Enter the roughness coefficient (n Value), slope, and hydraulic radius into the calculator to determine the velocity of water in an open channel using Kutter’s formula.
Kutter’s Formula
The following formula is used to calculate the velocity of water in an open channel.
V = (1.486 / n) * R^{(2/3)} * S^{(1/2)}Variables:
- V is the velocity of water in the channel (ft/s)
- n is the roughness coefficient (dimensionless)
- R is the hydraulic radius (ft)
- S is the slope of the channel bed (ft/ft)
To calculate the velocity of water in an open channel, divide 1.486 by the roughness coefficient, multiply by the hydraulic radius to the power of 2/3, and then multiply by the square root of the slope of the channel bed.
What is Kutter’s Formula?
Kutter’s formula is an empirical equation used to estimate the velocity of water in an open channel flow. It takes into account the roughness of the channel’s surface, the hydraulic radius which is the cross-sectional area of the flow divided by the wetted perimeter, and the slope of the channel bed. This formula is widely used in civil engineering for designing irrigation channels, drainage systems, and similar water conveyance structures.
How to Calculate Velocity using Kutter’s Formula?
The following steps outline how to calculate the velocity of water in an open channel using Kutter’s Formula.
- First, determine the roughness coefficient (n) of the channel’s surface.
- Next, determine the slope (S) of the channel bed in ft/ft.
- Next, determine the hydraulic radius (R) of the channel in feet.
- Next, gather the formula from above = V = (1.486 / n) * R^(2/3) * S^(1/2).
- Finally, calculate the velocity (V) in feet per second (ft/s).
- After inserting the variables and calculating the result, check your answer with the calculator above.
Example Problem :
Use the following variables as an example problem to test your knowledge.
n Value (roughness coefficient) = 0.013
Slope (S) = 0.0002 ft/ft
Hydraulic Radius (R) = 2 ft
