CIVE 632 - COMPUTATIONAL HYDRAULICS AND HYDROLOGY
FALL 2021
HOMEWORK 3: MUSKINGUM-CUNGE METHOD SOLUTION

EQUATIONS IN MUSKINGUM-CUNGE METHOD

q = (1.486/n) d^5/3 S^1/2

q = α d^β

α = (1.486/n) S^1/2

α = (1.486 / 0.02972) (1 / 5280) ^1/2 = (1.486 / 0.02972) (0.000189394) ^1/2 = 0.688

β = 5/3

d = (q/α) ^(1/β)

d = (q/α) ^(1/β) = (125 / 0.688) ^3/5 = 22.677

v = q/d = q (q/α)^{- (1/β)}

v = q/d = q (q/α)^{- (1/β)} = (125 / 22.677) = 5.512

c = βv = β q (q/α)^{- (1/β)}

c = βv = β q (q/α)^{- (1/β)} = (5/3) 5.512 = 9.1868

C = c Δt/Δx

C = c Δt/Δx = 9.1868 (6 × 3600 ) / (25 × 5280) = 1.5

D = q /(S_o c Δx)

D = q /(S_o c Δx) = 125 / (0.000189394 × 9.1868 × 25 × 5280) = 0.544

N = t_r S_o (g/d)^1/2 > 15

N = t_r S_o (g/d)^1/2 = 48 (3600) ( 0.000189394) (9.81 / 22.677 ) ^1/2 = 21 > 15 OK!

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