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25 April, 12:14

Suppose that 9 inches of rain falls in a 24-hour period. If the cross-sectional area of a stream in the region is essentially constant (perhaps under a highway bridge), what must happen to the velocity of the stream if it is to accommodate the extra water

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  1. 25 April, 12:33
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    The velocity of stream must be increased

    Explanation:

    Here we have amount of rain given as 9 inches

    Duration of rainfall = 24 hours

    As the rain falls, the volume of water in the stream continues to increase

    The volume of water in the stream is given as

    Cross-sectional area of the stream * Length of the stream

    Since the length of the stream and the cross-sectional area of the stream are constant, to accommodate more rain fall, the excess water will have to be moved out. That is

    Rate of rainfall must be equal to water evacuation at the stream;

    Rate of rain fall = 9 inch / 24 hour = Cross-sectional area of the stream * Velocity of stream

    Since the cross-sectional area of the stream = Constant, K we have;

    Rate of rain fall = 9 inch / 24 hour = K * Velocity of stream

    Increase in rainfall will require increase in velocity of stream.

    Hence, to accommodate the extra water, the velocity of stream must be increased.
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