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Flow Rate Through a Water Hose

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Two children, Ferdinand and Isabella, are playing with a water hose on a sunny summer day. Isabella is holding the hose in her hand 1.0 meters above the ground and is trying to spray Ferdinand, who is standing 10.0 meters away. To increase the range of the water, Isabella places her thumb on the hose hole and partially covers it. Assuming that the flow remains steady, what fraction f of the cross-sectional area of the hose hole does she have to cover to be able to spray her friend? Assume that the cross section of the hose opening is circular with a radius of 1.5 centimeters. Express your answer as a percentage to the nearest integer. (Note: I've tried both 68%, 32%, and 50%, and all of those answers were incorrect.) (Note: This is all the other information I have for this problem: Isabella will not be able to spray Ferdinand under the following conditions - If the water is flowing out of the hose at a constant speed v_0 of 3.5 meters per second. Assume that the hose is pointed parallel to the ground and take the magnitude of the acceleration g due to gravity to be 9.81 meters per second, per second.

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Solution Summary

The solution provides a step-by-step calculation for finding the fraction of a water hose hole needed to be covered in order to have water still spraying out the other end.

Solution Preview

Vo = 3.5 m/s

Vertical travel:
---------------
s = ut + (1/2)gt^2
u = 0; s = 1 m; g = 0.81 m/s
t = sqrt(2s/g) = 0.45 sec
...

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