Solution
Step 1: Understand the Measured Efficiency
The measured efficiency ($\eta_{measured} = 24\%$) was calculated based on the assumption that all the fuel supplied to the setup was consumed by the engine. Let the total power of the fuel supplied be $P_{in}$. $$ P_{out} = \eta_{measured} \times P_{in} = 0.24 P_{in} $$
The measured efficiency ($\eta_{measured} = 24\%$) was calculated based on the assumption that all the fuel supplied to the setup was consumed by the engine. Let the total power of the fuel supplied be $P_{in}$. $$ P_{out} = \eta_{measured} \times P_{in} = 0.24 P_{in} $$
Step 2: Determine Actual Fuel Consumed
It was found that 4% of the fuel leaked and was not actually used by the engine. Therefore, the actual power input to the engine, $P_{actual}$, is the remaining 96% of the total input. $$ P_{actual} = P_{in} – 0.04 P_{in} = 0.96 P_{in} $$
It was found that 4% of the fuel leaked and was not actually used by the engine. Therefore, the actual power input to the engine, $P_{actual}$, is the remaining 96% of the total input. $$ P_{actual} = P_{in} – 0.04 P_{in} = 0.96 P_{in} $$
Step 3: Calculate True Efficiency
The true efficiency, $\eta_{true}$, is the ratio of the useful output power to the actual fuel power consumed (burned) by the engine. $$ \eta_{true} = \frac{P_{out}}{P_{actual}} $$ Substituting the values we derived: $$ \eta_{true} = \frac{0.24 P_{in}}{0.96 P_{in}} $$ $$ \eta_{true} = \frac{0.24}{0.96} = \frac{1}{4} = 0.25 $$
The true efficiency, $\eta_{true}$, is the ratio of the useful output power to the actual fuel power consumed (burned) by the engine. $$ \eta_{true} = \frac{P_{out}}{P_{actual}} $$ Substituting the values we derived: $$ \eta_{true} = \frac{0.24 P_{in}}{0.96 P_{in}} $$ $$ \eta_{true} = \frac{0.24}{0.96} = \frac{1}{4} = 0.25 $$
Conclusion:
The efficiency of the engine after the repair (true efficiency) is 25%.
The efficiency of the engine after the repair (true efficiency) is 25%.