Calculate the optimum diameter of the input piston which

Question

Scenario

As part of a design engineering team working on building a new ship, you are expected to carry out simple calculations to determine what will happen to the ship at sea water with different density. A simplified version of this scenario is presented in Task 1.

Learning Outcome 1

1: Determine the hydrostatic pressure and thrust on immersed surfaces

1) A plastic cube that can be used to design a ship (illustrated in figure 1)has a dimension of 10 cm on each sideand mass 0.20 kg, with appropriate calculations explain:

a. What happens if the cube is placed in salt water (ρ = 1050kg/m³)?

b. What happens if the cube is placed in fresh water (ρ = 1000kg/m³)?

Determine the volume of the water displaced and the submerged depth in (m) in questions (a) and (b) above. Explain also the difference in the answers obtained in (a) and (b) above.

2) A cylindrical steel drum is to be used as a buoy in sea water (ρ = 1050 kg/m³). The drum is 700mm in diameter and 1100mm long and has a mass of 250kg. It is required to float two thirds (2/3) submerged, as shown in Figure 2 below.

a. Calculate the hydrostatic pressure on the drum and the weight of water displaced when the buoy floats 2/3 submerged.

b. Calculate the mass which must be placed in the bottom of the drum to ensure that it floats 2/3 submerged.

Learning Outcome 2

1.2: Determine the centre of pressure on immersed surfaces

3) A tank is 500mm by 1100mm in plan and contains water (ρ = 1000 kg/m³) to a depth of 350mm. Calculate the total hydrostatic thrust force and depth to the centre of pressure for:

a. The shorter side, and
b. The longer side.
c. Comment on your findings.

4) A tank of fuel (ρ = 850 kg/m³) has a circular valve, 0.40m in diameter, which opens when the level of fuel in the tank reaches 1.35m above the hinge. The valve is kept closed by a spring, mounted on the lower edge of the valve, as shown in Figure 3 below.

a. Calculate the thrust on the valve and the depth to the centre of pressure, shown as y in the figure.

b. Calculate the minimum force required in the spring to hold the valve closed at the required level.

Learning Outcome 3

1.3: Determine the parameters of devices in which a fluid is used to transmit force

A hydraulic press is required to deliver a force of 90kN onto the work surface as shown in Figure 4 below. The piston in the press has a diameter of 320mm.

a. The maximum force which can be applied at the input piston is 1750N. Calculate the optimum diameter of the input piston which will allow the press to operate. Again, ignore any frictional losses.

Answer 1

For the following engineering numerical problems, provide solution to each by providing the whole computation part. Q1. A cylindrical steel drum is to be employed as a buoy in the sea water (? = 1050 kg/m3). The drum is 700mm in diameter and 1100mm long and consists of a mass of 250kg. This is required to float two thirds submerged, as illustrated. a) Compute the hydrostatic pressure on drum and weight of water displaced if the buoy floats 2/3 submerged. b) Compute the mass that must be put in the bottom of the drum to make sure that it floats 2/3 submerged. Q2. A tank is 500mm x 1100mm in plan and consists of water to a depth of 350mm. Compute the net hydrostatic thrust force and depth to the center of pressure for: a) Shorter side b) Longer side c) Remark on your findings