Calculate the bore (in inches) of a single cylinder for an engine with the following parameters: 4 cylinders, a stroke length of 0.57 feet, has an indicated mean effective pressure (IMEP) of 810 psi per cylinder, operating at 2710 rpm , and operates at 2800 horsepower. Round to 1 decimal place.

To calculate the bore of a single cylinder in an engine, we can use the following formula that relates the engine's power output, IMEP, stroke length, and bore: \[ \text{Power} = \frac{IMEP \times V_d \times N}{33,000} \] Where: - Power is in horsepower (hp) - IMEP is in psi - \( V_d \) is the displacement volume per cylinder in cubic inches - \( N \) is the number of power strokes per minute ### Step 1: Calculate the displacement volume per cylinder The displacement volume \( V_d \) for a single cylinder can be calculated using the formula: \[ V_d = \frac{\pi}{4} \times D^2 \times L \] Where: - \( D \) is the bore in inches - \( L \) is the stroke length in inches ### Step 2: Calculate the number of power strokes per minute For a 4-cylinder engine operating on a 4-stroke cycle, the number of power strokes per minute \( N \) is: \[ N = \frac{\text{RPM}}{2} = \frac{2710}{2} = 1355 \text{ power strokes per minute} \] ### Step 3: Rearranging the power formula We can rearrange the power formula to solve for \( D \): \[ D^2 = \frac{Power \times 33,000}{IMEP \times N} \times \frac{4}{\pi L} \] ### Step 4: Convert stroke length to inches The stroke length \( L \) is given as 0.57 feet. Converting this to inches: \[ L = 0.57 \text{ feet} \times 12 \text{ inches/foot} = 6.84 \text{ inches} \] ### Step 5: Substitute the values into the formula Now we can substitute the values into the formula: - Power = 2800 hp - IMEP = 810 psi - \( N = 1355 \) power strokes per minute - \( L = 6.84 \) inches \[ D^2 = \frac{2800 \times 33,000}{810 \times 1355} \times \frac{4}{\pi \times 6.84} \] Calculating the right-hand side step by step: 1. Calculate \( 2800 \times 33,000 \): \[ 2800 \times 33,000 = 92,400,000 \] 2. Calculate \( 810 \times 1355 \): \[ 810 \times 1355 = 1,098,150 \] 3. Calculate \( \frac{92,400,000}{1,098,150} \): \[ \frac{92,400,000}{1,098,150} \approx 84.2 \] 4. Calculate \( \frac{4}{\pi \times 6.84} \): \[ \pi \approx 3.14159 \implies \pi \times 6.84 \approx 21.5 \] \[ \frac{4}{21.5} \approx 0.186 \] 5. Now multiply the two results: \[ D^2 \approx 84.2 \times 0.186 \approx 15.7 \] ### Step 6: Calculate the bore \( D \) Taking the square root to find \( D \): \[ D \approx \sqrt{15.7} \approx 3.96 \text{ inches} \] ### Final Result Rounding to one decimal place, the bore of a single cylinder is: \[ \boxed{4.0} \text{ inches} \]