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the maximum Froude number is 1.47. If more time is
Consider the flow in a wide channel over a bump, as in
available, it is instructive to examine a complete family
Fig. P10.62. One can estimate the waterdepth change or
of surface profiles for 1 cm hmax 52 cm (which is
transition with frictionless flow. Use continuity and the
the solution to Prob. 10.67).
Bernoulli equation to show that
*P10.69 Given is the flow of a channel of large width b under a
sluice gate, as in Fig. P10.69. Assuming frictionless
dy
dh/dx
steady flow with negligible upstream kinetic energy, de2
dx
1 V /(gy)
rive a formula for the dimensionless flow ratio
3
Is the drawdown of the water surface realistic in Fig.
Q2/(y1b2g) as a function of the ratio y2/y1. Show by difP10.62? Explain under what conditions the surface might
ferentiation that the maximum flow rate occurs at y2
rise above its upstream position y0.
2y1/3. V1
y0 y ( x) V0 Gate y1 V ( x) y2 Bump
V2 h ( x) P10.69 P10.62 P10.64 In Fig. P10.62 let V0 1 m/s and y0 1 m. If the max P10.70
imum bump height is 15 cm, estimate (a) the Froude number over the top of the bump an...
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This note was uploaded on 10/27/2009 for the course MAE 101a taught by Professor Sakar during the Spring '08 term at UCSD.
 Spring '08
 Sakar

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