Hydraulic Radius using Manning Equation Calculator

✖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.ⓘ Stream Velocity [v]			+10% -10%
✖Manning’s Roughness Coefficient represents the roughness or friction applied to the flow by the channel.ⓘ Manning’s Roughness Coefficient [n]			+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%

✖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 using Manning Equation [r_H]

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Formula

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Hydraulic Radius using Manning Equation

Formula

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

Example

`"0.310729m"=(("2.227m/s"*"0.412")/(("4.0")^(1/2)))^(3/2)`

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Hydraulic Radius using Manning Equation Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Variables Used

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.
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.
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

Stream Velocity: 2.227 Meter per Second --> 2.227 Meter per Second No Conversion Required
Manning’s Roughness Coefficient: 0.412 --> No Conversion Required
Bed Slope: 4 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_H = ((v*n)/(S̄^(1/2)))^(3/2) --> ((2.227*0.412)/(4^(1/2)))^(3/2)

Evaluating ... ...

r_H = 0.310728548336497

STEP 3: Convert Result to Output's Unit

0.310728548336497 Meter --> No Conversion Required

FINAL ANSWER

0.310728548336497 ≈ 0.310729 Meter <-- Hydraulic Radius

(Calculation completed in 00.004 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

Hydraulic Radius using Manning Equation Formula

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

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 Hydraulic Radius using Manning Equation?

Hydraulic Radius using Manning Equation calculator uses Hydraulic Radius = ((Stream Velocity*Manning’s Roughness Coefficient)/(Bed Slope^(1/2)))^(3/2) to calculate the Hydraulic Radius, The Hydraulic Radius using Manning Equation formula is defined as the ratio of the cross-sectional area A of flow to the wetted perimeter P of the channel or pipe influenced by the parameters of discharge, roughness coefficient and geometry of the water body. Hydraulic Radius is denoted by r_H symbol.

How to calculate Hydraulic Radius using Manning Equation using this online calculator? To use this online calculator for Hydraulic Radius using Manning Equation, enter Stream Velocity (v), Manning’s Roughness Coefficient (n) & Bed Slope (S̄) and hit the calculate button. Here is how the Hydraulic Radius using Manning Equation calculation can be explained with given input values -> 0.310729 = ((2.227*0.412)/(4^(1/2)))^(3/2).

FAQ

What is Hydraulic Radius using Manning Equation?

The Hydraulic Radius using Manning Equation formula is defined as the ratio of the cross-sectional area A of flow to the wetted perimeter P of the channel or pipe influenced by the parameters of discharge, roughness coefficient and geometry of the water body and is represented as r_H = ((v*n)/(S̄^(1/2)))^(3/2) or Hydraulic Radius = ((Stream Velocity*Manning’s Roughness Coefficient)/(Bed Slope^(1/2)))^(3/2). 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 represents the roughness or friction applied to the flow by the channel & 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 Hydraulic Radius using Manning Equation?

The Hydraulic Radius using Manning Equation formula is defined as the ratio of the cross-sectional area A of flow to the wetted perimeter P of the channel or pipe influenced by the parameters of discharge, roughness coefficient and geometry of the water body is calculated using Hydraulic Radius = ((Stream Velocity*Manning’s Roughness Coefficient)/(Bed Slope^(1/2)))^(3/2). To calculate Hydraulic Radius using Manning Equation, you need Stream Velocity (v), Manning’s Roughness Coefficient (n) & Bed Slope (S̄). With our tool, you need to enter the respective value for Stream Velocity, Manning’s Roughness Coefficient & Bed Slope and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Hydraulic Radius?

In this formula, Hydraulic Radius uses Stream Velocity, Manning’s Roughness Coefficient & Bed Slope. We can use 1 other way(s) to calculate the same, which is/are as follows -

Hydraulic Radius = Cross-Sectional Area/Wetted Perimeter

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