Velocity profiles for the transition region in an open rectangular channel
Caruthers, Phillip Allen
Master of Science
The region of transition from laminar to turbulent flow in an open channel was investigated by means of velocity profiles. Water was used as the experimental fluid. The velocity profiles were measured by a hot-wire anemometer. The flow was varied over a range of Reynolds numbers from 1084 to 32,208. All velocity profiles indicated a momentum flux at the surface in the direction of the outward normal to the surface. This phenomena caused the maximum velocity and the point of zero velocity gradient to occur beneath the surface. It is postulated that this momentum flux is due to wave action at the surface. In order to correlate the profiles at different Reynolds numbers, it was necessary to evaluate the profiles from the wall to the depth of zero velocity gradient only. This negates the effect of the momentum flux through the surface, and also makes the results comparable to similar results obtained in pipes and between parallel plates. The above mentioned range of Reynolds numbers is based on this method. Laminar profiles can be uniquely correlated by plotting . The friction velocity is defined as y is the distance from the wall, and u is the velocity at the point y. Normally, profiles in the turbulent region can be uniquely correlated by a graph of u+ vs. y+. However, velocity profiles in the transition region demonstrate a Reynolds number dependence which causes a deviation of the velocity profile from the normal turbulent flow correlation. If the u+ and y+ values of a transition velocity profile are multiplied by (uav/umax)tube and (umax/uav)tube, respectively, a unique correlation based on these modified values is obtained. The factor (uav/umax)tube of the average to the maximum velocity in a tube; this factor must be evaluated at a tube Reynolds number which is related to the open channel Reynolds number. The experimental profiles indicate that the transition from laminar to fully turbulent flow occurs over the range 300<Re<32 ,000.