Chapter 4, Problem 148P

Liquid flowing at high speed in a wide, horizontal open channel under some conditions can undergo a hydraulic jump, as shown. For a suitably chosen control volume, the flows entering and leaving the jump may be considered uniform with hydrostatic pressure distributions (see Example 4.7). Consider a channel of width w, with water flow at D₁ = 0:6 m and V₁ = 5 m/s. Show that in general, $D_2=D_1\left[\sqrt{1+8V_1^2/g{D}_1}-1\right]/2$.