Final answer:
To calculate the air standard efficiency of a diesel engine with a compression ratio of 17 and a cutoff at 10% of the stroke, the efficiency formula (η) for an ideal diesel cycle is used with a specified heat ratio (γ) of 1.4. The calculated efficiency is approximately 56.2%.
Step-by-step explanation:
The air standard efficiency of a diesel engine can be calculated using the formula for the efficiency (η) of an ideal diesel cycle:
- η = 1 - (1/rγ-1)[(rcγ - 1) / (γ(rc - 1))]
where:
- r is the compression ratio,
- γ is the ratio of specific heats (1.4 for air in this question),
- rc is the cutoff ratio (the ratio of volume before combustion to the volume after cutoff).
In the given question, r = 17 and the cutoff takes place at 10% of the stroke, which means the cutoff ratio rc is 1 + 0.1 = 1.1 since the volume increases by 10% during the cutoff process. Using these values, we can find out the air standard efficiency of the diesel engine.
Calculation:
- First, calculate rγ-1 = 171.4-1.
- Then, calculate (rcγ - 1) = (1.11.4 - 1).
- Now compute the denominator γ(rc - 1) = 1.4(1.1 -1).
- Finally, calculate the efficiency (η).
After performing the calculations:
- η ≈ 1 - (1/170.4)[(1.11.4 - 1) / (1.4(1.1 - 1))]
η ≈ 0.562, or 56.2%
The air standard efficiency for the diesel engine in this case is approximately 56.2%.