Diameter of Grain given Rugosity Coefficient Calculator

✖Dimensional constant indicates important characteristics of sediments present in the sewage. Its value usually varies from 0.04 (start of scouring of clean grit) to 0.08 (full removal of sticky grit).ⓘ Dimensional constant [k]			+10% -10%
✖Specific gravity of sediment is the ratio of density of sediment to density of standard substance.ⓘ Specific gravity of sediment [G]			+10% -10%
✖Self Cleansing Velocity is the rate of change of displacement.ⓘ Self Cleansing Velocity [V_s]			+10% -10%
✖Rugosity coefficient depend upon the type of channel surface.ⓘ Rugosity coefficient [n]			+10% -10%
✖The Hydraulic mean depth is defined as the area of the flow section divided by the top water surface width.ⓘ Hydraulic mean depth [m]			+10% -10%

✖Diameter of the grain means the diameter of the particle of sediments.ⓘ Diameter of Grain given Rugosity Coefficient [d^']

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Formula

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Diameter of Grain given Rugosity Coefficient

Formula

`"d"^{"'"} = (1/("k"*("G"-1)))*("V"_{"s"}*"n"/("m")^(1/6))^2`

Example

`"0.034812m"=(1/("0.04"*("1.3"-1)))*("2m/s"*"0.015"/("10m")^(1/6))^2`

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Diameter of Grain given Rugosity Coefficient Solution

STEP 0: Pre-Calculation Summary

Formula Used

Diameter of the grain = (1/(Dimensional constant*(Specific gravity of sediment-1)))*(Self Cleansing Velocity*Rugosity coefficient/(Hydraulic mean depth)^(1/6))^2
d^' = (1/(k*(G-1)))*(V_s*n/(m)^(1/6))^2
This formula uses 6 Variables

Variables Used

Diameter of the grain - (Measured in Meter) - Diameter of the grain means the diameter of the particle of sediments.
Dimensional constant - Dimensional constant indicates important characteristics of sediments present in the sewage. Its value usually varies from 0.04 (start of scouring of clean grit) to 0.08 (full removal of sticky grit).
Specific gravity of sediment - Specific gravity of sediment is the ratio of density of sediment to density of standard substance.
Self Cleansing Velocity - (Measured in Meter per Second) - Self Cleansing Velocity is the rate of change of displacement.
Rugosity coefficient - Rugosity coefficient depend upon the type of channel surface.
Hydraulic mean depth - (Measured in Meter) - The Hydraulic mean depth is defined as the area of the flow section divided by the top water surface width.

STEP 1: Convert Input(s) to Base Unit

Dimensional constant: 0.04 --> No Conversion Required
Specific gravity of sediment: 1.3 --> No Conversion Required
Self Cleansing Velocity: 2 Meter per Second --> 2 Meter per Second No Conversion Required
Rugosity coefficient: 0.015 --> No Conversion Required
Hydraulic mean depth: 10 Meter --> 10 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

d^' = (1/(k*(G-1)))*(V_s*n/(m)^(1/6))^2 --> (1/(0.04*(1.3-1)))*(2*0.015/(10)^(1/6))^2

Evaluating ... ...

d^' = 0.0348119162520958

STEP 3: Convert Result to Output's Unit

0.0348119162520958 Meter --> No Conversion Required

FINAL ANSWER

0.0348119162520958 ≈ 0.034812 Meter <-- Diameter of the grain

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Environmental Engineering » Hydraulic Designs of Sewers and S. W. Drain Sections » Minimum Velocity to be Generated in Sewers » Diameter of Grain » Diameter of Grain given Rugosity Coefficient

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Birsa Institute of Technology (BIT), Sindri

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< 4 Diameter of Grain Calculators

Diameter of Grain given Rugosity Coefficient

Go Diameter of the grain = (1/(Dimensional constant*(Specific gravity of sediment-1)))*(Self Cleansing Velocity*Rugosity coefficient/(Hydraulic mean depth)^(1/6))^2

Diameter of Grain for given Friction Factor

Go Diameter of the grain = (Self Cleansing Velocity)^2/((8*Acceleration due to Gravity*Dimensional constant*(Specific gravity of sediment-1))/Friction Factor)

Diameter of Grain given Self Cleaning Invert Slope

Go Diameter of the grain = Self Cleaning Invert Slope/((Dimensional constant/Hydraulic mean depth)*(Specific gravity of sediment-1))

Diameter of Grain given Self Cleansing velocity

Go Diameter of the grain = (Self Cleansing Velocity/Chezy's constant)^2/(Dimensional constant*(Specific gravity of sediment-1))

Diameter of Grain given Rugosity Coefficient Formula

What is specific gravity ?

