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Criteria for answers;

1) All answers must be set out in a structured order

2) All formula used must be defined

3) All working out must be explained at each step.

4) Where rearrangement of formula is used, this must be explained.

Mechanical Principles

Task 1

A. With a neat diagram, explain and formulate gear ratio or velocity ratio.

C. In a reverted epicyclic gear train, the arm A carries two gears B and C and a compound gear D – E. The gear B meshes with gear E and the gear C meshes with gear D. The number of teeth on gears B, C and D are 75, 30 and 90 respectively.

Find the speed and direction of gear C, when gear B is fixed and arm A makes 100 rpm clockwise.

Task 2

B. Derive any expression for the tension ratio in a v-belt.

D. The shaft of an engine, rotating at 250 rpm drives the shaft of a grinding machine at 350 rpm and transmit 7.5 kW through the belt. The flat belt has a width of 150 mm and the distance between the shafts is 4.5 m.

Calculate the dimensions of the belt, if the width to thickness ratio is 10 to 1 and the stress in the belt must not be more than 1.5 MPa with friction coefficient of 0.25 between the belt and the pulley.

Task 3

A. What are the factors to relevant in the capacity of power transmission through clutches?

B. Derive expressions for the torque developed in clutches under uniform pressure and uniform wear.

C. Two co-axial shafts A and B are connected by a single plate friction clutch of internal diameter 120 mm and external diameter 200 mm, both sides of the plate being used. Shaft A is rotating at a constant angular speed of 200 rpm and B is initially stationary. The torque acting on shaft B is 83.8 Nm.

If the coefficient of friction is 0.3 and the uniform pressure condition can be assumed, what is the required spring force?

Fluid Mechanics

Task 1

A pump draws water through a 150 mm diameter pipe from a reservoir whose surface level is at datum level and discharges it through a 100 mm diameter pipe to another reservoir whose surface level is 72 m above the datum level. The pump is 6 m below the datum level. The loss of head in the 150 mm suction pipe is 3 times the velocity head in the 150 mm pipe and the loss of head in the 100 mm delivery pipe is 20 times the velocity head in the 100 mm pipe.

When the pump discharge is 0.91 m3/min, calculate:

i. the power output of the pump

ii. the pressure heads at the inlet and outlet of the pump

Task 2

A 1.5 m tall firefighter is combating a fire from the floor of a building 15 m high. He directed his nozzle vertically up from his head level to reach the floor. Assuming that the jet remains conically circular with a diameter 17.1 mm at the floor and neglecting any loss of energy, what will be the diameter the firefighter will reduce the nozzle to if the velocity the jet water at the floor level is 6 m/s?

Task 3

Two reservoirs are connected by a pipeline which is 250 mm in diameter for the 8 m, 150 mm in diameter for the next 7 m and 100 mm diameter for the 5 m. The entrance and exit of each section are sharp and the change of each section is sudden. The water surface in the upper reservoir is 10 m above that in the lower.

i. Indicate the losses of head which occur,

ii. Calculate the rate of flow in m3/s and

iii. Draw the total energy gradient and the hydraulic gradient

Assume the coefficient of friction f in the pipe sections from the upper reservoir to the lower be 0.0025, 0.002 and 0.001 respectively.

Task 4

i. Give mathematical expression of Reynolds number and show how it is a dimensionless parameter.

ii. Determine its value when for water at 70oC with density 977.8 kg/m3; viscosity 4.042 x 10-4 Ns/m2 flowing with velocity 2 m/s in a 100 mm diameter pipe.

iii. Discuss the type of flow in question (ii) above.

Derive an expression, by using dimensional analysis, for the drag force FD on a spherical submerged in fluid, which is dependent on the diameter D of the sphere, the relative velocity V between the sphere and the fluid, the fluid density ? and the fluid viscosity µ.

Task 5

Assume that the wing of an aeroplane is rectangular in plane having a span of 15 m and chord of 1.8 m. In a horizontal flight at 360 km/h, the total aerodynamic force acting on the wing is 35 kN in an assumed perfect air of density 1.2 kg/m3.

If the lift-drag ratio is 10, determine the:

i. coefficient of lift and drag and

ii. power required for the flight at this moment.

