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Ratio of Bed Slope given Velocity Ratio Calculator

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Bed Slope of Circular Sewer Area of Cross Section of Circular Sewer Discharge and Discharge Ratio through Circular Sewer Flow Velocity through Circular Sewer

✖The Velocity Ratio compares the flow velocity in a partially full pipe to that in a fully running pipe.ⓘ Velocity Ratio [νsV_ratio]			+10% -10%
✖The Roughness Coefficient for Running Full accounts for uniform surface resistance affecting flow velocity and friction loss.ⓘ Roughness Coefficient for Running Full [N]			+10% -10%
✖Roughness Coefficient Partially Full means roughness coefficient of pipe while running partially full.ⓘ Roughness Coefficient Partially Full [n_p]			+10% -10%
✖Hydraulic Mean Depth for Partially Full refers to the cross-sectional area of flow divided by the wetted perimeter, adapting to varying water levels.ⓘ Hydraulic Mean Depth for Partially Full [r_pf]			+10% -10%
✖Hydraulic Mean Depth while Running Full refers to the ratio of the pipe's full cross-sectional area to its full wetted perimeter.ⓘ Hydraulic Mean Depth while Running Full [R_rf]			+10% -10%

✖The Bed Slope Ratio refers to the slope of a partially full pipe to the slope when it is completely full.ⓘ Ratio of Bed Slope given Velocity Ratio [S]

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Formula

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Ratio of Bed Slope given Velocity Ratio

Formula

S = {(\frac{νsV ratio}{(\frac{N}{n p}) \cdot {(\frac{r pf}{R rf})}^{\frac{2}{3}}})}^{2}

Example

1.63225 = {(\frac{0.76}{(\frac{0.74}{0.9}) \cdot {(\frac{3.2 m}{5.2 m})}^{\frac{2}{3}}})}^{2}

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Download Proportionate Hydraulic Elements for Circular Sewers Formulas PDF PDF Image

Ratio of Bed Slope given Velocity Ratio Solution

STEP 0: Pre-Calculation Summary

Formula Used

Bed Slope Ratio = (Velocity Ratio/((Roughness Coefficient for Running Full/Roughness Coefficient Partially Full)*(Hydraulic Mean Depth for Partially Full/Hydraulic Mean Depth while Running Full)^(2/3)))^2
S = (νsV_ratio/((N/n_p)*(r_pf/R_rf)^(2/3)))^2
This formula uses 6 Variables

Variables Used

Bed Slope Ratio - The Bed Slope Ratio refers to the slope of a partially full pipe to the slope when it is completely full.
Velocity Ratio - The Velocity Ratio compares the flow velocity in a partially full pipe to that in a fully running pipe.
Roughness Coefficient for Running Full - The Roughness Coefficient for Running Full accounts for uniform surface resistance affecting flow velocity and friction loss.
Roughness Coefficient Partially Full - Roughness Coefficient Partially Full means roughness coefficient of pipe while running partially full.
Hydraulic Mean Depth for Partially Full - (Measured in Meter) - Hydraulic Mean Depth for Partially Full refers to the cross-sectional area of flow divided by the wetted perimeter, adapting to varying water levels.
Hydraulic Mean Depth while Running Full - (Measured in Meter) - Hydraulic Mean Depth while Running Full refers to the ratio of the pipe's full cross-sectional area to its full wetted perimeter.

STEP 1: Convert Input(s) to Base Unit

Velocity Ratio: 0.76 --> No Conversion Required
Roughness Coefficient for Running Full: 0.74 --> No Conversion Required
Roughness Coefficient Partially Full: 0.9 --> No Conversion Required
Hydraulic Mean Depth for Partially Full: 3.2 Meter --> 3.2 Meter No Conversion Required
Hydraulic Mean Depth while Running Full: 5.2 Meter --> 5.2 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

S = (νsV_ratio/((N/n_p)*(r_pf/R_rf)^(2/3)))^2 --> (0.76/((0.74/0.9)*(3.2/5.2)^(2/3)))^2

Evaluating ... ...

