Question

A one-liter cubic capacity, four-stroke, four-cylinder SI engine has a brake thermal efficiency of 30%, and the indicated power is 40 kW at full load. At half load, it has a mechanical efficiency of 65%. Assuming constant mechanical losses, evaluate the following:

(i) Brake power
(ii) Frictional power
(iii) Mechanical efficiency at full load
(iv) Indicated thermal efficiency
If the volume decreases by eight-fold during the compression stroke, calculate the clearance volume.
A) (i) 40 kW, (ii) 14 kW, (iii) 75%, (iv) 30%, Clearance volume = 0.125 liters
B) (i) 40 kW, (ii) 26 kW, (iii) 45%, (iv) 65%, Clearance volume = 0.125 liters
C) (i) 26 kW, (ii) 40 kW, (iii) 75%, (iv) 30%, Clearance volume = 0.125 liters
D) (i) 26 kW, (ii) 40 kW, (iii) 45%, (iv) 65%, Clearance volume = 0.125 liters

Answer 1

The brake power is 26 kW, the frictional power is -14 kW, the mechanical efficiency at full load is 65%, the indicated thermal efficiency is 65%, and the clearance volume is 0.125 liters.

Step-by-step explanation:

(i) To calculate the brake power, we can use the formula:

Brake Power = Indicated Power * Mechanical Efficiency

Given that the indicated power is 40 kW and the mechanical efficiency at full load is 65%, we can calculate the brake power:

Brake Power = 40 kW * 0.65 = 26 kW

(ii) To calculate the frictional power, we can use the formula:

Frictional Power = Brake Power - Indicated Power

Using the brake power calculated in the previous step, we can calculate the frictional power:

Frictional Power = 26 kW - 40 kW = -14 kW

(iii) The mechanical efficiency at full load is given as 65%.

(iv) The indicated thermal efficiency can be calculated using the formula:

Indicated Thermal Efficiency = Brake Power / Indicated Power

Using the brake power and indicated power, we can calculate the indicated thermal efficiency:

Indicated Thermal Efficiency = 26 kW / 40 kW = 0.65 (or 65%)

Given that the volume decreases by eight-fold during the compression stroke, we can calculate the clearance volume:

Clearance Volume = 1 liter / 8 = 0.125 liters