Estimating the manning coefficient from an average bed roughness in open channels

The Manning coefficient of roughness in open channels plays an important role in the determination of discharge by slope‐area methods. It is not a constant for different depths of flow in a channel, but varies as the depth to the one‐sixth power, as well as in some relation to the average height of bed roughness. Through use of the logarithmic velocity‐distribution equation for flow in open channel, these relations can be evaluated. When the Manning coefficient is expressed in terms of height of channel roughness, its determination is much simplified in the field as the roughness can be estimated with considerable error without materially affecting the coefficient. As a second means of determining the Manning coefficient, the distribution of velocity in the vertical at gaging stations provides a useful tool. The logarithmic velocity‐distribution equation and the Manning equation can be solved for the Manning coefficient in terms of the ratio of the velocities at two‐tenths and eight‐tenths the depth. The coefficient thus determined can be used in the computation of main‐channel flows following floods that could not be measured by the current meter. Curves of relation between the Manning coefficient and the ratio of average depth to average height of roughness and between the coefficient and the ratio of the velocities at 0.2 and 0.8 depth are presented.