Conditions for Critical, Subcritical and Supercritical Flow
Let's take a look at the conditions for critical flow first. It's the dividing line between subcritical and supercritical flow. The parameter, specific energy, is often used to introduce the concepts of critical, subcritical, and supercritical flow. The specific energy of a liquid flowing in an open channel is defined to be the sum of its kinetic and potential energy per unit weight of flowing liquid, relative to the channel bottom.
Thus: E = y + V2/2g, where
E = specific energy, ft-lb/lb,
y = depth of flow above the channel bottom, ft,
g = acceleration due to gravity = 32.2 ft/sec2, and
V = average flow velocity, ft/sec, = Q/A, where
Q = volumetric flow rate, cfs, and
A = cross-sectional area of flow normal to the direction of flow, ft2.
The figure at the right above, shows a plot of specific energy versus depth of flow for a particular rectangular channel example. It shows the general pattern for how specific energy, E, varies with depth. At large values of depth, E is large because y is large. For very small values of y, E is large because the flow velocity, V, becomes large, making the kinetic energy large. In between there will be a point at which the specific energy, E, is a minimum. This is the point that is defined to have critical flow conditions (occurring a depth of flow = critical depth). Flows with a shallower depth and higher flow velocity are called supercritical flow and flows with a higher depth and smaller flow velocity are called subcritical flow, as shown on the diagram.
By using a little calculus (setting dE/dy = 0 and solving for y), it can be shown that yc = (q2/g)1/3, for a rectangular channel, where
yc = critical depth (depth of flow at critical flow conditions), ft,
q = Q/b, cfs/ft, and
b = width of the rectangular channel, ft.