The fresh water behind a reservoir dam has a depth D. Ahorizontal pipe of radius

Question

The fresh water behind a reservoir dam has a depth D. Ahorizontal pipe of radius r is located at a depth d and passesthrough the dam. A plug has been firmly inserted at the end of thepipe, as depicted in the diagram. Standard gravity acts verticallydownward. Standard atmospheric pressure is present. a) the magnitude of the friction force that must exist betweenthe plug and the pipe wall, assuming that the plug remains inplace, b) the total volume of water that exits the pipe during a 3-hrtime interval if the plug is removed from the pipe. Hint: Assume that the reservoir is vast, and that its liquidlevel is unaffected by the drainage of this relatively-small amountof water. Step by step solutions please...

Explanation / Answer

(a)            Themagnitude of the friction force that must exist between the plugand the pipe wall is                       F = gdA = g d r2      Substituting values we get                       F = 1000 * 9.8 * 6.0 * 3.14 * 0.02 * 0.02                          = 73.85 n (b) the total volume of water that exits the pipe during a3-hr time interval if the plug is removed from the pipe.                      V = A v dt                         = A (2gd ) dt                         = 3.14 * 0.02 * 0.02 * ( 2 *9.8 * 6 ) * 3 * 60 * 60                        = 147m3

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