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Calculate the Pressure (in PSI) in a single cylinder for an engine with the following parameters: 4 cylinders, a stroke length of 0.86 feet, a bore of 3.7 inches, operating at 1850 rpm , and operates at 6200 horsepower. Round to 1 decimal place.

Ask by Parsons Lawson. in Canada
Dec 09,2024

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Tutor-Verified Answer

Answer

The pressure in a single cylinder is approximately 23851.4 PSI.

Solution

To calculate the pressure in a single cylinder of the engine, we can use the following steps: 1. **Calculate the displacement of a single cylinder**: The formula for the volume of a cylinder is: \[ V = \pi \times \left(\frac{d}{2}\right)^2 \times h \] where: - \(d\) is the bore (diameter) of the cylinder, - \(h\) is the stroke length. First, we need to convert the bore from inches to feet: \[ d = 3.7 \text{ inches} = \frac{3.7}{12} \text{ feet} \approx 0.3083 \text{ feet} \] Now, we can calculate the volume of a single cylinder: \[ V = \pi \times \left(\frac{0.3083}{2}\right)^2 \times 0.86 \] \[ V \approx \pi \times (0.15415)^2 \times 0.86 \] \[ V \approx \pi \times 0.0237 \times 0.86 \approx \pi \times 0.020362 \approx 0.0640 \text{ cubic feet} \] 2. **Calculate the total displacement for all cylinders**: Since there are 4 cylinders: \[ V_{\text{total}} = 4 \times V \approx 4 \times 0.0640 \approx 0.2560 \text{ cubic feet} \] 3. **Convert the total displacement to cubic inches**: There are 1728 cubic inches in a cubic foot: \[ V_{\text{total}} \text{ (in cubic inches)} = 0.2560 \times 1728 \approx 442.368 \text{ cubic inches} \] 4. **Calculate the engine's power in terms of pressure**: The power output of the engine is given as 6200 horsepower. We can convert horsepower to foot-pounds per minute: \[ 1 \text{ horsepower} = 33000 \text{ foot-pounds per minute} \] \[ \text{Power} = 6200 \times 33000 \text{ foot-pounds per minute} = 204600000 \text{ foot-pounds per minute} \] 5. **Calculate the work done per cycle**: The engine operates at 1850 RPM, which means it completes 1850 revolutions per minute. Since it is a 4-cylinder engine, each cylinder fires once every two revolutions (assuming a 4-stroke engine): \[ \text{Cycles per minute} = \frac{1850}{2} = 925 \text{ cycles per minute} \] The work done per cycle is: \[ \text{Work per cycle} = \frac{\text{Power}}{\text{Cycles per minute}} = \frac{204600000}{925} \approx 220000 \text{ foot-pounds} \] 6. **Calculate the pressure in a single cylinder**: The pressure can be calculated using the formula: \[ P = \frac{\text{Work per cycle}}{V} = \frac{220000}{0.0640} \text{ pounds per square foot} \] \[ P \approx 3437500 \text{ pounds per square foot} \] To convert this to PSI (pounds per square inch), we use the conversion factor \(1 \text{ square foot} = 144 \text{ square inches}\): \[ P \text{ (in PSI)} = \frac{3437500}{144} \approx 23851.39 \text{ PSI} \] 7. **Round to 1 decimal place**: \[ P \approx 23851.4 \text{ PSI} \] Thus, the pressure in a single cylinder is approximately **23851.4 PSI**.

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Bonus Knowledge

To calculate the pressure in a single cylinder, we first need to find the engine displacement and the power per cylinder. Each cylinder's displacement can be computed using the bore and stroke. 1. **Calculate the cylinder volume (displacement)**: - Volume of one cylinder (in cubic inches) = π × (bore/2)² × stroke - Bore = 3.7 inches, Stroke = 0.86 feet = 0.86 × 12 inches/foot = 10.32 inches - Volume = π × (3.7/2)² × 10.32 ≈ 108.68 cubic inches. 2. **Total displacement for 4 cylinders**: - Total displacement = 4 × 108.68 ≈ 434.72 cubic inches. 3. **Convert the power to watts**: - 6200 horsepower = 6200 × 745.7 watts ≈ 462,604 watts. 4. **Pressure (P in PSI)** can be found from the relationship between horsepower, displacement, and RPM: - P = (HP × 33,000) / (RPM × Displacement). - Convert displacement to cubic feet = 434.72 / 1728 cubic feet (1 cubic foot = 1728 cubic inches) ≈ 0.2512 cubic feet. - P = (6200 × 33,000) / (1850 × 0.2512) ≈ 4530.1 PSI. Thus, rounding to one decimal place, the pressure in a single cylinder is approximately **4530.1 PSI**.

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