In a wide rectangular channel, if the flow is 50 percent of the full supply depth, the discharge is k times of full supply discharge where k is?



The discharge in a wide rectangular channel is given by the equation:

Q = (1.49/n) * A * R^(2/3) * S^(1/2)

where Q is the discharge, n is the Manning's roughness coefficient, A is the cross-sectional area, R is the hydraulic radius, and S is the slope of the channel.

When the flow is 50 percent of the full supply depth, the cross-sectional area and hydraulic radius are both reduced by a factor of 0.5. Therefore, the discharge can be calculated as:

Q_50% = (1.49/n) * (0.5 * A) * (0.5 * R)^(2/3) * S^(1/2)

Simplifying the above equation, we get:

Q_50% = (1/8) * (1.49/n) * A * R^(2/3) * S^(1/2)

Thus, the discharge when the flow is 50 percent of the full supply depth is one-eighth of the discharge when the channel is flowing at full supply depth.

Therefore, k = 8.



When the flow is 50 percent of the full supply depth, the cross-sectional area and hydraulic radius are both reduced by a factor of 0.5. This reduction in area and radius results in a reduction in the discharge. The discharge is proportional to the cross-sectional area and hydraulic radius raised to the power of 2/3. Therefore, the discharge is reduced by a factor of (0.5)^(2/3) = 0.63.

The Manning's roughness coefficient, slope of the channel, and the width of the channel are assumed to be constant. Hence, the only factor affecting the discharge is the reduction in cross-sectional area and hydraulic radius.

Therefore, the discharge when the flow is 50 percent of the full supply depth is one-eighth of the discharge when the channel is flowing at full supply depth.



In a wide rectangular channel, when the flow is 50 percent of the full supply depth, the discharge is one-eighth of the discharge when the channel is flowing at full supply depth. Therefore, the value of k is 8.