The critical depth of an open channel is important for two reasons:

  • The critical depth is the depth where the energy of the flow has been minimized (i.e. the critical depth maximized efficiency in the system)
  • If the depth of the flow is less than the critical depth a hydraulic jump may appear

Also, the critical flow & critical velocity occur at the critical depth. When the depth of flow exceeds the critical depth the flow is considered subcritical, when the depth of flow is less than the critical depth the flow is considered supercritical. A convenient method of determining what type of flow exists in a channel is to use the froude number?.

Critical Depth for a Rectangular Channel

For a rectangular channel[1], the critical depth exists when:

d_c \text{}^3 = \frac{Q^2}{gb^2}
d_c = \sqrt[3]{\frac{Q^2}{gb^2}}

where

  • dc = the critical depth of the channel (ft)
  • Q = the flow in the channel (ft3/sec or m3/sec)
  • g = gravitational constant (32.2 ft/sec2 or 9.81 m/sec2)
  • b = the width of the channel (ft)

The critical depth of a channel can be correlated to the minimum specific energy present in the channel by...

d_c = \frac{2}{3}E

where

Critical Depth for Circular & Trapezoidal Channels:

Although hard to read, the following provides the critical depth for circular channels[2] given the diameter of the pipe, flow, etc.

Critical Depth for Circular Channels
Figure 1: Critical Depth for Circular Channels (US)


Other Circular/Trapezoidal Depth Curves:

Critical Depth for Non-Rectangular Channels:

The critical depth for non rectangular channels is taken by a trial and error approach.

References

  1. V.T. Chow, "Open Channel Hydraulics", 1959
  2. http://www.fhwa.dot.gov/engineering/hydraulics/pubs/08090/04.cfm

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