We appreciate your visit to Pumping Equipment Capacity A single piston reciprocating pump has a 12 inch diameter piston with a 24 inch stroke and makes 25 strokes per minute. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
Pumping rate in cubic feet per stroke ≈ 1.5708 cubic feet
Pumping rate in gallons per stroke ≈ 11.75 gallons
Pumping rate in gallons per minute ≈ 293.75 gallons
To determine the pumping rate for a single-piston reciprocating pump, we can start by calculating the volume displaced per stroke and then use this to find the rates in different units. Here’s how to do it step-by-step:
Calculate the volume per stroke in cubic feet:
Convert the piston diameter and stroke length to feet:
- Diameter = 12 inches = 1 foot
- Radius (r) = Diameter / 2 = 0.5 feet
- Stroke length (h) = 24 inches = 2 feet
Use the formula for the volume of a cylinder:
[tex]V = \pi r^2 h[/tex]Substituting the values:
[tex]V = \pi (0.5)^2 (2)[/tex]
[tex]V = \pi (0.25) (2)[/tex]
[tex]V = \pi (0.5)[/tex]
[tex]V \approx 1.5708 \text{ cubic feet}[/tex]
Convert the pumping rate to gallons per stroke:
- There are 7.48 gallons in 1 cubic foot.
- Volume per stroke in gallons = 1.5708 cubic feet * 7.48 gallons/cubic foot
- Volume per stroke in gallons ≈ 11.75 gallons
Determine the pumping rate in gallons per minute:
- The pump makes 25 strokes per minute.
- Pumping rate in gallons per minute = 11.75 gallons/stroke * 25 strokes/minute
- Pumping rate in gallons per minute ≈ 293.75 gallons/minute
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Final answer:
The pumping rate of the single-piston reciprocating pump is 1.57 cubic feet per stroke, 11.72 gallons per stroke, and 293 gallons per minute.
Explanation:
To find the pumping rate in cubic feet per stroke, we need to calculate the volume of the piston. The volume of a cylinder is given by the formula V = πr^2h, where r is the radius and h is the height. In this case, the radius is half the diameter, so r = 6 inches. The height is the stroke, so h = 24 inches. Plugging in these values, we get V = 3.14 * 6^2 * 24 = 2714.88 cubic inches. To convert cubic inches to cubic feet, we divide by 1728 (since there are 12^3 cubic inches in a cubic foot), so the pumping rate is 2714.88 / 1728 = 1.57 cubic feet per stroke.
To find the pumping rate in gallons per stroke, we need to know the conversion factor from cubic feet to gallons. 1 cubic foot is equal to 7.48 gallons. Therefore, the pumping rate is 1.57 * 7.48 = 11.72 gallons per stroke.
To find the pumping rate in gallons per minute, we multiply the pumping rate in gallons per stroke by the number of strokes per minute. In this case, the pumping rate is 11.72 * 25 = 293 gallons per minute.
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