Flux in channel flow Consider the flow of water in a

QUESTION:

Flux in channel flow Consider the flow of water in a channel whose boundaries are the planes \(y=\pm L\) and \(z=\pm \frac{1}{2}\). The velocity field in the channel is \(\mathbf{v}=\left\langle v_{0}\left(L^{2}-y^{2}\right), 0,0\right\rangle\). Find the flux across the cross section of the channel at x = 0 in terms of \(v_{0}\) and L.

Text Transcription:

y = pmL

z = pm1/2

v = langle v_0(L^2 - y^2), 0, 0 rangle

v_0