Mechanical Engineering Assignment Help
Mechanical Engineering is the branch of engineering that involves the production and usage of heat and mechanical power for the design, production, and operation of machines and tools. It is one of the oldest and broadest engineering disciplines.
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 Mechanics
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Mechanical Engineering Sample Assignment
1. A 4x4 ft glass plate heated uniformly to 180^{o}F is cooled in a horizontal position by air flow parallel to the plate at 64^{o}F and a free stream velocity of 3 fps. Calculate the rate of cooling of the plate in Btu/hr
ANS:
Assuming it is forced convection
Glass plate 






Calculating the average film temperature:
Air properties at is:
Temperature (^{o}F) 
Density (lbm/ft^{3}) 
Specific Heat (Btu/lbm.R) 
Thermal Conductivity (Btu/h.ft.R) 
Thermal Diffusivity (ft^{2}/s) 
Dynamic Viscosity (lbm/ft.s) 
Kinematic Viscosity (ft^{2}/s) 
Prandtl Number 
120 
0.068430 
0.2405 
0.015760 
2.660E04 
1.316E05 
1.923E04 
0.7230 
122 
0.068198 
0.2405 
0.015806 
2.677E04 
1.319E05 
1.935E04 
0.7227 
130 
0.067270 
0.2405 
0.015990 
2.746E04 
1.332E05 
1.981E04 
0.7216 
The values above were gotten by interpolation.
For instance, to obtain the density at 122,
Same process was used to obtain other values.
This is a laminar flow because it is less than
Therefore the rate of cooling on one side is 1088.36 Btu/hr
2. Air at atmospheric pressure and 22^{o}C enters a 3 cm diameter pipe at an average velocity of 5 m/s.
a) If the pipe wall temperature is 80^{o}C, how long must the pipe be to increase the bulk temperature of the air to 32^{o}C
ANS:
Calculating the average film temperature:
Air properties at is:
Temp.(^{o}C) 
Density (kg/m^{3}) 
Specific Heat (J/kg.K) 
Thermal Conductivity (W/m.K) 
Thermal Diffusivity (m^{2}/s) 
Dynamic Viscosity (kg/m.s) 
Kinematic Viscosity (m^{2}/s) 
Prandtl Number 
30 
1.164000 
1007 
0.025880 
2.208E05 
1.872E05 
1.608E05 
0.7282 
32 
1.156400 
1007 
0.026028 
2.236E05 
1.881E05 
1.627E05 
0.727640 
35 
1.145000 
1007 
0.026250 
2.277E05 
1.895E05 
1.655E05 
0.7268 
The values above were gotten by interpolation.
For instance, to obtain the density at 122,
Same process was used to obtain other values.
This is a turbulent flow because Re is greater than 2300
b) Repeat this problem for an average velocity of 0.5 m/s.
ANS:
This is a laminar flow because Re is less than 2300
3. Water having a kinetic viscosity of flows through a smooth, 2.0 inch inside diameter tube at a volumetric flow rate of . For this condition, the wall shear stress may be taken as . Determine:
a. Whether the flow is laminar or turbulent
ANS:
The mean velocity can be expressed as:
This is a turbulent flow because Re is greater than
b. If turbulent, the thickness of the laminar sublayer and the thickness of the combined laminar sublayer and buffer layer assuming the turbulent boundary layer core to begin at
ANS:
The thickness of the laminar sublayer can be expressed as:
The density of water is 62.428 lb/ft^{3}
c. The maximum and average velocities and their ratio.
ANS:
The shear velocity can be expressed as:
The velocity will be maintained at:
Therefore, at ,
The Average velocity can be calculated as:
The ratio can be defined as:
d. If given the shear stress is a valid engineering value.
ANS:
Yes, shear stress is a valid engineering value.
4. On a hot summer day you bought a 12can box of CocaCola. By the time you brought them home they are 30^{o}C. You put two cans in your freezer to cool the can to 5^{o}C. The freezer is at 10^{o}C. One of the can is put vertically and the other horizontally. Determine which can will reach the desired temperature of 5^{o}C faster?
ANS:
L_{1} 
L_{2} 
A: Vertically positioned can 
B: Horizontally positioned can 
g 
Figure 1. Analysis of freezer cooling
Assuming that the position H_{1} is 3 times Position H_{2}
Thus,
From the first law of thermodynamics
Therefore,
Where m is the mass of the drink in the bottle and c is the specific heat capacity of the drink in the bottle, h is convective heat transfer coefficient and A is the surface area of the bottle across which the convective heat transfer from the drink to the air takes place.
For vertical cylinders
For horizontal cylinders
From the analysis above it is clear that
Recall that the rate of heating is directly proportional to the heat transfer coefficient. But the time of heating is inversely proportional to the heat transfer coefficient. In addition, the heat transfer coefficient is inversely proportional to the characteristic length.
Assuming natural convection in the freezer.
Therefore,
where C is a constant of proportionality
Therefore,
Therefore,
This mean that the will always be greater than .
Or
This means the time required to cool in the vertical position (position A inFigure 1) for the drink in thecanis 31.60% times longer than that required when the bottleis kept in horizontal position (position B inFigure 1) inside the freeezer
5.
a) Determine the Nusselt Number.
ANS:
Insulation 
() 
() 
(+) 
(+) 
Plastic Tube 
Flow Passage 
Heater Electric lead 
Copper block 
Figure 1. Schematic diagram of the equipment.
Given:
Water properties at is:
Temp.(^{o}C) 
Density (kg/m^{3}) 
Specific Heat (J/kg.K) 
Thermal Conductivity (W/m.K) 
Thermal Diffusivity (m^{2}/s) 
Dynamic Viscosity (kg/m.s) 
Kinematic Viscosity (m^{2}/s) 
Prandtl Number 
40 
992.2 
4179 
0.6350 
1.521E08 
6.53E04 
6.58E07 
0.7228 
Approximate values of copper properties at is:
Temp.(^{o}C) 
Density (kg/m^{3}) 
Specific Heat (J/kg.K) 
Thermal Conductivity (W/m.K) 
Thermal Diffusivity (m^{2}/s) 
Dynamic Viscosity (kg/m.s) 
Kinematic Viscosity (m^{2}/s) 
Prandtl Number 
30 
8933 
385 
401 
117 



