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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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Mechanical Engineering Sample Assignment

 1.                  A 4x4 ft glass plate heated uniformly to 180oF is cooled in a horizontal position by air flow parallel to the plate at 64oF 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 (oF)

Density (lbm/ft3)

Specific Heat (Btu/lbm.R)

Thermal Conductivity (Btu/h.ft.R)

Thermal Diffusivity (ft2/s)

Dynamic Viscosity (lbm/ft.s)

Kinematic Viscosity (ft2/s)

Prandtl Number

120

0.068430

0.2405

0.015760

2.660E-04

1.316E-05

1.923E-04

0.7230

122

0.068198

0.2405

0.015806

2.677E-04

1.319E-05

1.935E-04

0.7227

130

0.067270

0.2405

0.015990

2.746E-04

1.332E-05

1.981E-04

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 22oC enters a 3 cm diameter pipe at an average velocity of 5 m/s.

 

a)      If the pipe wall temperature is 80oC, how long must the pipe be to increase the bulk temperature of the air to 32oC

ANS:

Calculating the average film temperature:

 

Air properties at  is:

Temp.(oC)

Density (kg/m3)

Specific Heat (J/kg.K)

Thermal Conductivity (W/m.K)

Thermal Diffusivity (m2/s)

Dynamic Viscosity (kg/m.s)

Kinematic Viscosity (m2/s)

Prandtl Number

30

1.164000

1007

0.025880

2.208E-05

1.872E-05

1.608E-05

0.7282

32

1.156400

1007

0.026028

2.236E-05

1.881E-05

1.627E-05

0.727640

35

1.145000

1007

0.026250

2.277E-05

1.895E-05

1.655E-05

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/ft3

 

 

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 12-can box of Coca-Cola. By the time you brought them home they are 30oC. You put two cans in your freezer to cool the can to 5oC. The freezer is at -10oC. One of the can is put vertically and the other horizontally. Determine which can will reach the desired temperature of 5oC faster?

ANS:

 

L1

L2

A: Vertically positioned can

B: Horizontally positioned can

g

Figure 1. Analysis of freezer cooling

Assuming that the position H1 is 3 times Position H2

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.(oC)

Density (kg/m3)

Specific Heat (J/kg.K)

Thermal Conductivity (W/m.K)

Thermal Diffusivity (m2/s)

Dynamic Viscosity (kg/m.s)

Kinematic Viscosity (m2/s)

Prandtl Number

40

992.2

4179

0.6350

1.521E-08

6.53E-04

6.58E-07

0.7228

 

Approximate values of copper properties at  is:

Temp.(oC)

Density (kg/m3)

Specific Heat (J/kg.K)

Thermal Conductivity (W/m.K)

Thermal Diffusivity (m2/s)

Dynamic Viscosity (kg/m.s)

Kinematic Viscosity (m2/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 5oC

 

 

 

 

 

 

 

                                                               

1.                  A 4x4 ft glass plate heated uniformly to 180oF is cooled in a horizontal position by air flow parallel to the plate at 64oF 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 (oF)

Density (lbm/ft3)

Specific Heat (Btu/lbm.R)

Thermal Conductivity (Btu/h.ft.R)

Thermal Diffusivity (ft2/s)

Dynamic Viscosity (lbm/ft.s)

Kinematic Viscosity (ft2/s)

Prandtl Number

120

0.068430

0.2405

0.015760

2.660E-04

1.316E-05

1.923E-04

0.7230

122

0.068198

0.2405

0.015806

2.677E-04

1.319E-05

1.935E-04

0.7227

130

0.067270

0.2405

0.015990

2.746E-04

1.332E-05

1.981E-04

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 22oC enters a 3 cm diameter pipe at an average velocity of 5 m/s.

 

a)      If the pipe wall temperature is 80oC, how long must the pipe be to increase the bulk temperature of the air to 32oC

ANS:

Calculating the average film temperature:

 

Air properties at  is:

Temp.(oC)

Density (kg/m3)

Specific Heat (J/kg.K)

Thermal Conductivity (W/m.K)

Thermal Diffusivity (m2/s)

Dynamic Viscosity (kg/m.s)

Kinematic Viscosity (m2/s)

Prandtl Number

30

1.164000

1007

0.025880

2.208E-05

1.872E-05

1.608E-05

0.7282

32

1.156400

1007

0.026028

2.236E-05

1.881E-05

1.627E-05

0.727640

35

1.145000

1007

0.026250

2.277E-05

1.895E-05

1.655E-05

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/ft3

 

 

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 12-can box of Coca-Cola. By the time you brought them home they are 30oC. You put two cans in your freezer to cool the can to 5oC. The freezer is at -10oC. One of the can is put vertically and the other horizontally. Determine which can will reach the desired temperature of 5oC faster?

ANS:

 

L1

L2

A: Vertically positioned can

B: Horizontally positioned can

g

Figure 1. Analysis of freezer cooling

Assuming that the position H1 is 3 times Position H2

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,