I.C. Engine Question. Solve for: Mean Effective Pressure & Volumetric Efficiency

[Jr.]

Hello all. I am new to the forums. I am having trouble solving a couple of questions. Maybe some of you can help me out. Thanks in advance!

Homework Statement

Number of cylinders 4
Stroke cycle 4
running at 4400 rpm
Volume compression ratio 7.6:1
Cylinder diameter 78 mm
Stroke 105 mm
Brake Power 38 KW
Indicated Power 47.5 KW
Air consumption 21 kg/kg fuel
Fuel consumption 13.6 kg/l
Each kg of fuel releases 41800 kg of energy
Given R = 0.287 kJ/kgK

Find:
a. Mechanical efficiency
b. The mean effective pressure
c. The volumetric efficiency (refer to 101.3 kpa and 0 C)
d. Brake thermal efficiency

The Attempt at a Solution

I think I solved for both parts a and d. I'll show them below.
I am however having a very hard time with parts b and c. Any help would be great.

a. Mechanical efficiency = (Brake Power / Indicated Power) x 100
= (38000 w / 47500 w) x 100
= 80 %

d. Brake thermal efficiency
Brake Thermal Efficiency = 3600 x Brake Power / Fuel consumption x calorific value
= 3600 x 38 KW / 13.6 kg/l x 41800 kg of energy
= 136800 / 568480
= 0.24 or 24%

 

[KataKoniK]

Hello and welcome to the forums! It looks like you're making good progress on your calculations. Here are some tips to help you with parts b and c:

b. The mean effective pressure (MEP) is a measure of the average pressure that acts on the piston during the power stroke. It is calculated by dividing the indicated power by the displacement volume (volume of the cylinder swept by the piston during one stroke) and the number of power strokes per minute (N/2). In this case, the displacement volume can be calculated by using the cylinder diameter and stroke length. So your equation would look like this:

MEP = (Indicated Power / (Displacement Volume x N/2))

c. Volumetric efficiency is a measure of how well the engine is able to fill the cylinder with air/fuel mixture. It is calculated by dividing the actual mass of air/fuel mixture entering the cylinder by the theoretical mass of air/fuel mixture that would fill the cylinder at atmospheric pressure and temperature. In this case, you will need to use the air consumption and fuel consumption values to calculate the actual mass of air/fuel mixture entering the cylinder. The theoretical mass can be calculated using the ideal gas law (PV = mRT) and the given values for pressure (101.3 kPa) and temperature (0°C). Your equation would look like this:

Volumetric efficiency = (Actual mass of air/fuel mixture / Theoretical mass of air/fuel mixture) x 100

I hope this helps! Let me know if you have any other questions. Good luck with your calculations!