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Consider the flow to be Newtonian, incompressible, with uniform dynamic viscosity. | 0 |
A tank at latex0 feeds air ( latex1 ) into a nozzle with a throat area of latex2 and an exit area of latex3 . | 0 |
Calculate the temperature and pressure at the nose of the aerofoil. | 1 |
The obtained solution will be compared against the more accurate Blasius solution. | 0 |
Finally, plot the concentration as a function of latex6 . | 1 |
What should the kinematic viscosity ( latex13 ) of the model test fluid be compared to the kinematic viscosity of sea water? | 1 |
The interface between *fluid 'a'* (top) and *fluid 'b'* (bottom) is half way between the upper and lower plate. | 0 |
A particle of mass latex0 moves in the latex1 direction under the action of a conservative force. | 0 |
Search around online and try to figure out what this series of polynomials is called (remembering that the sign of each polynomium is not well defined). | 1 |
Consider the polynomial latex0 , where latex1 , latex2 , and latex3 may be complex and latex4 . | 0 |
This makes it very convenient to complete the question yourself. | 0 |
The river bed comprises of sediment with size: latex3 . | 0 |
Does this flow satisfy the boundary conditions you suggested? | 1 |
The traps are then reset and allowed to capture animals again for the same period of time. | 0 |
Write down the formula for Reynolds number, defining any symbols. | 1 |
What is the shear stress of the fluid on the top plate? | 1 |
Initially, the first pendulum is stationary at the equilibrium position, while the second is moving and has all the energy. | 0 |
**(L7/8)**: For each of the following sets of simultaneous equations, determine if there is: 1. | 1 |
Determine the tension latex3 in each rod if latex4 and latex5 . | 1 |
For example for latex8 , use latex27 .The left column is three-dimensional bodies of revolution; the right column is two-dimensional bodies extending infinitely into the \`page' | 0 |
The rate of elimination of caffeine from the human body can be approximated by first-order kinetics; that is, the rate of change in the concentration of caffeine latex0 in the blood over time ( latex1 ) can be modelled in the following way: latex2 where latex3 is the rate constant for elimination. | 0 |
What are the two eigenvectors of latex14 (write in normalised form)? | 1 |
Hence show that latex11 Hence, show that latex12 | 1 |
Disc latex3 is coupled to a small electric motor mounted on latex6 , and latex0 and latex3 are meshed together at their outside diameter. | 0 |
What is the order in which the light from the lamps reach the person driving the car? | 1 |
Calculate the area of the transformed shape. | 1 |
\ \ Guide to the data files: * A \`starter' script is provided to read in the data and it indicates which lines to code your solutions for latex9 . | 0 |
Describe physically the implications of the 1D diffusion equation. | 1 |
How many molecules of latex2 are reduced by the complete oxidation of a single latex0 molecule to latex1 ? | 1 |
What are the physical dimensions ( latex1 ) of the equations as derived in the Lecture? | 1 |
What is the momentum of latex4 in the centre-of-mass frame? | 1 |
Find an expression for the force latex1 acting on the particle at time latex2 . | 1 |
The steel cylinder of a hydraulic press has an internal diameter of latex0 and the water pressure is latex1 . | 0 |
(ii) Recalculate the net specific work. | 1 |
Find the range of values of latex0 such that the roots of the characteristic equation are: Overdamped. | 1 |
In its rest frame, a rod of length latex14 is lying along the latex11 axis with the left hand end at latex16 . | 0 |
Verify that the components are perpendicular to each other. | 1 |
Show that the wall thickness of the hemisphere should be latex0 times the cylinder wall thickness. | 1 |
(ii) from the criterion for the second partial derivatives of latex1 with respect to latex3 and latex4 . | 0 |
A fuel is burnt first with the stoichiometric amount of air and then with the stoichiometric amount of pure oxygen. | 0 |
A plane figure is bounded by the parabola latex0 , the latex1 axis, and the line latex2 . | 0 |
A plane source located at latex0 releases at latex1 a slug of contaminant of diffusivity latex2 . | 0 |
What would the strain gauge record in service if subjected to the same torque as before? | 1 |
The block is raised in temperature by latex6 and subjected to stresses of latex7 in the latex3 -direction and latex9 in the latex5 -direction. | 0 |
For fully steady laminar flow in a pipe with constant circular cross-section, latex0 where latex1 are cylindrical coordinates with latex2 parallel to the pipe axis; latex3 is the constant pressure gradient; latex4 is the radius of the pipe; latex5 is the fluid dynamic viscosity. | 0 |
At steady-state the turbine performs work equal to latex5 of steam flowing through the turbine. | 0 |
The system is at rest for latex0 . | 0 |
Draw the compound stage and give suitable values to all elements in the circuit (note that there exist an infinite number of valid solutions to this problem). | 1 |
A sealed room is heated. | 0 |
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 |
Use latex4 to diagonalise latex1 . | 1 |
The system shown above represents a process control plant with an output measurement transducer. | 0 |
What is the transfer function of the system? | 1 |
