The Chezy’s formula was given by the French hydrologist Antonie Chezy. He related the discharge (Q) of the water flowing through an open channel with the respective channel dimensions and slope of the bed.
Also Read: What is Open Channel Flow?
The Chezy’s formula for determination of discharge of water in open channels and methods to determine the Chezy’s constant are briefly explained in this article.
Chezy’s Formula for Open Channel Flow
For a steady uniform flow of liquid through an open channel, the rate of flow of fluid or the discharge is given by the formula:
This equation is called as Chezy’s Formula. Where, A is the area of flow of water, m is the hydraulic mean depth or hydraulic radius, ‘i’ is the slope of the bed and ‘C’ is the Chezy’s Constant.
In the above equation, the velocity is given by,
If ‘P’ is the wetter perimeter of the cross-section, then hydraulic mean depth or hydraulic radius is given by the formula, m = A/P;
The chezy formula is directly related to the:
- Frictional Coefficient (F)
- Reynolds Number
- Hydraulic Mean Depth
Determination of Chezy’s Constant by Empirical Formula
The chezy’s constant ‘C’ is a dimensionless quantity which can be calculated by three formulas, namely:
- Bazin Formula
- Ganguillet -Kutter Formula
- Manning’s Formula
1. Bazin Formula
This formula is developed in MKS units. The Basin formula is given by:
K = Bazin’s Constant; m = Hydraulic mean depth or hydraulic radius
The bazin’s constant is dependent on the roughness of the channel surface. More the roughness of the surface, higher is the value of Bazin’s Constant.
2. Ganguillet -Kutter Formula
This formula is developed in MKS units as
From the above equation, the roughness coefficient is given by ‘N’ which is called as Kutter’s Constant. The value of Kutter’s constant is also dependent on the roughness of the surface.
The slope of the bed is given by ‘i’ and the hydraulic mean depth or hydraulic radius is given by ‘m’.
3. Manning’s Formula
The Manning’s formula is given by:
Where ‘m’ is the hydraulic mean depth or hydraulic radius; ‘N’ is called as the Manning’s constant. For a normal range of slope and hydraulic depth, the value of manning’s constant and the Kutter’s formula remains the same.