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latex0 Find where latex1 is discontinuous Find the minima and maxima of latex1 Find limiting values of latex1 as latex4 . | 1 |
Assume the first mode of vibration (whole bubble pulsating). | 0 |
Comment on the ratio latex3 where latex1 is the distance along the wall. | 1 |
What are the values of latex10 corresponding to each of these normal modes? | 1 |
Gaseous fuel must be provided for combustion in gas turbines. | 0 |
Consider the functions latex0 , latex1 with Fourier transforms latex2 and latex3 respectively. | 0 |
Using a torsion balance, Roll, Krotkov and Dicke [Ann. | 1 |
The percentage error introduced when assuming perfect gas behaviour of latex6 ? | 1 |
Calculate the height latex8 . | 1 |
Calculate the electrostatic potential energy associated with two deuterium nuclei separated by latex0 m (the distance required for fusion). | 1 |
The overall mass of the spool is latex5 kg. | 0 |
This section is morphodynamically stable with no time variation of the bed level. | 0 |
If the surface temperatures of the wall are measured to be latex3 on the left side and latex4 on the right side, do steady-state conditions exist? | 1 |
Two electric resistance strain gauges are used to measure the strains on the surface of a latex0 diameter solid steel propeller shaft rotating at latex1 . | 1 |
What are the forces acting on **all** hydrostatic fluids? | 1 |
At the same time, the house is cooling down such that the rate at which the temperature drops is proportional to the difference between the inside and the outside temperature (Newton's Law of Cooling). | 0 |
At section 1, where latex1 , a pitot static tube arrangement measures a stagnation pressure of latex2 and a static pressure of latex3 . | 0 |
A company releases a sand mining disposal in the water surface of a wide river of water depth latex0 and average river slope of latex1 . | 0 |
Find the pressure on the wall BC if the upstream pressure is atmospheric. | 1 |
Using the SFEE and the second latex2 equation, latex3 , show that the specific work required to pump an incompressible fluid from pressure latex4 to pressure latex5 , in a reversible, adiabatic, flow process with negligible K.E. | 1 |
What deflection angle will produce a shock with wave angle of latex3 at latex4 ? | 1 |
If the pointed edge is facing forward, what will be the pressure at point A? | 1 |
Find a value for the turbulent mixing coefficient when latex4 . | 1 |
Experience with similar designs suggests that the total-to-total isentropic efficiency will be latex4 . | 0 |
For the digital-to-analogue converter in the figure above: Calculate the input resistance for each of the input pins as a function of latex0 . | 1 |
For the case where both ends of the tube are open, find the values of latex5 and latex6 and show that the wavelength of the sound wave is latex7 , where latex8 is an integer. | 1 |
A bench top is supported by four tubular steel legs latex0 long, with cross-section latex1 outer diameter and latex2 wall thickness. | 0 |
The power supplied by a fluid between two points with total head, latex0 and latex1 . | 0 |
The bob feels the gravitational force latex5 and the tension force latex6 acting along the string towards latex1 . | 0 |
latex2 latex3 latex4 latex5 latex6 latex7 latex8 latex9 | 0 |
Using the exponential function of particle decay, and the lifetime observed in Earth's frame, what percentage of muons is predicted to reach the Earth's surface now? | 1 |
In Figure 1, the velocity *u* = | 0 |
A truck travels through shallow water at some speed latex7 . | 0 |
* Can you prove that it is a global minimum, and not a maximum or indeed a local minimum? | 1 |
What is the difference between the values in parts 5b and 5a? | 1 |
The diagram below shows two possible paths from the origin, latex13 , to the point latex14 in the latex5 - latex16 plane. | 0 |
*** *Start by attempting the integral with Green's theorem, then you may wish to evaluate the line integral directly. | 1 |
**(L3)** Consider two vectors in latex0 : latex1 and latex2 . | 0 |
Considering the flow to be statistically stationary, discuss whether the averaging period is sufficient to have converged statistics. | 1 |
Discuss if the sampling frequency is sufficient to capture the Kolmogorov scales. | 1 |
Estimate the drag on the ship Estimate the power required to drive the ship at 5 m/s. | 1 |
A cycloid is defined by latex0 Show that the length of one arch latex1 of the cycloid is latex2 . | 0 |
**\[Boas 6.6.1]** Find the gradient of latex0 at latex1 . | 1 |
Sketch latex5 . | 1 |
The heat capacity ratio latex20 is latex21 . | 0 |
The figure below shows two equal masses attached to either end of a light stiff rod, which is mounted in the middle on a vertical axle. | 0 |
The dredged river-section is sufficiently large to model this problem as 1-dimensional (in latex1 ). | 0 |
Convert your answer to a decimal and type it in the answer box below | 1 |
(Based on P4.34, White) A three-dimensional incompressible flow field has the following form: latex0 Determine if this field is a valid solution to the continuity and Navier--Stokes equations in a gravitational field with acceleration latex1 , and find the associated pressure field latex2 . | 1 |
