Anthony T. answered • 04/19/24
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One gallon is 0.134 ft^3. The volume flowing through the radiator in cubic feet/sec is
5 gal/4x60 x0.134 ft^3 = 0.00279 ft^3 / sec.
Since the pipe is 2 inches in diameter, this is equal to 2/12 = 0.167 ft. The volume of the pipe can be expressed as Vp = 3.14 x 0.167^2/4 x L where L is the linear dimension of the pipe.
Equate the flow in ft^3/sec to Vp and solve for L.
0.00279 ft^3 /s = 3.14 x 0.167^3 ft^2 /4 x L.
L = 4 x 0.00279 ft^3 /s / (3.14 x 0.167^2 ft^2 ) = 1.27 ft/s
Go through the math as the use of / for division may make it difficult to visualize.
Anthony T.
When I redid the calculation, I realized that I made a decimal point error. The corrected result would be 0.127 ft/sec. This is far away from your answer key result! If you work backwards from 1.5 ft/s, convert to gallons/sec by multiplying by pipe area and converting to gallons/sec and then to gallons in 4 minutes, you get 18.7 gallons! Try it yourself.
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04/20/24
George T.
Hello Mr. T, thank you so much for helping me out! However, my answer key says the answer is 1.5 feet/second.04/20/24