radius ( latex3 ). | 0 |
The sand disposal is characterised by a medium sediment size latex2 . | 0 |
\[Note: for exponents, use \*\* instead of ^. ] | 0 |
The flow is uniform along the plate (i.e along latex2 and latex3 coordinates as shown in the image) and the ambient pressure latex4 is uniform and constant. | 0 |
What observation did we make about the boundary layer to start the approximation? | 1 |
For a narrow channel ( latex2 ) and moderate Reynolds number ( latex3 ) which terms can be neglected and which terms are the highest order? | 1 |
Its polar equation is latex0 where latex1 and latex2 . | 0 |
BONUS QUESTION (to think about...) Can you think of a way to use the result shown in part (c) to construct a parabola with a given target, axis and range? | 1 |
What will be the voltage at the op-amp’s inverting input? | 1 |
Take latex16 . | 0 |
The mean radius and axial velocity are constant. | 0 |
Controlled fusion is challenging because the positively charged nuclei must overcome their electrostatic repulsion such that the strong force takes over and they fuse. | 0 |
*\[Riley 11.26]* A vector field latex0 is defined in cylindrical polar coordinates latex1 by latex2 Calculate, as a surface integral, the flux of latex0 through the closed surface bounded by the cylinders latex4 and latex5 and the planes latex6 . | 0 |
* Show that the pressure in the water is: latex7 where latex8 is a constant. | 1 |
Solve this using the trial solution latex11 , where latex12 is a complex amplitude to find the unknown parameters latex13 and latex14 . | 1 |
Two strain gauges are fitted at latex0 to the axis of a latex1 diameter steel shaft. | 0 |
Construct the integral solution to the 1-D diffusion equation of a contaminant with initial concentration latex0 Starting from the fundamental solution for an instantaneous point release, show that the integral can be evaluated to give latex1 Hint: make a change of variables latex2 to solve the integral. | 1 |
Find latex9 , latex10 , latex11 , latex12 , and latex13 . | 1 |
The pressure force in a hydrostatic fluid is a vector given by latex0 . | 0 |
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