The doubling time/half-life of a population undergoing exponential growth/decay is latex12 Calculate the rate of growth of an animal population of latex13 individuals, whose doubling time is latex14 . | 1 |
Assume that latex5 and that the total sediment transport is dominated by bed load transport latex6 . | 0 |
*** **Figure**: Foucault pendulum of length latex0 , free to rotate in the latex3 - latex4 plane; the pendulum is at angle latex2 from the latex1 axis (referred to as latitude). | 0 |
Use the tools on the Imperial Visualisations website [embedded] to draw the field lines for the following arrangements of charges: Two separated charges of magnitudes latex0 and latex1 | 1 |
If the stresses latex3 and latex4 are fixed in magnitude, determine the greatest permissible value of latex5 if tensile stresses are to be avoided anywhere in the element. | 1 |
We will attempt to verify Lorentz contraction using the same method. | 0 |
A transition is defined as a mutation that converts a purine to another purine, or a pyrimidine to another pyrimidine. | 0 |
When the gas and latex1 excess air are both supplied to the burners at latex2 , latex3 atm, the temperature of the flue gases (i.e products) is found to be latex4 . | 1 |
To appreciate what this means, make a sketch of latex2 as a function of latex5 , indicating the half-power frequencies on this sketch. | 1 |
The encoder is attached to a lead screw of **0.8mm** pitch, which controls the linear position of a slider. | 0 |
Calculate the shaft power produced. | 1 |
**(L4)**: Identify the following surfaces described for latex0 . | 1 |
Assuming that the flow discharge and water depth remain constant. | 0 |
The pressure is latex7 Pa, where latex8 is the distance parallel to the flow (measured in metres). | 0 |
For the function latex0 , Find the stationary points of latex1 and determine their nature Sketch the graph of latex2 . | 1 |
This is maximized on resonance, i.e when latex1 . | 0 |
The trapdoor is hinged along its top edge (and has a catch on the bottom edge to hold it closed). | 0 |
Which of the following graphs belongs in each section above? | 1 |
Non-Dimensionalise the one-dimensional Cartesian form of the advection-diffusion equation by introducing appropriate length, velocity, concentration, and time scales. | 1 |
A population of bacteria is growing exponentially: latex0 latex1 is the number of bacteria at time latex2 (or some measure for that, such as the optical density at latex3 , latex4 ), latex5 is the number of bacteria at latex6 and latex7 is the exponential growth rate constant, which is related to the dou... | 0 |
The height of both the fluid layers is constant and equal to latex6 . | 0 |
A normal shock occurs at the exit of the nozzle, and just behind the normal shock the temperature is latex4 . | 0 |
Bonus question: if you cannot make the assumption that the base current is negligible (i.e latex4 = latex5 + latex6 ), what would the voltage latex7 in the circuit in (a) be? | 1 |
Consider the steady laminar flow of two immiscible fluids between two parallel flat plates which are infinitely-long in both latex0 and latex1 directions. | 0 |
A ship of mass latex0 is towing another of mass latex1 using a steel wire rope whose effective elasticity is such that a tension of latex2 produced a latex3 increase in length. | 0 |
Imperial College, in trying to maximise revenue from its new White City campus, decides to build a roller coaster using new, frictionless technology developed in the Mechanical Engineering department. | 0 |
When the same person accelerates from rest in the carriage to a final velocity of latex11 m latex2 s latex3 relative to the carriage, latex14 which is latex15 times higher than the result when the train is at rest. | 1 |
Can you help Damien to resolve this apparent paradox? | 1 |
What will the peak-to-peak amplitude of the ripple voltage be after filtering? | 1 |
Numerical exercises on oscillators, damped and driven. | 0 |
The diameter of the pipe upstream is latex0 cm, whilst the diameter of the jet is latex1 cm. | 0 |
Plot values of latex7 and compare them to latex8 . | 0 |
Show that the last two equations can be combined to give: latex17 where latex18 . | 1 |
The radius of the bubble in time is the *real part* of latex4 . | 0 |
A planet moves on an elliptical orbit with the Sun at a focus. | 0 |
The specific humidity of the air. | 0 |
Find expressions for latex4 and latex6 (for light damping). | 1 |
The rotor inlet and exit relative flow angles are symmetrical, i.e latex1 . | 0 |
Distance latex0 travelled by woman relative to lake: | 0 |
The stress tensor is illustrated to aid understanding, however this is not necessary for the problem. | 0 |
Determine the strain components parallel and normal to the shaft axis. | 1 |
The presence of wind is neglected. | 0 |
The response of a train speed in the Jubilee line is described by latex0 . | 0 |
Newton had already formulated that the propagation of sound in air followed from the oscillatory motion of the fluid particles (which he viewed as ``the law of the oscillating pendulum''). | 0 |
Sketch a latex0 diagram of the processes, assuming non-isentropic compressor and turbine and some frictional pressure loss in the heat exchanger. | 1 |
What values of latex9 are given by i) latex10 ? | 1 |
A thin cylindrical pressure vessel has a bore of latex0 and a wall thickness of latex1 . | 0 |
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