||November 25, 2012 23:37
Originally Posted by triple_r
This is when you define a fully-developed flow as a linear pressure drop. For velocity profile to become fully developed you need a bit longer channel.
A better definition of fully-developed flows is that all independent flow parameters no longer depend on the streamwise coordinate. In other words, the gradients of velocity (x, y, z velocity), and gradient of pressure gradient , are 0 in the streamwise direction. Fully-developed flows are only spoken of in the time-average, statistically stationary sense.
Fully developed flows are not defined only by linear pressure drop. Otherwise, a linear pressure gradient (flow in a converging duct) could also be considered fully developed flow, but they are not. However, it is true that fully developed flows do have a constant pressure gradient (in the absence of other body forces). The fully developed property is more restrictive and requires all independent dynamical flow variables to be constant (pressure & velocity).
Further, only for compressible flows is both velocity and pressure a dynamical variable. For incompressible flows, pressure and velocity are not both dynamical variables (only one or the other). Usually velocity is taken to be the dynamical variable. Hence, to use pressure in determining whether a flow is fully developed or not in that case is a bit non-sensical.