State how Mindlin Theory differs from Thin Plate Theory and suggest an application.

1.        

(a) Using a normal distribution, define what is meant by both “ machine” and “process” capability and explain the difference by providing three measures that are used in each case.                                                                     [8 marks]

(b) The following data was obtained from subgroups of parts manufactured to 10.5 mm +/- 0.5 mm

Size Range (mm)                     Quantity

10.0-10.2                                 1

10.2 -10.4                                4

10.4 -10.6                                9

10.6-10.8                                 6

Determine :

The mean and standard deviation [use N = 20 ]                          [6 marks]

The values of the capability indices Cm and Cp                          [4 marks]

If the operation can be judged as “capable” if considered to be a machine or alternatively a process? [2 marks]

Derive the flexural rigidity of a sandwich beam whose breadth is b, which has a core of thickness c and skins of thickness t each. The distance between the centroids of the skins is d, the skin and core moduli are Es and Ec respectively.

Explain two reasons why plate structures affects significantly the lightweight (i.e. ship hull, machinery, outfit and permanent equipment, etc) of a ship.

0.025 of moist air at 18°C dry-bulb and 10°c wet-bulb temperatures mixes with 0.005 kg/s of air at 38°C and 29°c wet-bulb. What is the mixture dry-bulb temperature, humidity ratio, relative humidity, and dew point? What are these parameters if the second stream flow rate is increased to 0.01 kg/s?

For the elastic body defined in Question 1 (below), define the boundary conditions in terms of displacement, assuming the boundary surface at the point in question has direction cosines with respect to x and y and z equal to l=0.8 and m=0.6 and n=0 . Consider the case when the change in volume is negligible.

Are all the compatibility equations satisfied for the Plane Stress conditions? If not, which equations are not satisfied? Explain the case for the Plane Strain conditions?

Question 1:

Write down the equilibrium equations for a three-dimensional isotropic material in terms of displacements. Assume that the material modulus of elasticity, Poisson ratio and density are, and that the body forces are due to the material weigh and the constant gravitational accelerations applied in z-direction.

Based on experimental observations, the acceleration of a particle is defined by the relation a = –(0.1 + sin x/b), where a and x are expressed in m/s² and meters, respectively. Know that b = 0.96 m and that v = 1 m/s when x = 0.

1)The velocity of the particle

2)The position where velocity is maximum

3)Determine the maximum velocity. (Round the final answer to three decimal places.)
The maximum velocity

Write down the equilibrium equations for a three-dimensional isotropic material in terms of displacements. Assume that the material modulus of elasticity, Poisson ratio and density are, and that the body forces are due to material weigh and the constant gravitational accelerations applied in the z-direction.

A gas turbine used for power generation is producing 57MW of power. The turbine’s exhaust temperature is 541°C at a mass flow rate of 132.8 kg/s and is currently emitted to the atmosphere.

Your task is to design a heat exchanger that recovers the waste heat from the exhaust. The recovered heat is to be used to heat water from 40°C to 60°C for use in a closed-loop hydronic heating system for an office building. The heat exchanger is to be placed between the gas turbine’s exhaust and the attached power generator. To not interfere with the power generator, the pressure drop across the hot flow path should not exceed 600Pa. The maximum gas mass flow rate possible through the heat exchanger has been restricted to 4% of the exhaust gas flow rate of the turbine.

QUESTIONS

1.DO LMTD CALCULATION

2. TEMPERATURE CORRECTION FACTOR CALCULATION

A chicken house (20' x 10'x 8') with walls and roof with R-value = 5 hr ^oF ft²/BTU.

There are 2 wooden doors ( 80” x 36”) with an R-value of 2.5 hr ºF sq.ft/BTU.

The inside temperature is held at 35^oC and the exterior temperature is 20^oF.

There are 19 chickens in the house with a body temperature of 42^oC that can be assumed to radiate as a sphere with a 14" diameter and a emissivity of 0.85.

PART A. Calculate the Heat generation by the chickens in BTU/hr.

Select one:

a. 99.05 BTU/hr

b. 1223 BTU/hr

c. 1040 BTU/hr

d. 1.209e4 BTU/hr

e. 3.440e4 BTU/hr

f. 3276 BTU/hr

4. Explain with schematics the two-photon polymerization technique. What is its advantage over stereo lithography?

A thin plate is suspended in air at 1 atm. with T_infinite= 15°C. Air flows on both sides of the plate where the bottom side absorbs a uniform radiative heat flux of 1542 W/m2. The plate is oriented parallel to the flow and the length along the flow direction is 60 cm. Consider the plate is negligibly thin and the width of the plate (perpendicular to the flow) is large, so that the problem can be considered as a 2D problem.
1. If the temperature of the plate is not to exceed 80°C at any position, what air velocity would be required? Evaluate the air properties at 310 K. (3 pts)
2. Using the velocity calculated in part 1, find an expression for the heat transfer coefficient (h) and surface temperature (Ts) as a function of distance from the leading edge (x). Graph h and Ts for x = 1 ~ 60 cm.
3. If the length of the plate increases to 1.2 m and other conditions (including the air properties) remain the same as in parts 1 and 2, what is the surface temperature at the end of the plate? Graph h and Ts for x = 0.6 ~ 1.2 m

This is the Matlab practice so needs Matlab code
2. Numerical Integration
Consider an industrial tank in the shape of an inverted cone. The radius of the tank at the top rim is 3 m, and the total height of the tank is 4 m.
The volume of the tank in m3 is given by: V = (1/3) R2 H.
The volume of liquid in the tank when filled to a height h measured from the bottom vertex is:
V = (1/3)pi* (R/H)2 h3
The Lab will consist of a single script, divided in two parts. In each part, the filling schedule will be different. A filling schedule is a function that provides flow rate, in m3 / h, as a function of time.
In Part I, your script will calculate the level of the liquid, h, after a two-hour filling schedule is completed. The filling schedule for Part I, Schedule I, is as follows:
During the first 30 minutes, the flow rate will increase linearly from zero to 10 m3 / h
During the following 60 minutes, the flow rate will stay constant at 10 m3 / h
During the last 30 minutes, the flow rate will decrease linearly from 10 m3 / h down to zero
In Part II, your script will calculate the time it takes to completely fill the tank with a different filling schedule, Schedule II, given by the equation:
Flow Rate (m3 / h) = 10 (1 - e-2t ) m3 / h
where t is time in hours, and the exponent, 2t, is dimensionless
Part I:
The volume of liquid calculated in Part I, from which the height of the liquid in the tank will be calculated, should be obtained by using the built-in function to integrate polynomials, polyint( )
Part I generates a single output to the console: "The height of the liquid after Schedule I is ____ meters."
Part II:
In Part II, your script first defines Schedule II as an anonymous function
In Part II your script calculates the volume at a given time by integrating Schedule II using the built-in function quad( )
For Option A, it is acceptable to use a loop to find the time at which the tank gets completely full. If you will use an iterative approach, check the tank volume in 0.01 hour steps
Part II generates a single output to the console: "The time required to fill up the tank with Schedule II is ____ hours."

A soft-drink bottler purchases nonreturnable glass bottles from a supplier. The lower specification on bursting strength in the bottles is 225 psi. The bottler wishes to use variables sampling to sentence the lots and has decided to use an AQL of 1.5%. Find an appropriate set of normal and tightened sampling plans from the standard. Suppose that a lot is submitted, and the sample results yield ???= 250 and s = 10. Determine the disposition of the lot using Procedure The lot size is N = 150,000.

How would you put the alloy HR15 in the heat treatment solution?