S = 1.63224965092651

STEP 3: Convert Result to Output's Unit

1.63224965092651 --> No Conversion Required

FINAL ANSWER

1.63224965092651 ≈ 1.63225 <-- Bed Slope Ratio

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Environmental Engineering » Hydraulic Designs of Sewers and S. W. Drain Sections » Proportionate Hydraulic Elements for Circular Sewers » Bed Slope of Circular Sewer » Ratio of Bed Slope given Velocity Ratio

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Created by Suraj Kumar

Birsa Institute of Technology (BIT), Sindri

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< Bed Slope of Circular Sewer Calculators

Bed Slope for Partial Flow given Velocity Ratio

Go Bed Slope of Partial Flow = Bed Slope of Channel*(Velocity Ratio/((Roughness Coefficient for Running Full/Roughness Coefficient Partially Full)*(Hydraulic Mean Depth for Partially Full/Hydraulic Mean Depth while Running Full)^(2/3)))^2

Bed Slope for Full Flow given Velocity Ratio

Go Bed Slope of Channel = Bed Slope of Partial Flow/(Velocity Ratio/((Roughness Coefficient for Running Full/Roughness Coefficient Partially Full)*(Hydraulic Mean Depth for Partially Full/Hydraulic Mean Depth while Running Full)^(2/3)))^2

Bed Slope for Full Flow given Bed Slope for Partial Flow

Go Bed Slope of Channel = (Bed Slope of Partial Flow*Hydraulic Mean Depth for Partially Full)/Hydraulic Mean Depth while Running Full

Bed Slope for Partial Flow

Go Bed Slope of Partial Flow = (Hydraulic Mean Depth while Running Full*Bed Slope of Channel)/Hydraulic Mean Depth for Partially Full

Ratio of Bed Slope given Velocity Ratio Formula

What is Bed Slope?

The Slope of Bed is used to calculate the shear stress at the bed of an open channel containing fluid that is undergoing steady, uniform flow. It is widely used in river engineering.

How to Calculate Ratio of Bed Slope given Velocity Ratio?

Ratio of Bed Slope given Velocity Ratio calculator uses Bed Slope Ratio = (Velocity Ratio/((Roughness Coefficient for Running Full/Roughness Coefficient Partially Full)*(Hydraulic Mean Depth for Partially Full/Hydraulic Mean Depth while Running Full)^(2/3)))^2 to calculate the Bed Slope Ratio, The Ratio of Bed Slope given Velocity Ratio calculates the ratio of bed slope of partial flow to bed slope of full flow. Bed Slope Ratio is denoted by S symbol.

How to calculate Ratio of Bed Slope given Velocity Ratio using this online calculator? To use this online calculator for Ratio of Bed Slope given Velocity Ratio, enter Velocity Ratio (νsV_ratio), Roughness Coefficient for Running Full (N), Roughness Coefficient Partially Full (n_p), Hydraulic Mean Depth for Partially Full (r_pf) & Hydraulic Mean Depth while Running Full (R_rf) and hit the calculate button. Here is how the Ratio of Bed Slope given Velocity Ratio calculation can be explained with given input values -> 11.30367 = (velocity_ratio_/((0.74/0.9)*(3.2/5.2)^(2/3)))^2.

FAQ

What is Ratio of Bed Slope given Velocity Ratio?

The Ratio of Bed Slope given Velocity Ratio calculates the ratio of bed slope of partial flow to bed slope of full flow and is represented as S = (νsV_ratio/((N/n_p)*(r_pf/R_rf)^(2/3)))^2 or Bed Slope Ratio = (Velocity Ratio/((Roughness Coefficient for Running Full/Roughness Coefficient Partially Full)*(Hydraulic Mean Depth for Partially Full/Hydraulic Mean Depth while Running Full)^(2/3)))^2. The Velocity Ratio compares the flow velocity in a partially full pipe to that in a fully running pipe, The Roughness Coefficient for Running Full accounts for uniform surface resistance affecting flow velocity and friction loss, Roughness Coefficient Partially Full means roughness coefficient of pipe while running partially full, Hydraulic Mean Depth for Partially Full refers to the cross-sectional area of flow divided by the wetted perimeter, adapting to varying water levels & Hydraulic Mean Depth while Running Full refers to the ratio of the pipe's full cross-sectional area to its full wetted perimeter.

How to calculate Ratio of Bed Slope given Velocity Ratio?

The Ratio of Bed Slope given Velocity Ratio calculates the ratio of bed slope of partial flow to bed slope of full flow is calculated using Bed Slope Ratio = (Velocity Ratio/((Roughness Coefficient for Running Full/Roughness Coefficient Partially Full)*(Hydraulic Mean Depth for Partially Full/Hydraulic Mean Depth while Running Full)^(2/3)))^2. To calculate Ratio of Bed Slope given Velocity Ratio, you need Velocity Ratio (νsV_ratio), Roughness Coefficient for Running Full (N), Roughness Coefficient Partially Full (n_p), Hydraulic Mean Depth for Partially Full (r_pf) & Hydraulic Mean Depth while Running Full (R_rf). With our tool, you need to enter the respective value for Velocity Ratio, Roughness Coefficient for Running Full, Roughness Coefficient Partially Full, Hydraulic Mean Depth for Partially Full & Hydraulic Mean Depth while Running Full 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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