A 6-cylinder, two-stroke, diesel engine produces 1200 hp at 360 rpm. The engine has an expansion ratio of 5.2, a percent clearance of 6.0%, and a mechanical efficiency of 82% when operating at 32∘C and 99.3 kPa standard atmospheric conditions. It is then used as a generating unit by a plant at an elevation of 2846 ft where it gave a brake heat rate of 18,530 kJ/kW-hr at \( k = 1.37 \) using a fuel having a heating value of 42,566 kJ/kg. Determine at this elevation the pressure in kPa. Use four (4) decimal places in your solution and answer.

a. Define the following quantities clearly; provide equations and units for all quantities:
- (i) Weight
- (ii) Density
- (iii) Pressure
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b. With the aid of a diagram, explain the operation of the Gear Pump. State its strengths and a common application.
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c. A hydraulic actuator has a piston area of 0.03 m² in contact with hydraulic fluid and is required to lift a 10000 kg mass. What pressure must be supplied to the hydraulic fluid to do this? Calculate the volume of fluid that a pump would need to provide to move the actuator by 10 cm.
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Weight: The force of gravity acting on an object is referred to as weight. You may figure it out by using the equation: Weight = Mass × Gravity, Unit: Newtons (N).

The mass of a substance per unit volume is known as its density. You may figure it out by using the equation:

Density = Mass / Volume

Unit: Kilograms per cubic meter (kg/m³)

The force applied per unit area is referred to as pressure. You may figure it out by using the equation:

Pressure = Force / Area

Unit: Pascals (Pa)

How a Gear Pump Works: A Gear Pump is a form of Positive Displacement Pump that pumps fluids using meshing gears. The following describes how a gear pump works:

The pump has two gears: an input gear that is powered by an engine or motor and an output gear.
A vacuum is created at the intake when the input gear spins, drawing fluid into the pump.
As the gears revolve, the fluid is carried around the pump's housing because it becomes wedged between the gear teeth and the housing.
As the gears mesh and the amount of the trapped fluid decreases, the fluid is subsequently driven out through the outlet.

Hydraulic Actuator: To use a hydraulic actuator to raise a 10,000 kg mass, we must determine the necessary pressure.

Pressure = Force / Area

Force = Mass × Gravity

So,

Force = 10,000 kg × 9.8 m/s²

Pressure = (10,000 kg × 9.8 m/s²) / 0.03 m²

Now,

Volume = Area × Distance

Area = 0.03 m²

Distance = 10 cm = 0.1 m

Volume = 0.03 m² × 0.1 m

Thus, these are the definition asked.

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