Open Channel Flow

1. Introduction

Open channel flow refers to the flow of a liquid (usually water) with a free surface exposed to the atmosphere. Unlike pipe flow, the flow is primarily driven by gravity rather than pressure.

Examples

• Rivers and streams
• Canals and irrigation channels
• Drainage systems
• Spillways in dams

2. Types of Open Channels

(a) Natural Channels

• Rivers, streams
• Irregular shape and roughness

(b) Artificial Channels

• Canals, flumes
• Designed shapes like rectangular, trapezoidal

3. Geometric Elements of Channel

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Key Parameters

• Area (A): Cross-sectional flow area
• Wetted Perimeter (P): Length in contact with water
• Top Width (T): Width of free surface
• Hydraulic Radius (R):

$$R = \frac{A}{P}$$R=PA​

• Hydraulic Depth (D):

$$D = \frac{A}{T}$$D=TA​

4. Types of Flow in Open Channels

(a) Based on Time

• Steady Flow: Properties do not change with time
• Unsteady Flow: Properties vary with time

(b) Based on Space

• Uniform Flow: Depth and velocity constant along channel
• Non-uniform Flow:
  • Gradually Varied Flow (GVF)
  • Rapidly Varied Flow (RVF)

5. Velocity Distribution

• Velocity is maximum below the free surface (not exactly at surface due to air resistance)
• Zero velocity at channel bed (no-slip condition)

6. Chezy’s Formula

$V = C \sqrt{R S}$V=CRS​

Where:

• $V$V = Velocity
• $C$C = Chezy’s constant
• $R$R = Hydraulic radius
• $S$S = Slope of channel

7. Manning’s Formula (Most Important)

$V = \frac{1}{n} R^{2/3} S^{1/2}$V=n1​R2/3S1/2

Where:

• $n$n = Manning’s roughness coefficient
• $R$R = Hydraulic radius
• $S$S = Slope

8. Flow Regimes (Based on Reynolds Number)

$$Re = \frac{\rho V R}{\mu}$$Re=μρVR​

• Laminar Flow: $Re < 500$Re<500
• Turbulent Flow: $Re > 2000$Re>2000

9. Froude Number (Most Important in Open Channel)

$Fr = \frac{V}{\sqrt{g D}}$Fr=gD​V​

Where:

• $D$D = Hydraulic depth

Flow Types

• Subcritical Flow (Fr < 1) → Slow, deep flow
• Critical Flow (Fr = 1) → Minimum energy condition
• Supercritical Flow (Fr > 1) → Fast, shallow flow

10. Specific Energy

$$E = y + \frac{V^2}{2g}$$E=y+2gV2​

Where:

• $y$y = Depth of flow

Key Concept

• Minimum specific energy occurs at critical flow

11. Hydraulic Jump

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Definition

A sudden transition from supercritical flow to subcritical flow, causing a rise in water depth.

Features

• Energy dissipation
• Turbulence and mixing

Applications

• Spillways
• Energy dissipation structures

12. Uniform Flow in Channels

Occurs when:

• Depth remains constant
• Slope of channel = slope of energy line

Discharge:$$Q = A \times V$$Q=A×V

13. Most Economical Channel Section

Condition for maximum discharge (minimum cost):

• For rectangular channel:

$$\text{Width} = 2 \times \text{Depth}$$

14. Applications of Open Channel Flow

• Irrigation canals
• Flood control systems
• Sewer systems
• Hydropower plants
• River engineering

15. Key Points Summary

• Open channel flow has a free surface
• Driven by gravity
• Manning’s formula is most widely used
• Froude number determines flow regime
• Hydraulic jump is important for energy dissipation

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