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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.

The engine is used as a generating unit by a plant at an elevation of 2846 ft, where it has a brake heat rate of 18,530 kJ/kW-hr, with \(k = 1.37\) using a fuel having a heating value of 42,566 kJ/kg.

Determine the pressure at this elevation in kPa. Use four decimal places in your solution and answer.

Answer :

The pressure at the given elevation is 104.5 kPa.

First, we need to calculate the indicated power of the engine. We can use the formula:

Indicated Power = (2 πn Vd Pmep) / 60

Where:

n = engine speed in rpm

Vd = displacement volume in m^3

Pmep = mean effective pressure in Pa

We'll start by calculating the displacement volume:

Vd = (6 π (0.235²) 0.4) / 4

Vd = 0.041 m³

Next, we'll calculate the mean effective pressure:

Pmep = (Pmax (1 - c) - Pmin) / (r - 1)

Pmax = (1200 × 1000) / (2 π × 0.235² × 360 / 60)

Pmax = 6.95 MPa

Pmin = Pmax / 5.2

Pmin = 1.34 MPa

c = 0.06

r = 5.2

Pmep = (6.95 10⁶ (1 - 0.06) - 1.34 × 10⁶) / (5.2 - 1)

Pmep = 1.15 MPa

Finally, we can calculate the indicated power:

Indicated Power = (2 π × 360 × 0.041 × 1.15 × 10⁶) / 60

Indicated Power = 2,212 kW

Next, we need to calculate the brake power of the engine at the given elevation. We can use the formula:

Brake Power = Indicated Power / (mechanical efficiency / 100)

Brake Power = 2,212 / (0.82)

Brake Power = 2,695 kW

Now, we can calculate the fuel consumption rate:

Fuel Consumption Rate = Brake Power / (heating value × k)

Fuel Consumption Rate = 2,695 / (42,566 × 1.37)

Fuel Consumption Rate = 0.055 kg/kW-hr

Finally, we can calculate the pressure at the given elevation using the ideal gas law:

P₁V₁/T₁ = P₂V₂/T₂

Assuming that the temperature remains constant at 32°C, we can simplify this to:

P₁V₁ = P₂V₂

P₁ = P₂ V₂ / V₁

We'll need to know the volumes of the intake and exhaust strokes, which we can calculate using the displacement volume and the clearance volume:

Vc = Vd × c Vc = 0.041 × 0.06

Vc = 0.00246 m³

Vi = Vd + Vc

Vi = 0.041 + 0.00246

Vi = 0.04346 m³

Ve = Vc Ve = 0.00246 m³

Now, we can calculate the pressures:

P₂ = 99.3 kPa

V₂ = Vi (1 / 0.2846)

V₁ = Vi (1 / 0.4)

P₁ = P₂ * V₂ / V₁ P₁

= 99.3 (0.04346 / 0.041)

P₁ = 104.5 kPa

So, the pressure at the given elevation is 104.5 kPa.

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