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

2024
Views:

240

Pages:

5
Author:

Jabin F.

MCQ Q.2 Q/B = 2 m^3/s/m So = 0.002 n = 0.012 Slope = ? R = y_n Q = (A/n) * R^(2/3) * So^(1/2) Q/B = (B * y_n / (n * B)) * (y_n)^(2/3) * (So)^(1/2) 2 = (y_n / n) * (y_n)^(2/3) * (So)^(1/2) 2 = (y_n)^(5/3) * (1 / 0.012) * (0.002)^(1/2) 2 = (y_n)^(5/3) * (1 / 0.012) * 0.04472 2 = (y_n)^(5/3) * 3.7267 (y_n)^(5/3) = 2 / 3.7267 = 0.5366 y_n = (0.5366)^(3/5) = 0.688 m y_c = (q^2 / g)^(1/3) = ((Q/B)^2 / g)^(1/3) = (2^2 / 9.81)^(1/3) = (4 / 9.81)^(1/3) = (0.4077)^(1/3) = 0.745 m y_n < y_c MCQ Q.3 B = 4m (written above, crossed out and replaced by 1m = B) 1m = B wide Rect. R = y_n n = 0.012 So = 0.001 Slope = ? Q = 16 m^3/s g = 10 m/s^2 Q = (A/n) * R^(2/3) * So^(1/2) Q = (B * y_n / n) * (y_n)^(2/3) * (So)^(1/2) 16 = (1 * y_n / 0.012) * (y_n)^(2/3) * (0.001)^(1/2) 16 = (y_n / 0.012) * (y_n)^(2/3) * 0.03162 16 = (y_n)^(5/3) * 2.635 (y_n)^(5/3) = 16 / 2.635 = 6.072 y_n = (6.072)^(3/5) = 2.284 m Below these calculations, further calculations are shown: y_n = 1.284 (This seems to be a recalculation or a separate case) y_c = (q^2 / g)^(1/3) = ((Q/B)^2 / g)^(1/3) = ((16/4)^2 / 10)^(1/3) = (4^2 / 10)^(1/3) = (16 / 10)^(1/3) = (1.6)^(1/3) = 1.169 m (The B value used here is 4m) y_c = ((16/1)^2 / 10)^(1/3) = (16^2 / 10)^(1/3) = (256 / 10)^(1/3) = (25.6)^(1/3) = 2.944 m (Recalculation with B=1m) Using y_n = 1.284 m and y_c = 1.169 m: y_n > y_c MCQ Q.5 B = 1m wide So = 0.0016 n = 0.04 y_n = 0.5 m y = 0.6 m (This 'y' likely refers to the flow depth at a specific point, not normal depth) R = (B * y) / (B + 2y) (Formula for hydraulic radius of a rectangular channel) R = (1 * 0.6) / (1 + 2 * 0.6) = 0.6 / (1 + 1.2) = 0.6 / 2.2 = 3/11 (This calculation seems incorrect based on the formula written next to it) R = (B * y) / (B + 2y) = (1 * 0.5) / (1 + 2 * 0.5) = 0.5 / (1 + 1) = 0.5 / 2 = 1/4 (Using y_n) Q = (A/n) * R^(2/3) * So^(1/2) Q = (1 * 0.5 / 0.04) * (1/4)^(2/3) * (0.0016)^(1/2) Q = (0.5 / 0.04) * (0.3968) * (0.04) Q = 12.5 * 0.3968 * 0.04 = 0.1984 m^3/s y_c = (q^2 / g)^(1/3) = ((Q/B)^2 / g)^(1/3) = ((0.1984 / 1)^2 / 9.81)^(1/3) = (0.03936 / 9.81)^(1/3) = (0.004012)^(1/3) = 0.1589 m y_n > y_c Flow profile = ? y > y_n > y_c M1