Engr Help

Open Channel Flow Gradually Varying Flow (continued)

Specific Energy Plot for Open Channel Flow

Find the minimum value for E by differentiation of E = y + q²/2gy² .

dE/dy = 1 - q²/gy³ = 0 So y_c = ( q²/g) ^1/3 Put y_c into E to obtain min E.

Emin = y_c + y_c³/2y_c² = (3/2) y_c

Recall V = q/y. So for the critical velocity, V_c= q/y_c

But q² = y_c³ g So q = √ (y_c³ g) and therefore

V_c= q/y_c = √ gy_c Recall F_r= V/√gy

So the result is that at E_min the Froude Number, F_r = 1 .