## Open-channel Flow

##### Mannings Equation

**Learning Objectives:**

- Understand the concepts and equations used in open channel flow.
- Determine velocity and discharge using Manning's equation.

- An open channel is the one in which the stream is not completely enclosed by solid boundaries and therefore has a free surface subjected only to atmospheric pressure.
- Open channel flow includes rivers, canals, streams and open sewage systems.

#### Manning's Equation:

where,

Q = Discharge

n = Roughness coefficient

R$_H$ = Hydraulic Radius

A = Cross-sectional area of flow

K = 1.486 for USCS units, or 1.0 for SI units

**Solved Example: 9902-01**

A rectangular open channel carries a discharge of 15 cumecs at depth of flow of 1.5 m and bed slope as 1:1440. If the only slope is changed to 1:1000 with the same depth of flow, discharge will be:

A. 21.6 cumecs

B. 18.0 cumecs

C. 14.4 cumecs

D. 12.5 cumecs

According to the Manning's Equation, \[Q = \dfrac{K}{n}AR_H^{\frac{2}{3}}S^{\frac{1}{2}}\] which means, all other things kept same, $Q \propto \sqrt{S}$ \[\dfrac{Q_1}{Q_2} = \sqrt{\dfrac{S_1}{S_2}}\]

Correct Answer: **B**

**Solved Example: 9902-02**

A 1.2 m wide rectangular channel of bed slope 0.0004 and Manning's coefficient 0.01, carrying the discharge of 0.5 $m^3/s$. The normal depth of the channel is:

A. 0.13

B. 0.32

C. 0.43

D. 0.5

Correct Answer: **D**

##### Drag

**Learning Objectives:**

- To calculate drag coefficient for spheres, disks, and cylinders.

\[C_D = \dfrac{2FD}{\rho v^2A}\]

To see variation of drag coefficient over different Reynold's Number for sphere, disk and cylinders, please refer graph on page 202 of FE-Reference handbook.