Mechanical Engineering Answers

1. Fluid flows in the negative y-direction between two infinite vertical plates as shown in the figure below. The plates are fixed and separated by some distance L. Assume incompressible, Newtonian steady, 1D, unidirectional, fully developed, laminar flow. Friction causes pressure loss in the direction of flow. Gravity acts in the negative y-direction.
a) Show that dP/dy is equal to a constant
b) Solve the Navier-Stokes equation to find the general solution of v(x)
c) Use boundary conditions to find the exact solutions of v(x) for the case where each of the plates are fixed.
d) Find the exact solution v(x) again, this time for the case where the left plate is moving at speed of U and the right plate is moving at speed of -U.
e) Show an accurate plot of the velocity profile across the plates for both cases c and d.

A conical Clutch transmits rotation from one rotating shaft to another though
frictional forces on the conical face.
Question: The following data is for a conical clutch
Inside Diameter (25.0 +/- 0.1) mm
Outside Diameter (100 +/- 1) mm
Coefficient of Friction 0.33 – no significant numerical uncertainty
Axial Force (1000 +/- 5) N
Included angle 100 degree – no significant numerical uncertainty
Rotational speed (1500 +/- 10) rev/minute
Calculate the Torque and Power that can be transmitted without slipping using
both theories
: Uniform Pressure Theory Uniform Wear Theory
Determine the numerical uncertainties of both Torque and Power using both theories.
Determine whether the Torque or Power values for each theory overlap

A smooth hard rubber tire (modulus of elasticity and Poisson's ratio are: E=5MPa, ν =0.5) with diameter 500mm and width 250mm is running at 25 m/s on a flat wet concrete surface. For the concrete, E= 10 GPA and ν =0.1. Water on the surface has a viscosity of 1 mPa-s. The load on the tire is 5kN. Assume the pressure-viscosity coefficient for water is 0.005 MPa-1.

Using the Dowson and Higginson's equation, what is the minimum film thickness?

Problem 3 You are building a replica of Stonehenge and need to move the Sarsen stones. The stones each weigh 350 kN. There are always at least 4 logs under the stone. The total width of the sleds supported on each stone is 750mm. The modulus of elasticity for the logs is 14.9 GPa and Poisson's ratio 0.033

If the maximum contact stress allowed on a log is 70 MPa, what is the minimum diameter for the logs?

A hydrostatic bearing is used to rotate a load. The load 500kN, fluid viscosity 500 mPa-s. The bearing has an outside diameter of 500mm and an inside diameter of 400mm.

a) What flow Q is required if the film thickness is 1mm?
b) What Pressure is required?
c) what is the friction torque if it is rotated at 3 rad/s?

A rectangular squeeze film bearing will be used to absorb intermittent loads. The bearing is 500mm wide. The initial gap between the bearing plates is 2mm. The applied load is 50N. Oil viscosity 1000 mPa-s.

a) If the bearing gap should change to 1mm in 0.5s, how long will you make the bearing?
b) Using your calculated length, how long will it take to move if the viscosity is changed to 300 mPa-s?

The displacement of the GX160 engine cylinder is 160 cm^3. Assuming the engine is running at a constant speed of 1200 rpm (revolutions per minute), and that the choke and throttle valve are fully open, what would the intake air flow rate into the engine cylinder be, in l/min (litres per minute) [Hint: The engine speed is the crankshaft rotation speed. Think about the 4-stroke cycle and crankshaft/camshaft sprocket diameter ratio]?

How many times per combustion cycle is each valve opened?

Analyse how different limit gauges used in engineering rely on principals of limits, fits and tolerances stated under the british standards for hole and shaft basis (ISO 4500)? Include the use of slip gauges in relation to this?

A gas turbine operates under steady flow condition between a pressure of 3.2 MPa and 100 kPa from a gas supply at 1227°C and 1.5 kg/s. The velocities of gas at the inlet are 5 m/s and the exit is 25 m/s. If the isentropic efficiency is 85% and the heat loss is 5% of the shaft power. Calculate: 1) exit temperature (°C) 2) shaft power output (kW). * Take CP = 1.005 kJ/kg K and CV = 0.718 kJ/kg K