Slope of Gradient of Stream Bed given Discharge in Manning's 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%
✖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.ⓘ Slope of Gradient of Stream Bed given Discharge in Manning's Equation [S̄]

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Formula

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

Formula

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

Example

`"5.973989"=(("2.227m/s"*"0.412")/("0.23m")^(2/3))^2`

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

STEP 0: Pre-Calculation Summary

Formula Used

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

Variables Used

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.
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.

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
Hydraulic Radius: 0.23 Meter --> 0.23 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

S̄ = ((v*n)/r_H^(2/3))^2 --> ((2.227*0.412)/0.23^(2/3))^2

Evaluating ... ...

S̄ = 5.97398899333278

STEP 3: Convert Result to Output's Unit

5.97398899333278 --> No Conversion Required

FINAL ANSWER

5.97398899333278 ≈ 5.973989 <-- Bed Slope

(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

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

Bed Slope = ((Stream Velocity*Manning’s Roughness Coefficient)/Hydraulic Radius^(2/3))^2
S̄ = ((v*n)/r_H^(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 Slope of Gradient of Stream Bed given Discharge in Manning's Equation?

Slope of Gradient of Stream Bed given Discharge in Manning's Equation calculator uses Bed Slope = ((Stream Velocity*Manning’s Roughness Coefficient)/Hydraulic Radius^(2/3))^2 to calculate the Bed Slope, The Slope of Gradient of Stream Bed given Discharge in Manning's Equation formula is defined as the slope measured by the difference in elevation between two points on a stream divided by the distance between the two points that the water flows. Bed Slope is denoted by S̄ symbol.

How to calculate Slope of Gradient of Stream Bed given Discharge in Manning's Equation using this online calculator? To use this online calculator for Slope of Gradient of Stream Bed given Discharge in Manning's Equation, enter Stream Velocity (v), Manning’s Roughness Coefficient (n) & Hydraulic Radius (r_H) and hit the calculate button. Here is how the Slope of Gradient of Stream Bed given Discharge in Manning's Equation calculation can be explained with given input values -> 5.805118 = ((2.227*0.412)/0.23^(2/3))^2.

FAQ

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

The Slope of Gradient of Stream Bed given Discharge in Manning's Equation formula is defined as the slope measured by the difference in elevation between two points on a stream divided by the distance between the two points that the water flows and is represented as S̄ = ((v*n)/r_H^(2/3))^2 or Bed Slope = ((Stream Velocity*Manning’s Roughness Coefficient)/Hydraulic Radius^(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 & 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.

How to calculate Slope of Gradient of Stream Bed given Discharge in Manning's Equation?

The Slope of Gradient of Stream Bed given Discharge in Manning's Equation formula is defined as the slope measured by the difference in elevation between two points on a stream divided by the distance between the two points that the water flows is calculated using Bed Slope = ((Stream Velocity*Manning’s Roughness Coefficient)/Hydraulic Radius^(2/3))^2. To calculate Slope of Gradient of Stream Bed given Discharge in Manning's Equation, you need Stream Velocity (v), Manning’s Roughness Coefficient (n) & Hydraulic Radius (r_H). With our tool, you need to enter the respective value for Stream Velocity, Manning’s Roughness Coefficient & Hydraulic Radius 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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