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\[So also does their sum.] | 0 |
A latex0 beam latex1 is supported by two rods having negligible mass and lengths of latex2 , as seen in the diagram below. | 0 |
Due to the characteristics of the generator, there will always be a “ripple” on the voltage signal caused by construction of the coils (stator and rotor rubbing against each other cause a high frequency noise which disrupts the main voltage). | 0 |
There is a time constraint in that latex2 . | 0 |
For the vector field latex0 , evaluate: latex1 over the open surface based on the cube of side 2 in the first octant that has as faces the latex2 and latex3 planes and three further faces parallel to the coordinate axes. | 0 |
For small amplitude swings, the equations of motion are latex5 (**Note**: latex6 and latex7 ), where latex8 and latex9 is the angular rate of the earth's rotation. | 0 |
Determine the value of the constant of integration. | 1 |
The Kolmogorov scales are the length, latex0 , time, latex1 , and velocity, latex2 scales for eddies that dissipate energy. | 0 |
latex0 latex1 latex2 | 0 |
How quickly a Fourier series converges depends on the properties of the function. | 1 |
Consider the thrust bearing pictured. | 0 |
See discussion in the worked solutions. | 0 |
In which of the sections is the continuum approach valid? | 1 |
If all sides of the tank have a length of latex2 , and there is latex3 water in the tank, will the tank overflow? | 1 |
What are the units for the X-axis? | 1 |
Rotational speed can be measured using a small generator producing a voltage which is proportional the rotational speed (as seen in MECH50004 - Mechatronics 2 - Lab 4). | 0 |
The cylinder is subjected to an internal pressure of latex2 and is known to carry an undetermined torsional load. | 0 |
Given the above statement, and your answer to part (f), derive an expression for the pressure field everywhere in the flow. | 1 |
Mark the axis with the relevant coordinate values. | 1 |
A latex0 long horizontal beam of rectangular cross section, depth latex1 and thickness latex2 is built in at one end. | 0 |
It is connected by means of a non-slip belt to a uniform disc latex4 , which has mass latex5 and radius latex6 . | 0 |
Write the order of magnitude of each term in the original equation. | 1 |
The container is filled with water with constant density, latex0 . | 0 |
If the cylinder is latex1 diameter, latex2 long and of wall thickness latex3 , calculate the change in volume of the vessel when pressurized to latex4 . | 1 |
In the lecture we have stated that the boundary-layer equations, which are partial differential equations (PDEs), could be transformed into a single ordinary differential equation (ODE) called the Blasius equation. | 0 |
What is the latex22 -intercept of this transform? | 1 |
Show that the wavefronts are planes whose normals are parallel to latex1 . | 1 |
Match the following velocity profiles to their respective pipe flows described in cylindrical polar co-ordinates. | 1 |
Its potential energy is given by latex2 where latex3 and latex4 are constants. | 0 |
Write down why. | 1 |
*Question 3* on *Problem Sheet 3* (repeated below) was about a woman walking along a plank on a frictionless frozen lake. | 0 |
How does this compare to your result in part (a)? | 1 |
If the radial expansions of the cylinder and the hemisphere at their junctions are to be the same when the vessel is pressurized. | 0 |
Hence find the angle between each pair of vectors in turn (give your answer in degrees). | 1 |
Use '/' for division, '\*' for times, and '(' and ')' as needed to group terms. | 1 |
The energy lost in the impact, latex6 . | 0 |
Very often, these populations grow (or decay) exponentially: For a population of bacteria growing in liquid culture, the population size is most easily measured using a spectrophotometer: the population size is proportional to the culture’s absorbance at latex0 (its turbidity). | 0 |
[table] Calculate where the points latex2 , latex3 , and latex4 are at latex5 , latex6 , and latex7 . | 1 |
o latex3 . | 0 |
In the latex0 momentum equation used to study boundary layers (Eqns. | 0 |
You have now been tasked to build a large Scalextric (see picture below) style motorbike powered by a small ICE. | 1 |
A latex0 reaction steam turbine stage of constant mean radius runs at latex1 . | 0 |
Show that your answer to (d) is equivalent to the Bernoulli on the streamline on latex4 . | 1 |
Find an expression for the force latex4 exerted by car latex5 on car latex6 when the acceleration of the train is latex7 . | 1 |
Substitute in the constant of integration, and write the particular solution for latex0 under these boundary conditions: The blood caffeine of a particular coffee drinker is measured at latex12 . | 1 |
Make sure to include the lower trigger voltage, latex10 , the upper trigger voltage latex25 , the source voltages latex7 and latex27 and numerical values for all x and y-axes intersects. | 0 |
The speed sensor used in the lab generates latex0 ripple voltage (peak to peak) at latex1 times the frequency of the speed measured. | 0 |
The binding of calcium ions to the signalling protein calmodulin can be modelled by the equation: latex0 Where: * latex1 is the fraction of calmodulin molecules bound to calcium * latex2 is the concentration of calcium * latex3 is a constant, greater than zero * latex4 is the apparent dissociation constant for the calmodulin/calcium complex; also a number greater than zero Consider a plot of latex1 ( latex6 -axis) against latex2 ( latex8 -axis). | 0 |
