Establishment of uniform flow
Today we are going to demonstrate
the establishment of uniform flow in an open channel,
under two Froude numbers:
... We use the friction equation ... S_{o} = f F^{2} ... in which S_{o} is the bottom slope, lower case f is the friction factor, and upper case F is the Froude number. ... The friction factor is equal to 1/8 of the DarcyWeisbach friction factor. It is equal to: f = g n^{2} / (k^{2} R^{1/3}) ... In SI units, g is equal to 9.81 m/s^{2} and k = 1. ... The wall of the flume is made out of lucite, i.e. acrylic glass. We assume a Manning n equal to 0.008. ... We estimate a hydraulics radius equal to 3 centimeters, that is, 0.03 m. ... Therefore: f = 0.002 ... We turn on the pump in the demonstration flume. ... We set the slope at 0.01, a steep slope, and check the level. ... The calculated Froude number is: F = (S_{o} / f )^{1/2} = (0.01 / 0.002)^{1/2} = 2.24 ... This Froude number corresponds to supercritical flow. ... Now we set the slope at 0.002, the critical slope, and check the level. ... The calculated Froude number is: F = (S_{o} / f )^{1/2} = (0.002 / 0.002)^{1/2} = 1. ... We have shown the flow in this channel operating under supercritical and critical conditions.
