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

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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