University:
Santa Fe College
Course:
PHY 2004 | Applied Physics 1
Academic year:

2024
Views:

121

Pages:

6
Author:

Jabin F.

Depth of Water check fr -> fr = sqrt(Q^2 T / (g A^3)) = sqrt(60^2 * (16) / (9.81 * (27.5)^2)) fr = 0.531 < 1 (Subcritical) E_1 = y_1 + V_1^2 / (2g) = 2.5 + 60^2 / ((27.5)^2 * 2 * 9.01) E_1 = 2.7426m Lowering of bed = Delta z = E_2 - E_1 Raising pi = Delta z = E_1 - E_2 E_2 = Delta z + E_1 = 0.6m + 2.743 E_2 = 3.343m for flow possible E_2 > E_c downstream E_c = (3/2) Y_c = (3/2) ((60/6)^2 / 9.01)^(1/3) E_c = 3.252 m > E_c < L Flow possible E_2 = y_2 + V_2^2 / (2g) 3.343 = y_2 + Q^2 / (A^2 * 2g) 3.343 = y_2 + 60^2 / ((6y_2)^2 * 2 * 9.01) y_2 -1.074 2.57 1.04 m X y_2 = 2.57m change in water surface elevation = 2.5 + 0.6 - 2.57 x = 0.53m Delta z min = E_1 - E_c (Raising) Delta z min = -E_1 + E_c (Lowering) = -2.743 + 3.252 Delta z min = 0.509 m Ass. Q.5 y = 6m ← 4m → V = 2 - 5.5e^(-y) Q/B = q = ? dQ = V_avg dA dQ = B dy (V) dQ = B dy (2 - 5.5e^(-y)) Integral dQ = Integral from 0 to 4 (2 - 5.5e^(-y)) dy Q = 4 (2y + 5.5e^(-y)) from 0 to 6 Q = 4 (2*6 + 5.5e^(-6) - 5.5e^(-0)) Q = 4 (12 + 5.5 (e^(-6) - 1)) Q = 26.054 q = Q/B = 26.054 / 4 = 6.51 m^3/s/m