What is open channel flow?

Open channel flow is a branch of fluid mechanics. It deals with the flow of fluid in an open conduit or free surface. In an open channel flow, gravity induces the flow of water whose surface is open to the air. This flow is free-falling rather than confined in rigid body conduits. The open channel flow depends upon two parameters that are the cross-section of the conduit and the velocity profile. Practical examples of open channel flow are streams, rivers, canals, and other drainage systems.
In open channel flow, the cross-sectional area of at least one of the sides is exposed to air, and the surface of water faces atmospheric pressure. This flow is also known as free gravity flow. The cross-sectional area of the conduit can be either man-made or a natural channel. For instance, the flow in rivers and streams are natural conduits, and the flow in a canal and sanitary systems are man-made or engineered channels.

Type of flows in open channel

The type of flow in an open channel depends on the area of cross-section of conduit, time, and speed of the flow.

• Uniform flow- When the flow depth is unchanged in a channel, it is, said to be uniform.
• Non-uniform flow- When the flow depth is changed in a channel through a cross-section, it is said to be non-uniform. It is further categorized into the gradually varied flow and rapidly varied flow. Rapidly varied flow is the flow in which the flow depth changes abruptly, causing the hydraulic jump. In a gradually varied flow, the flow depth changes gradually along the length of the cross-section, as in a canal network.
• Steady flow- In steady flow, the properties of the flow do not change with time.
• Unsteady flow- In this flow, the properties of the flow do change with time.
• Turbulent flow- Turbulent flow in a fluid is defined by the Reynolds number (R_e). It is a ratio of viscous force to inertia force. When R_e is greater than 2000, the flow is termed turbulent. It is the most common flow for hydraulic procedures.

Reynolds number is given by,

$R_e=\frac{\rho \nu R}{\mu }$

Where,

• $\rho$=density of water
• $\nu$=velocity of water
• $R$=hydraulic radius= hydraulic mean depth =$\frac{wetted area of the channel}{wetted perimeter}$
• $\mu$=absolute viscosity

Laminar flow- Laminar flow occurs when R_e is less than 500 and the flow is smooth like streamlines. It occurs when the water depth is low.

Subcritical flow- Subcritical flow is defined by the flow regime set by the Froude number. The Froude number is calculated by the ratio of gravity forces to inertial forces. It is a dimensionless number.

It is given by, 

$F_{\nu }=\frac{V}{\sqrt{gD}}$

Where,

• $F_{\nu }$= Froude number
• $V$= Velocity of the flow
• $D$= Hydraulic depth =$\frac{wetted area}{top width}$

Subcritical flow occurs when the Froude number is less than 1. In it, the bottom of the channel is large, and the rate of flow is very low. Therefore, the hydraulic jump does not occur. When the discharge and cross-section are uniform, the flow regime becomes the slope of the channel. For subcritical flow, the slope should be subcritical.

Supercritical flow- Supercritical flow occurs when the Froude number is greater than 1. This flow comprises low channel bottom and high flow rate, which result in the hydraulic jump. The hydraulic jump occurs when the slope changes from supercritical to subcritical.

Critical flow- In critical flow, the Froude number is equal to 1. For this flow to occur, the channel slope should be equal to the critical slope.

Discharge in open-channel flow

In open channel flow, velocity and discharge are measured by two equations.

Chezy equation

Chezy equation is given by,

$V=C·\sqrt{RS}$

Where,

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

Manning's equation

Manning's equation is given by,

                                  $V=\frac{1}{n}{R}^{\frac{2}{3}}\sqrt{S}$

Where,

$n$=manning's roughness coefficient.

The discharge of fluid in open channel is measured by flume. A flume is a static structure that governs the flow of water. Short throated flume is used to measure volumetric discharge in open channel flow. The velocity profile in open channel flow is not constant. Velocity changes from zero to maximum according to the depth of water, and velocity difference creates resistance in the flow.

Specific energy in open channel flow

Energy in a fluid flow is often described by the Bernoulli equation, where the work and energy theorem is applied. It is used to describe specific energy equations. Applying the Bernoulli equation at any point gives the sum of the vertical distance from datum, kinetic energy, and flow depth. The velocity and forces are calculated by the momentum equation. The energy grade line is given by,

$H=z+y+\frac{V^2}{2g}$

Where, 

• $H$= total energy 
• $y$= flow depth 
• $z$= horizontal datum 
• $V$= velocity of flow

Now, suppose the pressure is hydrostatic and the channel bottom is 0, then the total head above the channel bottom is defined as the specific energy.

$E=y+\frac{V^2}{2g}$

Now by using continuity equation, that is, Q=VA specific energy is given by,

$E=y+\frac{Q^2}{2g A^2}$

In a constant discharge situation, there are two depths possible with the same specific energy. These two depths are called alternate depth subscripts (y1, y2). The following discharge is derived by the momentum equation.

Most economical section

The most economical section is based upon the roughness, cross-section, and bed slope of the channel. For most economic sections, a designer chooses the channel with a minimum cross-section for the given discharge, slope, and flow rate. According to designers, the channel with the least wetted perimeter is the most economic one. The trapezoidal channel section has a hydraulic radius of half of the flow depth. Hence, it is the most economical section.

HEC-RAS

Hydrological Engineering Centre- River Analysis System is a one-dimensional hydraulic modeling program that helps in making models of natural rivers and water surface profiles. It also helps in flood management, dam breach analysis, environmental impact assessment, and so on.

Context and Applications

The study of open channel flow plays a major role in analyzing the water flow through various shaped conduits and how to control it. It helps in water treatment plants, irrigation, and helps in managing water throughout the year for usage purposes. By studying the discharge and velocity through open channel, one could analyze the amount of fluid that can be utilized for a particular city or village.

Courses in which open channel flow is studied are:

• Bachelors in Technology (Civil Engineering)
• Masters of Technology (Civil Engineering)

Practice Problems

Q1)What is the most economical channel?

1. Circle
2. Rectangular
3. Trapezoidal
4. Square

Correct option- c

Explanation- Trapezoidal section is the most economical section, as its hydraulics radius is half the flow depth of its depth.

Q2) Which of the following instruments is used to measure discharge in open channel flow?

1. Orifice
2. Flume
3. Venturi meter
4. U shaped venturi meter 

Correct option- b

Explanation- Flume is used to measure the discharge in an open channel flow, as they are static and restrict water flow.

Q3) Which of the following spillway is used in open channel flow?

1. Chute
2. Shaft
3. Ogee
4. Siphon

Correct option- a

Explanation- Chute spillway is used in open channel flow as they are dammed spillway and use principles of open channel flow to prevent dam failure.

Q4) For what purpose, the HEC-RAS is used?

1. Structure analysis
2. Load calculations
3. Hydraulics modeling
4. Seismic analysis

Correct option- c

Explanation- HES-RAS is computer software used for the hydraulic modeling of rivers or streams.

Q5) Which of the following ratios correctly denotes the Froude number?

1. Inertial force to gravity force
2. Critical flow to subcritical slow
3. Inertial to viscous force
4. Gravity force to inertial forces

Correct option- d

Explanation- Froude number is denoted by the ratio of gravity force to inertial force.

Related Concepts

• Reynolds number
• Fluid mechanics
• Specific energy