An engineer makes careful measurements with a weir that monitors a rectangular unfinished concretechannel laid on a slope of 1°. She finds, perhaps with surprise,that when the water depth doubles from 2 ft 2 inchesto 4 ft 4 inches, the normal flow rate more than doubles,from 200 to 500 ft3/s. (a) Is this plausible? (b) If so, estimatethe channel width.
An engineer makes careful measurements with a weir that monitors a rectangular unfinished concrete
channel laid on a slope of 1°. She finds, perhaps with surprise,
that when the water depth doubles from 2 ft 2 inches
to 4 ft 4 inches, the normal flow rate more than doubles,
from 200 to 500 ft3/s. (a) Is this plausible? (b) If so, estimate
the channel width.
(a)
The expression for the normal flow rate.
Here, Q is the normal flow rate, A is the cross sectional area, Rh is the hydraulic radius, S0 is the radius.
The expression for the hydraulic radius is given by,
Substitute the values in equation (1).
Let,
And, the width b = 1 ft.
The above expression reduces to,
When the depth is doubled. (h= 2h).
Divide equation (3) by (2).
For any value of h,
Thus,
The normal flow rate increases more than double if the depth is doubled.
Therefore, It is plausible.
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