Relative density, or specific gravity, is the ratio of the density of a substance to the density of a given reference material. Specific gravity for liquids is nearly always measured with respect to water at its densest; for gases, the reference is air at room temperature.

How to Calculate Diameter of Grain given Rugosity Coefficient?

Diameter of Grain given Rugosity Coefficient calculator uses Diameter of the grain = (1/(Dimensional constant*(Specific gravity of sediment-1)))*(Self Cleansing Velocity*Rugosity coefficient/(Hydraulic mean depth)^(1/6))^2 to calculate the Diameter of the grain, Diameter of Grain given Rugosity Coefficient calculates the diameter of the grain size of the sediments when we have prior information of other parameters. Diameter of the grain is denoted by d^' symbol.

How to calculate Diameter of Grain given Rugosity Coefficient using this online calculator? To use this online calculator for Diameter of Grain given Rugosity Coefficient, enter Dimensional constant (k), Specific gravity of sediment (G), Self Cleansing Velocity (V_s), Rugosity coefficient (n) & Hydraulic mean depth (m) and hit the calculate button. Here is how the Diameter of Grain given Rugosity Coefficient calculation can be explained with given input values -> 0.034812 = (1/(0.04*(1.3-1)))*(2*0.015/(10)^(1/6))^2.

FAQ

What is Diameter of Grain given Rugosity Coefficient?

Diameter of Grain given Rugosity Coefficient calculates the diameter of the grain size of the sediments when we have prior information of other parameters and is represented as d^' = (1/(k*(G-1)))*(V_s*n/(m)^(1/6))^2 or Diameter of the grain = (1/(Dimensional constant*(Specific gravity of sediment-1)))*(Self Cleansing Velocity*Rugosity coefficient/(Hydraulic mean depth)^(1/6))^2. Dimensional constant indicates important characteristics of sediments present in the sewage. Its value usually varies from 0.04 (start of scouring of clean grit) to 0.08 (full removal of sticky grit), Specific gravity of sediment is the ratio of density of sediment to density of standard substance, Self Cleansing Velocity is the rate of change of displacement, Rugosity coefficient depend upon the type of channel surface & The Hydraulic mean depth is defined as the area of the flow section divided by the top water surface width.

How to calculate Diameter of Grain given Rugosity Coefficient?

Diameter of Grain given Rugosity Coefficient calculates the diameter of the grain size of the sediments when we have prior information of other parameters is calculated using Diameter of the grain = (1/(Dimensional constant*(Specific gravity of sediment-1)))*(Self Cleansing Velocity*Rugosity coefficient/(Hydraulic mean depth)^(1/6))^2. To calculate Diameter of Grain given Rugosity Coefficient, you need Dimensional constant (k), Specific gravity of sediment (G), Self Cleansing Velocity (V_s), Rugosity coefficient (n) & Hydraulic mean depth (m). With our tool, you need to enter the respective value for Dimensional constant, Specific gravity of sediment, Self Cleansing Velocity, Rugosity coefficient & Hydraulic mean depth 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 Diameter of the grain?

In this formula, Diameter of the grain uses Dimensional constant, Specific gravity of sediment, Self Cleansing Velocity, Rugosity coefficient & Hydraulic mean depth. We can use 3 other way(s) to calculate the same, which is/are as follows -

Diameter of the grain = Self Cleaning Invert Slope/((Dimensional constant/Hydraulic mean depth)*(Specific gravity of sediment-1))
Diameter of the grain = (Self Cleansing Velocity/Chezy's constant)^2/(Dimensional constant*(Specific gravity of sediment-1))
Diameter of the grain = (Self Cleansing Velocity)^2/((8*Acceleration due to Gravity*Dimensional constant*(Specific gravity of sediment-1))/Friction Factor)

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