What is Open Channel Flow?
Open channel flow occurs in rivers, canals, irrigation systems, and storm sewers where the fluid surface is exposed to atmosphere. Unlike pipes, open channels have a free surface whose height varies with flow rate. Manning's equation is the standard tool for predicting flow velocity and discharge in natural and constructed channels.
Manning's equation: v = (1/n)R_h^(2/3)S^(1/2), where v is mean velocity, n is Manning's roughness coefficient, R_h is hydraulic radius, and S is channel slope.
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Step-by-step worked examples
Trapezoidal canal: R_h = 1 m, Manning's n = 0.03, slope S = 0.001. Flow velocity?
v = (1/n)R_h^(2/3)S^(1/2) v = (1/0.03) × 1^(2/3) × (0.001)^(1/2) v = 33.33 × 1 × 0.0316 = 1.05 m/s
Rectangular canal: width 5 m, depth 1.2 m (n=0.025, S=0.0005). R_h and velocity?
A = 5 × 1.2 = 6 m²; P = 5 + 2(1.2) = 7.4 m R_h = A/P = 6/7.4 = 0.81 m v = (1/0.025) × 0.81^(2/3) × sqrt(0.0005) = 40 × 0.735 × 0.0224 = 0.66 m/s
Doubling slope (S = 0.001 to 0.002), velocity increases by?
v ∝ S^(1/2), so v_new/v_old = sqrt(2) ≈ 1.414 Velocity increases by ~41%
Flashcards
Quick quiz
Q1.Manning's equation shows velocity increases with…
Q2.Hydraulic radius defined as…
Q3.Manning's n is higher for…
Q4.Doubling channel slope increases velocity by…
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Common mistakes
Manning's equation applies to pressurized pipes. — Correct: Manning's is for open channels; use Darcy–Weisbach for pipes.
Higher Manning's n means lower resistance. — Correct: Higher n means MORE resistance; lower velocity for same slope.
Hydraulic radius is same as pipe diameter. — Correct: R_h = A/P only; in circular pipe R_h = D/4, not D/2.
Channel slope has linear effect on velocity. — Correct: Velocity increases with S^(1/2) — not linear.
FAQ
What is Manning's equation?
v = (1/n)R_h^(2/3)S^(1/2) — predicts flow velocity in open channels.
Why is Manning's coefficient important?
It quantifies channel roughness; higher n means slower flow and design impacts.
How to calculate discharge in a channel?
Q = A × v — area of cross-section times mean velocity from Manning's equation.
Can Manning's equation predict floods?
Yes — by calculating maximum discharge for given channel geometry and slope.