Engr Help

Summary for Open Channel Flow

1. For equilibrium flow apply Manning's equation: (semi-empirical relation)

Q = (k/n) A (R_H)^2/3 So ^1/2

where k = 1 for metric and 1.49 for English units

n = roughness coefficient (depends on material for channel)

A is the x-sectional area (any shape)

R_H = hydraulic radius = area / wetted perimeter

So = slope of channel

Applications involving equilibrium (or uniform) flow

Given Data Solve for:

Q, L, ν, size, shape, roughness coefficient	So
So, L, ν, size, shape, roughness coefficient	V, y, Q
So, Q, L, ν, size, shape, roughness coefficient	R_H, y

Solve first two by direct calculation. Last one requires iteration. (Hardest type)

2. For gradually varied flow in rectangular channels of width, w:

Conservation of mass: w y₁ V₁ = w y₂ V₂ = Q

Conservation of Energy: y₁ + V₁² / 2g = y₂ + V₂² / 2g + ( S_f ˗ So ) L

where y₁ and y₂ are the upstream and downstream depths

V₁ and V₂ are the upstream and downstream fluid speeds

S_f is the head loss per unit length of channel

So is the channel slope

L is the length along the channel

S_f ≈ [ (k/n) R_H^1/6] ^-2 V² / R_H

Since changes in y and V are gradual, the energy loss can be represented by the

Manning equation and can be used to evaluate the slope for gradually varied flow.

In addition, construct a specific energy plot to aid in evaluation.