Engine Power Calculation Explained

Understanding the power output of an Internal Combustion (I.C.) engine involves distinguishing between indicated power and brake power, and how mechanical efficiency relates them. This problem requires us to calculate the brake power of an I.C. engine given its indicated power and mechanical efficiency.

Mechanical Efficiency Concept

Mechanical efficiency is a key parameter that indicates how effectively an engine converts the power generated within its cylinders (indicated power) into usable power delivered at the crankshaft (brake power). It accounts for the power lost due to friction within the engine's moving parts, such as pistons, crankshaft, bearings, and other auxiliary components.

• Indicated Power (IP): This is the power developed inside the engine cylinders, calculated from the pressure-volume diagram. It represents the total power generated by the combustion of fuel.
• Brake Power (BP): This is the actual usable power available at the engine's crankshaft, which can be measured using a dynamometer. It is the power that is delivered to the load.
• Mechanical Efficiency (\(\eta_{mech}\)): It is the ratio of brake power to indicated power.

Formula for Mechanical Efficiency

The relationship between indicated power, brake power, and mechanical efficiency is given by the formula:

\[ \eta_{mech} = \frac{\text{Brake Power (BP)}}{\text{Indicated Power (IP)}} \]

From this formula, we can derive the expression for brake power:

\[ \text{Brake Power (BP)} = \text{Mechanical Efficiency } (\eta_{mech}) \times \text{Indicated Power (IP)} \]

Brake Power Calculation Steps

Let's use the given values to calculate the brake power of the I.C. engine:

• Given Indicated Power (IP): \(150 \text{ kW}\)
• Given Mechanical Efficiency (\(\eta_{mech}\)): \(80\%\)

First, convert the mechanical efficiency from percentage to a decimal:

\[ \eta_{mech} = 80\% = \frac{80}{100} = 0.80 \]

Now, apply the formula for brake power:

\[ \text{BP} = \eta_{mech} \times \text{IP} \]

Substitute the given values into the formula:

\[ \text{BP} = 0.80 \times 150 \text{ kW} \]

Perform the multiplication:

\[ \text{BP} = 120 \text{ kW} \]

Therefore, the brake power delivered by the I.C. engine is \(120 \text{ kW}\).