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 \(D_{1}=0.6 \mathrm{~m}\) and \(V_{1}=5 \mathrm{~m} / \mathrm{s}\). Show that in general, \(D_{2}=D_{1}\left[\sqrt{1+8 V_{1}^{2} / g D_{1}}-1\right] / 2\).

Evaluate the change in mechanical energy through the hydraulic jump. If heat transfer to the surroundings is negligible, determine the change in water temperature through the jump.

Data From Example 4.7

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D = 0.6 m V = 5 m/s P4.148 V2 D2