This is a laminar flow because Re is less than 1000
At constant surface temperature
b) Determine the excess inside wall temperature to raise average blood bulk temperature to 5^{o}C
1. A 4x4 ft glass plate heated uniformly to 180^{o}F is cooled in a horizontal position by air flow parallel to the plate at 64^{o}F and a free stream velocity of 3 fps. Calculate the rate of cooling of the plate in Btu/hr
ANS:
Assuming it is forced convection
Glass plate 






Calculating the average film temperature:
Air properties at is:
Temperature (^{o}F) 
Density (lbm/ft^{3}) 
Specific Heat (Btu/lbm.R) 
Thermal Conductivity (Btu/h.ft.R) 
Thermal Diffusivity (ft^{2}/s) 
Dynamic Viscosity (lbm/ft.s) 
Kinematic Viscosity (ft^{2}/s) 
Prandtl Number 
120 
0.068430 
0.2405 
0.015760 
2.660E04 
1.316E05 
1.923E04 
0.7230 
122 
0.068198 
0.2405 
0.015806 
2.677E04 
1.319E05 
1.935E04 
0.7227 
130 
0.067270 
0.2405 
0.015990 
2.746E04 
1.332E05 
1.981E04 
0.7216 
The values above were gotten by interpolation.
For instance, to obtain the density at 122,
Same process was used to obtain other values.
This is a laminar flow because it is less than
Therefore the rate of cooling on one side is 1088.36 Btu/hr
2. Air at atmospheric pressure and 22^{o}C enters a 3 cm diameter pipe at an average velocity of 5 m/s.
a) If the pipe wall temperature is 80^{o}C, how long must the pipe be to increase the bulk temperature of the air to 32^{o}C
ANS:
Calculating the average film temperature:
Air properties at is:
Temp.(^{o}C) 
Density (kg/m^{3}) 
Specific Heat (J/kg.K) 
Thermal Conductivity (W/m.K) 
Thermal Diffusivity (m^{2}/s) 
Dynamic Viscosity (kg/m.s) 
Kinematic Viscosity (m^{2}/s) 
Prandtl Number 
30 
1.164000 
1007 
0.025880 
2.208E05 
1.872E05 
1.608E05 
0.7282 
32 
1.156400 
1007 
0.026028 
2.236E05 
1.881E05 
1.627E05 
0.727640 
35 
1.145000 
1007 
0.026250 
2.277E05 
1.895E05 
1.655E05 
0.7268 
The values above were gotten by interpolation.
For instance, to obtain the density at 122,
Same process was used to obtain other values.
This is a turbulent flow because Re is greater than 2300
b) Repeat this problem for an average velocity of 0.5 m/s.
ANS:
This is a laminar flow because Re is less than 2300
3. Water having a kinetic viscosity of flows through a smooth, 2.0 inch inside diameter tube at a volumetric flow rate of . For this condition, the wall shear stress may be taken as . Determine:
a. Whether the flow is laminar or turbulent
ANS:
The mean velocity can be expressed as:
This is a turbulent flow because Re is greater than
b. If turbulent, the thickness of the laminar sublayer and the thickness of the combined laminar sublayer and buffer layer assuming the turbulent boundary layer core to begin at
ANS:
The thickness of the laminar sublayer can be expressed as:
The density of water is 62.428 lb/ft^{3}
c. The maximum and average velocities and their ratio.
ANS:
The shear velocity can be expressed as:
The velocity will be maintained at:
Therefore, at ,
The Average velocity can be calculated as:
The ratio can be defined as:
d. If given the shear stress is a valid engineering value.
ANS:
Yes, shear stress is a valid engineering value.
4. On a hot summer day you bought a 12can box of CocaCola. By the time you brought them home they are 30^{o}C. You put two cans in your freezer to cool the can to 5^{o}C. The freezer is at 10^{o}C. One of the can is put vertically and the other horizontally. Determine which can will reach the desired temperature of 5^{o}C faster?
ANS:
L_{1} 
L_{2} 
A: Vertically positioned can 
B: Horizontally positioned can 
g 
Figure 1. Analysis of freezer cooling
Assuming that the position H_{1} is 3 times Position H_{2}
Thus,
From the first law of thermodynamics
Therefore,
Where m is the mass of the drink in the bottle and c is the specific heat capacity of the drink in the bottle, h is convective heat transfer coefficient and A is the surface area of the bottle across which the convective heat transfer from the drink to the air takes place.
For vertical cylinders
For horizontal cylinders
From the analysis above it is clear that
Recall that the rate of heating is directly proportional to the heat transfer coefficient. But the time of heating is inversely proportional to the heat transfer coefficient. In addition, the heat transfer coefficient is inversely proportional to the characteristic length.
Assuming natural convection in the freezer.
Therefore,