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# Velocity Profile

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Recall from the previous slide that the empirical polynomial approximation of the velocity profile is given by

$V_e = 1 - \left( \frac{n-s}{n-1}\right)\left( 1 - \eta\right)^2 - \left( \frac{s-1}{n-1}\right)\left( 1 - \eta\right)^{2n}$

Use the slider to choose varying values of $$R_m$$; the values of $$R_\tau$$, $$n$$, and $$s$$ will simultaneously update.

The panel below will plot the velocity profile across the half-width of the channel in terms of $$\eta$$ (i.e. $$V_e \left(\eta\right)$$). Also on the graph is the familar parabolic profile for the laminar case ($$n = 0, s = 1$$). As expected, the velocity gradient is steeper than for the laminar flow.

$$R_\tau =$$ ,
$$n =$$ ,
$$s =$$