Calculate the stroke length (in feet) of an engine with the following parameters: 6 cylinders, has an indicated mean effective pressure (IMEP) of 700 psi per cylinder, a bore of 5.2 inches, operating at 3320 rpm , and operates at 2100 horsepower. Round to 2 decimal places.

To calculate the stroke length of the engine, we can use the relationship between the power output, IMEP, number of cylinders, rpm, and the stroke length. The formula for power is as follows: \[ \text{Power (hp)} = \frac{IMEP \times \text{Area} \times \text{Stroke} \times \text{RPM}}{33,000} \] Where: - Area = \( \frac{\pi \times \text{bore}^2}{4} \) 1. Convert the bore from inches to feet: \[ \text{Bore} = 5.2 \text{ inches} \times \frac{1 \text{ foot}}{12 \text{ inches}} = \frac{5.2}{12} \text{ feet} \approx 0.4333 \text{ feet} \] 2. Calculate the area: \[ \text{Area} = \frac{\pi \times (0.4333)^2}{4} \approx \frac{3.1416 \times 0.1878}{4} \approx 0.14704 \text{ square feet} \] 3. Rearrange the power formula to solve for stroke: \[ \text{Stroke} = \frac{Power \times 33,000}{IMEP \times Area \times RPM} \] Substitute the known values: - Power = 2100 hp - IMEP = 700 psi (we need to convert psi to feet of water, but use as-is for calculation) - RPM = 3320 - Area ≈ 0.14704 sq ft 4. Substitute back into the equation: \[ \text{Stroke} = \frac{2100 \times 33,000}{700 \times 0.14704 \times 3320} \] \[ \approx \frac{693,000,000}{700 \times 0.14704 \times 3320} \] \[ \approx \frac{693,000,000}{364,222.4} \approx 1901.01 \text{ feet} \] 5. As only the stroke length per cylinder is needed, divide this by the number of cylinders: \[ \text{Stroke Length per cylinder} = \frac{1901.01}{6} \approx 316.84 \text{ feet} \] Thus, the calculated stroke length of the engine, rounded to two decimal places, is approximately **316.84 feet**.