ANS:B - Manning

Chezy, Manning, Bazin, and Kutter are all empirical equations used to estimate the flow velocity in open channels such as rivers, streams, and sewers. These equations relate flow velocity to channel geometry, hydraulic roughness, and hydraulic parameters. Each equation has its own specific form and application, and they are used in different contexts depending on factors such as channel characteristics, flow conditions, and available data.

1. Chezy Equation: The Chezy equation is one of the oldest empirical equations used to estimate flow velocity in open channels. It was developed by the French engineer Antoine Chezy in the 18th century. The equation is expressed as: v=CRS​ Where:
   • v is the flow velocity
   • C is Chezy's coefficient (a dimensionless constant)
   • R is the hydraulic radius (the cross-sectional area of flow divided by the wetted perimeter)
   • S is the slope of the energy grade line
2. Manning Equation: The Manning equation is another widely used empirical equation for estimating flow velocity. It was developed by the Irish engineer Robert Manning in the 19th century. The equation is expressed as:v=n1​R2/3S1/2 Where:
   • v is the flow velocity
   • n is Manning's roughness coefficient (a dimensionless constant)
   • R is the hydraulic radius
   • S is the slope of the channel
3. Bazin Equation: The Bazin equation is a variation of the Chezy equation and is used for estimating flow velocity in open channels. It incorporates a roughness coefficient similar to Manning's equation. The equation is expressed as: v=CRS​(1+R1/6m​) Where:
   • v is the flow velocity
   • C is a coefficient (similar to Chezy's coefficient)
   • R is the hydraulic radius
   • S is the slope of the channel
   • m is a coefficient related to roughness
4. Kutter Equation: The Kutter equation is an empirical equation used for estimating flow velocity in open channels. It incorporates both roughness and geometric parameters. The equation is expressed as: v=n1​R2/3S1/2(1+R1/6k​) Where:
   • v is the flow velocity
   • n is Manning's roughness coefficient
   • R is the hydraulic radius
   • S is the slope of the channel
   • k is a coefficient related to the channel geometry

These equations are fundamental tools in hydraulic engineering for designing and analyzing open-channel flow systems. They provide engineers with a means to estimate flow velocities and predict hydraulic behavior in various types of channels under different conditions.