How to Get Subcritical Channel Flow -- Playing With Froude Number in the Real World

How can you get flow to be subcritical in an open channel? Raise n. F is proportional to 1/ n^(9/10). Double n and you will half F.

Let me explain.

Subcritical flow, critical flow, and supercritical flow are what we call regimes of open channel flow. The Froude (sounds like food) number (F) describes the flow regime numerically. For subcritical flow, F is less than 1. For supercritical flow, F is greater than 1. For critical flow, F is 1. For a wide rectangular channel, F=V/sqrt(g*D).

In the real world, you can experience flow regime by dropping a stone into a channel of uniform flow. If the stone is large enough to create a full-depth disturbance wave in the channel, you can note the flow regime by observing the ripples caused by the stone. If the ripples spread upstream, the channel flow regime is subcritical. If the ripples spread downstream only (causing no disturbance upstream) the flow regime is supercritical.

Since the Froude number is F=V/sqrt(g*D), it's proportional to V/sqrt(D). We can also say that for a given flow in a wide rectangular channel V is proportional to 1/D. Therefore, F in a wide rectangular channel is proportional to 1/D^(3/2). This means that if you roughen or flatten a wide channel to deepen and slow its flow to 1/4 its original value, the Froude number will cut to 1/8 its original value. In a more practical scenario, you would cut the Froude number in half by slowing the flow by 37% (to 63% of its original value).

Since depth in a wide rectangular channel varies in proportion to n^(3/5) (n=(C*S^(1/2)*W/Q)*D^(5/3)), F could be thought of as proportional to 1/n^(9/10). This means that you can roughly decrease F nearly inversely proportionally by increasing n on the bottom. Double n on the bottom, and F will cut nearly in half.