Manning's Equation Calculator

✖Manning’s Roughness Coefficient represents the roughness or friction applied to the flow by the channel.ⓘ Manning’s Roughness Coefficient [n]			+10% -10%
✖Hydraulic Radius is the ratio of the cross-sectional area of a channel or pipe in which a fluid is flowing to the wet perimeter of the conduit.ⓘ Hydraulic Radius [r_H]			+10% -10%
✖Bed Slope also called channel slope is the difference in elevation between two points on a stream divided by the distance between them measured along the stream channel.ⓘ Bed Slope [S̄]			+10% -10%

✖Stream Velocity is the speed of the water in the stream. It is greatest in midstream near the surface and is slowest along the stream bed and banks due to friction.ⓘ Manning's Equation [v]

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Formula

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Manning's Equation

Formula

`"v" = (1/"n")*("r"_{"H"})^(2/3)*("S̄")^(1/2)`

Example

`"1.822292m/s"=(1/"0.412")*("0.23m")^(2/3)*("4.0")^(1/2)`

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Manning's Equation Solution

STEP 0: Pre-Calculation Summary

Formula Used

Stream Velocity = (1/Manning’s Roughness Coefficient)*(Hydraulic Radius)^(2/3)*(Bed Slope)^(1/2)
v = (1/n)*(r_H)^(2/3)*(S̄)^(1/2)
This formula uses 4 Variables

Variables Used

Stream Velocity - (Measured in Meter per Second) - Stream Velocity is the speed of the water in the stream. It is greatest in midstream near the surface and is slowest along the stream bed and banks due to friction.
Manning’s Roughness Coefficient - Manning’s Roughness Coefficient represents the roughness or friction applied to the flow by the channel.
Hydraulic Radius - (Measured in Meter) - Hydraulic Radius is the ratio of the cross-sectional area of a channel or pipe in which a fluid is flowing to the wet perimeter of the conduit.
Bed Slope - Bed Slope also called channel slope is the difference in elevation between two points on a stream divided by the distance between them measured along the stream channel.

STEP 1: Convert Input(s) to Base Unit

Manning’s Roughness Coefficient: 0.412 --> No Conversion Required
Hydraulic Radius: 0.23 Meter --> 0.23 Meter No Conversion Required
Bed Slope: 4 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

v = (1/n)*(r_H)^(2/3)*(S̄)^(1/2) --> (1/0.412)*(0.23)^(2/3)*(4)^(1/2)

Evaluating ... ...

v = 1.82229214707637

STEP 3: Convert Result to Output's Unit

1.82229214707637 Meter per Second --> No Conversion Required

FINAL ANSWER

1.82229214707637 ≈ 1.822292 Meter per Second <-- Stream Velocity

(Calculation completed in 00.020 seconds)

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< 4 Manning's Equation Calculators

Manning's Equation

Go Stream Velocity = (1/Manning’s Roughness Coefficient)*(Hydraulic Radius)^(2/3)*(Bed Slope)^(1/2)

Hydraulic Radius using Manning Equation

Go Hydraulic Radius = ((Stream Velocity*Manning’s Roughness Coefficient)/(Bed Slope^(1/2)))^(3/2)

Slope of Gradient of Stream Bed given Discharge in Manning's Equation

Go Bed Slope = ((Stream Velocity*Manning’s Roughness Coefficient)/Hydraulic Radius^(2/3))^2

Hydraulic radius in Manning's formula

Go Hydraulic Radius = Cross-Sectional Area/Wetted Perimeter

Manning's Equation Formula

Stream Velocity = (1/Manning’s Roughness Coefficient)*(Hydraulic Radius)^(2/3)*(Bed Slope)^(1/2)
v = (1/n)*(r_H)^(2/3)*(S̄)^(1/2)

What is Manning's Equation & limitations of Manning's Equation?

Manning's equation is an empirical equation that applies to uniform flow in open channels and is a function of the channel velocity, flow area and channel slope. Under the assumption of uniform flow conditions, the bottom slope is the same as the slope of the energy grade line and the water surface slope.
Some limitations of Manning's Equation include the assumption of steady flow, uniform flow conditions, and the need for accurate estimation of the roughness coefficient. It may not be suitable for complex flow systems with non-uniform flow conditions.

What does a greater Hydraulic Radius indicate & where it is used?

The Hydraulic Radius indicates a channel's flow efficiency. The greater the hydraulic radius, the channel the more volume it can carry.
The hydraulic radius is one of the main properties that control the amount of fluid discharge of a channel and its ability to move sediments. A high hydraulic radius value indicates that the channel contains a lower volume of contact fluid and a greater cross-sectional area.

How to Calculate Manning's Equation?

Manning's Equation calculator uses Stream Velocity = (1/Manning’s Roughness Coefficient)*(Hydraulic Radius)^(2/3)*(Bed Slope)^(1/2) to calculate the Stream Velocity, The Manning's Equation formula is defined as the computation of the flow of water in open non-full channels and pipes without the need for a flume, weir, or other structure. Stream Velocity is denoted by v symbol.

How to calculate Manning's Equation using this online calculator? To use this online calculator for Manning's Equation, enter Manning’s Roughness Coefficient (n), Hydraulic Radius (r_H) & Bed Slope (S̄) and hit the calculate button. Here is how the Manning's Equation calculation can be explained with given input values -> 1.848607 = (1/0.412)*(0.23)^(2/3)*(4)^(1/2).

FAQ

What is Manning's Equation?

The Manning's Equation formula is defined as the computation of the flow of water in open non-full channels and pipes without the need for a flume, weir, or other structure and is represented as v = (1/n)*(r_H)^(2/3)*(S̄)^(1/2) or Stream Velocity = (1/Manning’s Roughness Coefficient)*(Hydraulic Radius)^(2/3)*(Bed Slope)^(1/2). Manning’s Roughness Coefficient represents the roughness or friction applied to the flow by the channel, Hydraulic Radius is the ratio of the cross-sectional area of a channel or pipe in which a fluid is flowing to the wet perimeter of the conduit & Bed Slope also called channel slope is the difference in elevation between two points on a stream divided by the distance between them measured along the stream channel.

How to calculate Manning's Equation?

The Manning's Equation formula is defined as the computation of the flow of water in open non-full channels and pipes without the need for a flume, weir, or other structure is calculated using Stream Velocity = (1/Manning’s Roughness Coefficient)*(Hydraulic Radius)^(2/3)*(Bed Slope)^(1/2). To calculate Manning's Equation, you need Manning’s Roughness Coefficient (n), Hydraulic Radius (r_H) & Bed Slope (S̄). With our tool, you need to enter the respective value for Manning’s Roughness Coefficient, Hydraulic Radius & Bed Slope and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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