The velocity profile for fully developed flow of castor oil at \(20^{\circ} \mathrm{C}\) between parallel plates with the upper plate moving is given by Eq. 8.8. Assume \(U=1.5 \mathrm{~m} / \mathrm{s}\) and \(a=5 \mathrm{~mm}\). Find the pressure gradient for which there is no net flow in the \(x\) direction. Plot the expected velocity distribution and the expected shear stress distribution across the channel for this flow. For the case where \(u=U\) at \(y / a=0.5\), plot the expected velocity distribution and shear stress distribution across the channel. Comment on features of the plots.

Data From Equation 8.8

Transcribed Image Text:

20-1] a U == + a a 2 dx du U dy = - a + a (op 2 - du =0 dy at no A a - U/a 2 (1/)(op/dx) ||