Datasets:
itisarainyday
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ml_classifier_bert_training

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Consider the flow to be Newtonian, incompressible, with uniform dynamic viscosity.
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A tank at latex0 feeds air ( latex1 ) into a nozzle with a throat area of latex2 and an exit area of latex3 .
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Calculate the temperature and pressure at the nose of the aerofoil.
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The obtained solution will be compared against the more accurate Blasius solution.
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Finally, plot the concentration as a function of latex6 .
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What should the kinematic viscosity ( latex13 ) of the model test fluid be compared to the kinematic viscosity of sea water?
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The interface between *fluid 'a'* (top) and *fluid 'b'* (bottom) is half way between the upper and lower plate.
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A particle of mass latex0 moves in the latex1 direction under the action of a conservative force.
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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).
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Consider the polynomial latex0 , where latex1 , latex2 , and latex3 may be complex and latex4 .
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This makes it very convenient to complete the question yourself.
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The river bed comprises of sediment with size: latex3 .
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Does this flow satisfy the boundary conditions you suggested?
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The traps are then reset and allowed to capture animals again for the same period of time.
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Write down the formula for Reynolds number, defining any symbols.
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What is the shear stress of the fluid on the top plate?
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Initially, the first pendulum is stationary at the equilibrium position, while the second is moving and has all the energy.
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**(L7/8)**: For each of the following sets of simultaneous equations, determine if there is: 1.
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Determine the tension latex3 in each rod if latex4 and latex5 .
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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'
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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.
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What are the two eigenvectors of latex14 (write in normalised form)?
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Hence show that latex11 Hence, show that latex12
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Disc latex3 is coupled to a small electric motor mounted on latex6 , and latex0 and latex3 are meshed together at their outside diameter.
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What is the order in which the light from the lamps reach the person driving the car?
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Calculate the area of the transformed shape.
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\ \ 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 .
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Describe physically the implications of the 1D diffusion equation.
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How many molecules of latex2 are reduced by the complete oxidation of a single latex0 molecule to latex1 ?
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What are the physical dimensions ( latex1 ) of the equations as derived in the Lecture?
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What is the momentum of latex4 in the centre-of-mass frame?
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Find an expression for the force latex1 acting on the particle at time latex2 .
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The steel cylinder of a hydraulic press has an internal diameter of latex0 and the water pressure is latex1 .
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(ii) Recalculate the net specific work.
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Find the range of values of latex0 such that the roots of the characteristic equation are: Overdamped.
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In its rest frame, a rod of length latex14 is lying along the latex11 axis with the left hand end at latex16 .
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Verify that the components are perpendicular to each other.
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Show that the wall thickness of the hemisphere should be latex0 times the cylinder wall thickness.
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(ii) from the criterion for the second partial derivatives of latex1 with respect to latex3 and latex4 .
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A fuel is burnt first with the stoichiometric amount of air and then with the stoichiometric amount of pure oxygen.
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A plane figure is bounded by the parabola latex0 , the latex1 axis, and the line latex2 .
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A plane source located at latex0 releases at latex1 a slug of contaminant of diffusivity latex2 .
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What would the strain gauge record in service if subjected to the same torque as before?
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The block is raised in temperature by latex6 and subjected to stresses of latex7 in the latex3 -direction and latex9 in the latex5 -direction.
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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.
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At steady-state the turbine performs work equal to latex5 of steam flowing through the turbine.
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The system is at rest for latex0 .
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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).
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A sealed room is heated.
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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.
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Use latex4 to diagonalise latex1 .
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The system shown above represents a process control plant with an output measurement transducer.
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What is the transfer function of the system?
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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 .
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Assume that latex5 and that the total sediment transport is dominated by bed load transport latex6 .
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*** **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).
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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
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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.
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We will attempt to verify Lorentz contraction using the same method.
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A transition is defined as a mutation that converts a purine to another purine, or a pyrimidine to another pyrimidine.
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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 .
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To appreciate what this means, make a sketch of latex2 as a function of latex5 , indicating the half-power frequencies on this sketch.
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The encoder is attached to a lead screw of **0.8mm** pitch, which controls the linear position of a slider.
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Calculate the shaft power produced.
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**(L4)**: Identify the following surfaces described for latex0 .
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Assuming that the flow discharge and water depth remain constant.
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The pressure is latex7 Pa, where latex8 is the distance parallel to the flow (measured in metres).
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For the function latex0 , Find the stationary points of latex1 and determine their nature Sketch the graph of latex2 .
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This is maximized on resonance, i.e when latex1 .
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The trapdoor is hinged along its top edge (and has a catch on the bottom edge to hold it closed).
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Which of the following graphs belongs in each section above?
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Non-Dimensionalise the one-dimensional Cartesian form of the advection-diffusion equation by introducing appropriate length, velocity, concentration, and time scales.
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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 doubling time, latex8 by the relationship latex9 .
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The height of both the fluid layers is constant and equal to latex6 .
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A normal shock occurs at the exit of the nozzle, and just behind the normal shock the temperature is latex4 .
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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?
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Consider the steady laminar flow of two immiscible fluids between two parallel flat plates which are infinitely-long in both latex0 and latex1 directions.
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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.
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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.
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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.
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Can you help Damien to resolve this apparent paradox?
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What will the peak-to-peak amplitude of the ripple voltage be after filtering?
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Numerical exercises on oscillators, damped and driven.
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The diameter of the pipe upstream is latex0 cm, whilst the diameter of the jet is latex1 cm.
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Plot values of latex7 and compare them to latex8 .
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Show that the last two equations can be combined to give: latex17 where latex18 .
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The radius of the bubble in time is the *real part* of latex4 .
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A planet moves on an elliptical orbit with the Sun at a focus.
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The specific humidity of the air.
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Find expressions for latex4 and latex6 (for light damping).
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The rotor inlet and exit relative flow angles are symmetrical, i.e latex1 .
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Distance latex0 travelled by woman relative to lake:
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The stress tensor is illustrated to aid understanding, however this is not necessary for the problem.
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Determine the strain components parallel and normal to the shaft axis.
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The presence of wind is neglected.
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The response of a train speed in the Jubilee line is described by latex0 .
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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'').
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Sketch a latex0 diagram of the processes, assuming non-isentropic compressor and turbine and some frictional pressure loss in the heat exchanger.
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What values of latex9 are given by i) latex10 ?
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A thin cylindrical pressure vessel has a bore of latex0 and a wall thickness of latex1 .
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