Exercise 6Water is flowing at a velocity of 3 m/s and a depth of 3 m in a channel of rectangularcross-section. Find the maximum allowable size of upward step for the upstream flowto remain as specified.SolutionFr = -3V9.81 x3= 0.55 – The flow regime is subcritical.The unit discharge is_q=v*y=9m’ IsSpecific Energy in the cross-section is_32E=y+2g=3+2×9.81-= 3.459mThe maximum size of the step which will not change the depth and velocity upstreamwill be one on which the critical depth will be formed.The critical depth is:Fr’ =19.81x yeyo = 2.02 mThe Specific Energy on the step is:E. = =y. = =x2.021 = 3.033 mTherefore the step size is:Az = E-E. =3.459-3.032Az = 0.427 mIf the step is above 0.427 m, the specific energy in front of the step (i.e. the depth) willincrease while the critical depth will form on the step.

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