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Diameter of Grain given Rugosity Coefficient Calculator

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✖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 sediment particle density to the density of water, indicating its heaviness.ⓘ Specific Gravity of Sediment [G]			+10% -10%
✖Self Cleansing Velocity refers to the minimum speed at which fluid must flow in a sewer to prevent sediment deposition and maintain a clear path.ⓘ Self Cleansing Velocity [v_s]			+10% -10%
✖The Rugosity Coefficient, also known as the Manning's n, quantifies surface roughness in channels, affecting flow velocity and resistance.ⓘ Rugosity Coefficient [n]			+10% -10%
✖The Hydraulic Mean Depth refers to the cross-sectional area of flow divided by the wetted perimeter, used to analyze fluid flow in channels.ⓘ Hydraulic Mean Depth [m]			+10% -10%

✖The Diameter of Particle is the straight-line distance across its widest point, typically measured in micrometers or millimeters.ⓘ Diameter of Grain given Rugosity Coefficient [d^']

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Formula

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Diameter of Grain given Rugosity Coefficient

Formula

d' = (\frac{1}{k \cdot (G - 1)}) \cdot {(\frac{v s \cdot n}{{(m)}^{\frac{1}{6}}})}^{2}

Example

0.113104 mm = (\frac{1}{0.04 \cdot (1.3 - 1)}) \cdot {(\frac{0.114 m/s \cdot 0.015}{{(10 m)}^{\frac{1}{6}}})}^{2}

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Diameter of Grain given Rugosity Coefficient Solution

STEP 0: Pre-Calculation Summary

Formula Used

Diameter of Particle = (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 Particle - (Measured in Meter) - The Diameter of Particle is the straight-line distance across its widest point, typically measured in micrometers or millimeters.
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 sediment particle density to the density of water, indicating its heaviness.
Self Cleansing Velocity - (Measured in Meter per Second) - Self Cleansing Velocity refers to the minimum speed at which fluid must flow in a sewer to prevent sediment deposition and maintain a clear path.
Rugosity Coefficient - The Rugosity Coefficient, also known as the Manning's n, quantifies surface roughness in channels, affecting flow velocity and resistance.
Hydraulic Mean Depth - (Measured in Meter) - The Hydraulic Mean Depth refers to the cross-sectional area of flow divided by the wetted perimeter, used to analyze fluid flow in channels.

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: 0.114 Meter per Second --> 0.114 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)))*((0.114*0.015)/(10)^(1/6))^2

Evaluating ... ...

d^' = 0.000113103915903059

STEP 3: Convert Result to Output's Unit

0.000113103915903059 Meter -->0.113103915903059 Millimeter (Check conversion here)

FINAL ANSWER

0.113103915903059 ≈ 0.113104 Millimeter <-- Diameter of Particle

(Calculation completed in 00.004 seconds)

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Birsa Institute of Technology (BIT), Sindri

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< Diameter of Grain Calculators

Diameter of Grain given Rugosity Coefficient

Go Diameter of Particle = (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 Particle = (Self Cleansing Velocity)^2/((8*[g]*Dimensional Constant*(Specific Gravity of Sediment-1))/Friction Factor)

Diameter of Grain given Self Cleaning Invert Slope

Go Diameter of Particle = Self Cleaning Invert Slope/((Dimensional Constant/Hydraulic Mean Depth)*(Specific Gravity of Sediment-1))

Diameter of Grain given Self Cleansing velocity

Go Diameter of Particle = (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 Particle = (1/(Dimensional Constant*(Specific Gravity of Sediment-1)))*((Self Cleansing Velocity*Rugosity Coefficient)/(Hydraulic Mean Depth)^(1/6))^2 to calculate the Diameter of Particle, Diameter of Grain given Rugosity Coefficient is defined as the straight-line distance across its widest point, typically measured in micrometers or millimeters. Diameter of Particle 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 -> 113.1039 = (1/(0.04*(1.3-1)))*((0.114*0.015)/(10)^(1/6))^2.

FAQ

What is Diameter of Grain given Rugosity Coefficient?

Diameter of Grain given Rugosity Coefficient is defined as the straight-line distance across its widest point, typically measured in micrometers or millimeters and is represented as d^' = (1/(k*(G-1)))*((v_s*n)/(m)^(1/6))^2 or Diameter of Particle = (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 sediment particle density to the density of water, indicating its heaviness, Self Cleansing Velocity refers to the minimum speed at which fluid must flow in a sewer to prevent sediment deposition and maintain a clear path, The Rugosity Coefficient, also known as the Manning's n, quantifies surface roughness in channels, affecting flow velocity and resistance & The Hydraulic Mean Depth refers to the cross-sectional area of flow divided by the wetted perimeter, used to analyze fluid flow in channels.

How to calculate Diameter of Grain given Rugosity Coefficient?

Diameter of Grain given Rugosity Coefficient is defined as the straight-line distance across its widest point, typically measured in micrometers or millimeters is calculated using Diameter of Particle = (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 Particle?

In this formula, Diameter of Particle 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 Particle = Self Cleaning Invert Slope/((Dimensional Constant/Hydraulic Mean Depth)*(Specific Gravity of Sediment-1))
Diameter of Particle = (Self Cleansing Velocity/Chezy's Constant)^2/(Dimensional Constant*(Specific Gravity of Sediment-1))
Diameter of Particle = (Self Cleansing Velocity)^2/((8*[g]*Dimensional Constant*(Specific Gravity of Sediment-1))/Friction Factor)

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