Find the suitable thickness for the cylinder wall if the greatest shear stress is not to exceed latex3 If the axial stress may be assumed to be negligible, calculate the change in inside and outside diameters of the cylinder in reaching maximum pressure from zero in (a). | 1 |
A thin layer of laminar flow water moves in the region from radius latex3 to latex0 . | 0 |
Deviations from these expected frequencies are evidence of interesting processes such as natural selection, migration, high mutation rates, non-random mating, or genetic drift. | 0 |
This question uses an example to illustrate the problem. | 0 |
The turbine inlet and outlet temperatures are latex4 and latex5 respectively. | 0 |
A latex24 solution of the p*H* indicator methyl red has an absorbance of latex25 at latex26 . | 0 |
The turbine isentropic efficiency is latex3 . | 0 |
Justify your answer. | 1 |
Use the order of magnitude that you wrote in part (b) as a guide.\ \ Solve the approximate equation. | 1 |
The conditions in the test section should match those on Mars, i.e the temperature and density are taken to be latex3 and latex4 . | 0 |
What is the value of latex6 at this wavelength? | 1 |
The absorbance, latex0 is related to the difference between the light entering ( latex1 ) and leaving ( latex2 ) the cuvette. | 0 |
By what factor is the radiated power reduced? | 1 |
Find an expression for the shear stress on the top wall ( latex2 ) and discuss how the shear stress changes as a function of latex12 . | 1 |
*\[Review of Oscillations and Waves Material]*. | 0 |
In an air-standard Diesel cycle with a compression ratio of latex0 , the heat addition in the process which models combustion is latex1 . | 0 |
A plant runs on a two-stage vapour-compression refrigeration cycle, with the usual "ideal" cycle assumptions, i.e: * Isentropic compressors, [embedded] * Evaporator exit state on the saturated vapour line [embedded] * Both expansion valve inlet states on the saturated liquid line. | 0 |
Is Equation (13.5) a reasonable approximation? | 1 |
ii) latex7 ? | 1 |
Explain in your own words the physical meaning of shear velocity. | 1 |
Apply mass conservation and show that latex2 Assuming that latex3 , show that latex4 . | 1 |
In order to make it more stable, the legs are attached rigidly to the floor. | 0 |
Again, check your answer before proceeding. | 0 |
A carriage weighs 1500 kg including the passengers. | 0 |
Suppose latex12 and latex13 have the same phase velocity, latex14 . | 0 |
A wave on a stretched string is given (in SI units) by latex0 . | 0 |
As steam (vaporised in a solar concentrator) at latex2 . | 0 |
The temperature of saturated water at latex2 bar. | 0 |
What does latex8 equal? | 1 |
Each of the small wheels has a mass of latex9 and a radius latex10 and may be considered to be a uniform circular disc. | 0 |
You are now required to select the components for the drivetrain. | 0 |
Draw the unit vectors latex4 and latex5 which are in the direction of latex6 and the direction of positive latex7 , the angle latex8 makes to the latex0 -axis, respectively. | 1 |
Remember that a volt is a joule ( latex2 ) of energy per coulomb ( latex3 ) of electric charge. | 0 |
The diameter of a pulley latex5 is also latex4 and its moment of inertia is latex7 . | 0 |
A person standing on the ground does not hear a supersonic aircraft flying at an altitude of latex0 until it is latex1 past them. | 0 |
The curve latex7 from latex8 to latex9 One branch of the 4-cusped hypocycloid expressed in parametric form latex10 from latex5 to latex12 . | 0 |
Starting from Eqs. | 0 |
(see lectures - Chapter 3). | 0 |
The deformation tensor is symmetric. | 0 |
If latex15 at latex16 , show that the solutions are of the form: latex17 Discuss if this makes sense in terms of the limit latex18 . | 1 |
The engine is started by using a permanent magnet DC motor with latex6 armature resistance. | 0 |
Give your answer to at least two decimal places. | 1 |
The ellipse latex0 has foci at latex1 and latex2 , where latex3 is the eccentricity. | 0 |
The fluid has a constant density latex0 and dynamic viscosity latex1 . | 0 |
Transform the velocity components into polar coordinates latex2 and latex3 using the relationships latex4 and latex5 . | 1 |
This relationship is called (surprisingly enough) the species/area relationship and it is modelled by the following equation: latex0 * latex1 Number of species * latex2 Area of the island * latex3 Data specific constant * latex4 Data specific constant Using logs, convert this equation into a linear form showing clearly what the gradient and intercept represent, and what you would need to plot to calculate them. | 1 |
A rigid vessel of volume latex0 contains latex1 of carbon monoxide and latex2 of air at latex3 . | 0 |
The flow in the gap is steady. | 0 |
Estimate the applied (nominal) tensile stress, latex3 , for the plate to fracture, assuming latex4 . | 1 |
Calculate the latex15 in a refrigeration application. | 1 |
If the motor voltage must not fall by more than latex4 from this value: Calculate the maximum possible value of the base resistor latex5 and the corresponding base current latex6 . | 1 |
Over 80% of the journey is spent in existing tunnels of cross-section area latex0 . | 0 |
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