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Fr 1.0 subcritical flow Fr 1.0 critical flow Fr 1.0 supercritical flow (10.6) The Froude number for irregular channels is defined in Sec. 10.4. As mentioned in Sec.
9.10, there is a strong analogy here with the three compressibleflow regimes of the
Mach number: subsonic (Ma 1), sonic (Ma 1), and supersonic (Ma 1). We shall
pursue the analogy in Sec. 10.4.
The Froudenumber denominator (gy)1/2 is the speed of an infinitesimal shallowwater surface wave. We can derive this with reference to Fig. 10.4a, which shows a
wave of height y propagating at speed c into still liquid. To achieve a steadyflow inertial frame of reference, we fix the coordinates on the wave as in Fig. 10.4b, so that
the still water moves to the right at velocity c. Figure 10.4 is exactly analogous to Fig.
9.1, which analyzed the speed of sound in a fluid.
For the control volume of Fig. 10.4b, the onedimensional continuity relation is, for
channel width b,
cyb (c
V or V)(y
c y)b y
y (10.7) y This is analogous to Eq. (9.10); the velocity change V i...
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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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