Calculate the indicated horsepower of the following engine: 7 cylinders, a stroke length of 0.91 feet, a bore of 5.2 inches, operating at 2400 rpm , and has an indicated mean effective pressure (IMEP) of 1030 psi per cylinder.

To calculate the indicated horsepower (IHP) of the engine, we can use the formula: \[ \text{IHP} = \frac{(N \times P_m \times V)}{33,000} \] Where: - \( N \) = Number of cylinders = 7 - \( P_m \) = Indicated mean effective pressure (IMEP) in psi = 1030 psi - \( V \) = Displacement volume per cycle in cubic feet First, we need to calculate the displacement volume \( V \) for one cylinder. We use the formula: \[ V = \frac{\pi}{4} \times (D^2) \times L \] Where: - \( D \) = Bore in feet (convert inches to feet): \( D = \frac{5.2 \text{ inches}}{12} \approx 0.4333 \text{ feet} \) - \( L \) = Stroke length in feet = 0.91 feet Now substituting into the volume formula: \[ V = \frac{\pi}{4} \times (0.4333^2) \times 0.91 \] Calculating the volume: \[ V \approx 0.045 \text{ cubic feet} \text{ (this is for one cylinder)} \] Now, since there are 7 cylinders, the total displacement volume will be: \[ V_{total} = 7 \times 0.045 \approx 0.315 \text{ cubic feet} \] Next, we can substitute into the IHP formula. However, we only need to calculate for one cycle to find the horsepower per minute then multiply by the number of revolutions per minute. The number of power strokes per minute for a four-stroke engine (which is usually the case) is half the RPM: \[ n = \frac{2400}{2} = 1200 \text{ power strokes/minute} \] Now substituting everything into our IHP formula: \[ \text{IHP} = \frac{(N \times P_m \times V_{total} \times n)}{33,000} \] Substituting the known values: \[ \text{IHP} = \frac{(7 \times 1030 \text{ psi} \times 0.045 \text{ cubic feet} \times 1200)}{33000} \] \[ \text{IHP} \approx 21.3 \text{ horsepower} \] So, the indicated horsepower of the engine is approximately 21.3 HP.