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Discharge Practice Sheet
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1.    You have measured the width of a stream as being 25 feet.  Its depth ranged from 5 to 7 feet with an average of 6 feet.  A chip of wood is seen to float downstream some 300 feet in 10 seconds.  What is the discharge of this stream

Discharge is calculated by multiplying the area of the stream (its width times its average depth) by the velocity of the moving water.

The area of this stream is 25 feet by 6 feet.

A = (25 feet) (6 feet)

    = 150 feet²

The  velocity of the stream is taken from the distance a piece of wood floats in a certain amount of time.  You want to reduce it to unit time so:

V = (300 feet)/ 10 seconds = 30 feet/second

Now you are ready to solve for discharge.

Discharge = (Area) (Velocity)

                  = (150 feet²) (30 feet/second)

                  = 4500 feet³/second

2.    You follow the stream downstream and come to a place where the stream is only 12.5 feet across.  You note that the discharge is probably the same as you calculated upstream.  The velocity is also the same as you determined upstream.  What is the probable depth of the stream at this new location?

To solve this problem you must understand that if the discharge at both places is the same than you can set your discharge equation for point A equal to the discharge equation for point B.  Then solve for the missing parameter.  Therefore:

Discharge _{point A} = Discharge _{point B}

4500 feet³/second = (Area _{point B}) (Velocity _{point B})

4500 feet³/second = (12.5 feet) (depth) (30 feet/second)

Depth =