Suspended sediment in rivers. Consider a steep-walled river channel with a width of 50 m, a bankfull depth of 3 m (to the levee tops), and a slope of 0.5 m/km (i.e., note that this is the tangent of the slope, which for small angles is equivalent to the slope, in radians: 0.0005). The bed of the river is made of coarse sand, organized into ripples that result in an effective roughness length (z_o) of 3 mm. The river at the moment is flooding at a stage of 0.5 m above bankfull. In the calculations below you will again need to recall that the shear velocity u_* is defined as

What is the water discharge in the channel, in m³/s

a) At bankfull ?

b) At 0.5 m above bankfull (i.e., at present) ?

In the latter calculation, ignore the contribution from that flow that escapes over the floodplain.

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Ux t/r, or u.= gHS. b