Criteria for answers;

1) All answers must be set out in a structured order

2) All formula used must be defined

3) All working out must be explained at each step.

4) Where rearrangement of formula is used, this must be explained.

Mechanical Principles

Task 1

A. With a neat diagram, explain and formulate gear ratio or velocity ratio.

C. In a reverted epicyclic gear train, the arm A carries two gears B and C and a compound gear D – E. The gear B meshes with gear E and the gear C meshes with gear D. The number of teeth on gears B, C and D are 75, 30 and 90 respectively.

Find the speed and direction of gear C, when gear B is fixed and arm A makes 100 rpm clockwise.

Task 2

B. Derive any expression for the tension ratio in a v-belt.

D. The shaft of an engine, rotating at 250 rpm drives the shaft of a grinding machine at 350 rpm and transmit 7.5 kW through the belt. The flat belt has a width of 150 mm and the distance between the shafts is 4.5 m.

Calculate the dimensions of the belt, if the width to thickness ratio is 10 to 1 and the stress in the belt must not be more than 1.5 MPa with friction coefficient of 0.25 between the belt and the pulley.

Task 3

A. What are the factors to relevant in the capacity of power transmission through clutches?

B. Derive expressions for the torque developed in clutches under uniform pressure and uniform wear.

C. Two co-axial shafts A and B are connected by a single plate friction clutch of internal diameter 120 mm and external diameter 200 mm, both sides of the plate being used. Shaft A is rotating at a constant angular speed of 200 rpm and B is initially stationary. The torque acting on shaft B is 83.8 Nm.

If the coefficient of friction is 0.3 and the uniform pressure condition can be assumed, what is the required spring force?

Fluid Mechanics

Task 1

A pump draws water through a 150 mm diameter pipe from a reservoir whose surface level is at datum level and discharges it through a 100 mm diameter pipe to another reservoir whose surface level is 72 m above the datum level. The pump is 6 m below the datum level. The loss of head in the 150 mm suction pipe is 3 times the velocity head in the 150 mm pipe and the loss of head in the 100 mm delivery pipe is 20 times the velocity head in the 100 mm pipe.

When the pump discharge is 0.91 m3/min, calculate:

i. the power output of the pump

ii. the pressure heads at the inlet and outlet of the pump

Task 2

A 1.5 m tall firefighter is combating a fire from the floor of a building 15 m high. He directed his nozzle vertically up from his head level to reach the floor. Assuming that the jet remains conically circular with a diameter 17.1 mm at the floor and neglecting any loss of energy, what will be the diameter the firefighter will reduce the nozzle to if the velocity the jet water at the floor level is 6 m/s?

Task 3

Two reservoirs are connected by a pipeline which is 250 mm in diameter for the 8 m, 150 mm in diameter for the next 7 m and 100 mm diameter for the 5 m. The entrance and exit of each section are sharp and the change of each section is sudden. The water surface in the upper reservoir is 10 m above that in the lower.

i. Indicate the losses of head which occur,

ii. Calculate the rate of flow in m3/s and

iii. Draw the total energy gradient and the hydraulic gradient

Assume the coefficient of friction f in the pipe sections from the upper reservoir to the lower be 0.0025, 0.002 and 0.001 respectively.

Task 4

i. Give mathematical expression of Reynolds number and show how it is a dimensionless parameter.

ii. Determine its value when for water at 70oC with density 977.8 kg/m3; viscosity 4.042 x 10-4 Ns/m2 flowing with velocity 2 m/s in a 100 mm diameter pipe.

iii. Discuss the type of flow in question (ii) above.

Derive an expression, by using dimensional analysis, for the drag force FD on a spherical submerged in fluid, which is dependent on the diameter D of the sphere, the relative velocity V between the sphere and the fluid, the fluid density ? and the fluid viscosity µ.

Task 5

Assume that the wing of an aeroplane is rectangular in plane having a span of 15 m and chord of 1.8 m. In a horizontal flight at 360 km/h, the total aerodynamic force acting on the wing is 35 kN in an assumed perfect air of density 1.2 kg/m3.

If the lift-drag ratio is 10, determine the:

i. coefficient of lift and drag and

ii. power required for the flight at this moment.

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