Nitrogen enters a turbine at a pressure of latex0 bar (absolute) and a temperature of latex1 , and leaves at a pressure of latex2 bar (absolute) and a temperature of latex3 . | 0 |
Do an explicit Lorentz transformation of latex0 and latex1 to an inertial frame moving with speed latex10 along the latex11 axis relative to the rest frame to find latex12 and latex13 . | 1 |
Does this flow satisfy conservation of mass? | 1 |
Let us revisit the problem on the sudden expansion in a previous problem set. | 0 |
Express these as a function of latex2 and latex4 . | 1 |
If latex0 and latex1 are any twice-differentiable functions, use the chain rule, along with new variables latex2 and latex3 , to show that latex4 satisfies the partial differential equation latex5 where the suffices denote partial derivatives. | 1 |
Is the channel stable in terms of initiation of motion for this flow? | 1 |
Discuss options that would reduce or circumvent the problem with air quality under these wind conditions. | 1 |
(In lambda, you can use latex7 or latex8 to represent natural log: both will work and are treated as synonymous). | 0 |
Check that this flow satisfies the appropriate equations governing mass and momentum conservation, and find the general solution for the pressure. | 1 |
This pendulum is given an initial angular displacement of 6 latex0 . | 0 |
latex1 latex2 latex3 | 0 |
A normal shock stands at section 1, where latex2 . | 0 |
Calculate the end thrust. | 1 |
*** This question makes use of **Section 4.4.1** in the notes on how to solve the heat flow equation using Fourier Transforms. | 0 |
Therefore, the final molarities will be: [table] The degree of dissociation is given by the acid dissociation constant, latex6 . | 0 |
For the data shown in the figure below, calculate the value of latex1 . | 1 |
Find latex0 where latex1 | 1 |
Find the net specific work and the thermal efficiency of the cycle. | 1 |
The tunnel is supplied from an air reservoir at latex1 , and the working section is held at atmospheric pressure latex2 . | 0 |
A wide freshwater stream has a smooth granular bed with a bed slope of latex0 , a uniform flow depth of latex1 and a median grain size of latex2 . | 0 |
What mass of citric acid do they need to weigh out to make the necessary volume of citric acid solution? | 1 |
Hence write down expressions for the height latex9 and drop time latex10 of the latex11 bounce, in terms of latex0 and latex5 respectively. | 1 |
Find the *real* eigenvalues and *normalised* eigenvectors of the following transformation matrices in latex0 , and use the information to identify the transformations. | 1 |
What is the pressure at latex2 and hence at latex3 ?. | 1 |
The photo represents one moment in time. | 0 |
Is this flow laminar or turbulent? | 1 |
Find the cycle net specific work and thermal efficiency. | 1 |
What is the Q-factor of this atomic oscillator? | 1 |
The charge of the *line element* latex3 is therefore latex4 . | 0 |
In the boundary layer equations (Eqns. | 0 |
The hollow, circular cross-section, steel shaft of a turbine is to transmit latex0 at a speed of latex1 . | 0 |
The recuperator (a heat exchanger) recovers some of the energy in the exhaust flow for pre-heating the compressor exit air. | 0 |
Remember that a volt is a joule ( latex2 ) of energy per coulomb ( latex3 ) of electric charge. | 0 |
Using three-dimensional Cartesian coordinates write all the components of: latex0 latex1 latex2 latex3 latex4 | 1 |
Apply a Lorentz transformation to the four-velocity formed from the three-velocity latex4 . | 1 |
What is the percentage error in comparison to the answer in part (a)? | 1 |
The common redox factor NADH absorbs strongly in the near ultraviolet at latex18 . | 0 |
(In the answer area, input the direction of maximum shear stress such that latex4 .) | 1 |
Repeat this calculation for every latex8 until latex9 . | 1 |
Find an expression for the **maximum** mass flow rate latex0 through a convergent-divergent nozzle as a function of latex1 , the throat area latex2 , and the reservoir density and speed of sound, latex3 and latex4 respectively. | 1 |
Does the person use latex15 times more energy? | 1 |
Give an expression for the trajectory of the particle before the collision. | 1 |
Five street lamps A, B, C, D, and E are located on a straight line along the latex0 axis at an equal distance apart as shown in the figure below. | 0 |
We derived time dilation and Lorentz contraction using just the postulates in the lectures in Week 2. | 0 |
Calculate the amplitude of the diffraction pattern as a function of latex9 . | 1 |
This graph is not very user-friendly as far as extracting latex3 and latex5 from a graph is concerned. | 0 |
Hence sketch the streamlines to be commented on in the next part. | 1 |
Squeezing toothpaste onto a toothbrush (viscosity of toothpaste is approx latex0 Pa s) Bacteria swimming. | 0 |
Estimate its flight speed under these conditions. | 1 |
In lectures, you saw how to use Newton鈥檚 second law for two particles, latex0 to show that the rate of change of the total momentum, latex1 , is equal to the total external force, latex2 . | 0 |