Diameter of Grain for given Friction Factor Calculator

✖Self Cleansing Velocity is the rate of change of displacement.ⓘ Self Cleansing Velocity [V_s]			+10% -10%
✖Acceleration due to Gravity is acceleration gained by an object because of gravitational force.ⓘ Acceleration due to Gravity [g]			+10% -10%
✖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%
✖The Friction factor or Moody chart is the plot of the relative roughness (e/D) of a pipe against Reynold's number.ⓘ Friction Factor [f]			+10% -10%

✖Diameter of the grain means the diameter of the particle of sediments.ⓘ Diameter of Grain for given Friction Factor [d^']

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Formula

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Diameter of Grain for given Friction Factor

Formula

`"d"^{"'"} = ("V"_{"s"})^2/((8*"g"*"k"*("G"-1))/"f")`

Example

`"2.678571m"=("2m/s")^2/((8*"9.8m/s²"*"0.04"*("1.3"-1))/"0.63")`

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Diameter of Grain for given Friction Factor Solution

STEP 0: Pre-Calculation Summary

Formula Used

Diameter of the grain = (Self Cleansing Velocity)^2/((8*Acceleration due to Gravity*Dimensional constant*(Specific gravity of sediment-1))/Friction Factor)
d^' = (V_s)^2/((8*g*k*(G-1))/f)
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.
Self Cleansing Velocity - (Measured in Meter per Second) - Self Cleansing Velocity is the rate of change of displacement.
Acceleration due to Gravity - (Measured in Meter per Square Second) - Acceleration due to Gravity is acceleration gained by an object because of gravitational force.
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.
Friction Factor - The Friction factor or Moody chart is the plot of the relative roughness (e/D) of a pipe against Reynold's number.

STEP 1: Convert Input(s) to Base Unit

Self Cleansing Velocity: 2 Meter per Second --> 2 Meter per Second No Conversion Required
Acceleration due to Gravity: 9.8 Meter per Square Second --> 9.8 Meter per Square Second No Conversion Required
Dimensional constant: 0.04 --> No Conversion Required
Specific gravity of sediment: 1.3 --> No Conversion Required
Friction Factor: 0.63 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

d^' = (V_s)^2/((8*g*k*(G-1))/f) --> (2)^2/((8*9.8*0.04*(1.3-1))/0.63)

Evaluating ... ...

d^' = 2.67857142857143

STEP 3: Convert Result to Output's Unit

2.67857142857143 Meter --> No Conversion Required

FINAL ANSWER

2.67857142857143 ≈ 2.678571 Meter <-- Diameter of the grain

(Calculation completed in 00.020 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 for given Friction Factor

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Created by Suraj Kumar

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 for given Friction Factor Formula

Diameter of the grain = (Self Cleansing Velocity)^2/((8*Acceleration due to Gravity*Dimensional constant*(Specific gravity of sediment-1))/Friction Factor)
d^' = (V_s)^2/((8*g*k*(G-1))/f)

What is friction factor ?

The friction factor is representing the loss of pressure of a fluid in a pipe due to the interactions in between the fluid and the pipe.

How to Calculate Diameter of Grain for given Friction Factor?

Diameter of Grain for given Friction Factor calculator uses Diameter of the grain = (Self Cleansing Velocity)^2/((8*Acceleration due to Gravity*Dimensional constant*(Specific gravity of sediment-1))/Friction Factor) to calculate the Diameter of the grain, The diameter of Grain for given Friction Factor calculates the diameter of the grain particles of sediments. Diameter of the grain is denoted by d^' symbol.

How to calculate Diameter of Grain for given Friction Factor using this online calculator? To use this online calculator for Diameter of Grain for given Friction Factor, enter Self Cleansing Velocity (V_s), Acceleration due to Gravity (g), Dimensional constant (k), Specific gravity of sediment (G) & Friction Factor (f) and hit the calculate button. Here is how the Diameter of Grain for given Friction Factor calculation can be explained with given input values -> 2.55102 = (2)^2/((8*9.8*0.04*(1.3-1))/0.63).

FAQ

What is Diameter of Grain for given Friction Factor?

The diameter of Grain for given Friction Factor calculates the diameter of the grain particles of sediments and is represented as d^' = (V_s)^2/((8*g*k*(G-1))/f) or Diameter of the grain = (Self Cleansing Velocity)^2/((8*Acceleration due to Gravity*Dimensional constant*(Specific gravity of sediment-1))/Friction Factor). Self Cleansing Velocity is the rate of change of displacement, Acceleration due to Gravity is acceleration gained by an object because of gravitational force, 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 & The Friction factor or Moody chart is the plot of the relative roughness (e/D) of a pipe against Reynold's number.

How to calculate Diameter of Grain for given Friction Factor?

The diameter of Grain for given Friction Factor calculates the diameter of the grain particles of sediments is calculated using Diameter of the grain = (Self Cleansing Velocity)^2/((8*Acceleration due to Gravity*Dimensional constant*(Specific gravity of sediment-1))/Friction Factor). To calculate Diameter of Grain for given Friction Factor, you need Self Cleansing Velocity (V_s), Acceleration due to Gravity (g), Dimensional constant (k), Specific gravity of sediment (G) & Friction Factor (f). With our tool, you need to enter the respective value for Self Cleansing Velocity, Acceleration due to Gravity, Dimensional constant, Specific gravity of sediment & Friction Factor 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 Self Cleansing Velocity, Acceleration due to Gravity, Dimensional constant, Specific gravity of sediment & Friction Factor. 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 = (1/(Dimensional constant*(Specific gravity of sediment-1)))*(Self Cleansing Velocity*Rugosity coefficient/(Hydraulic mean depth)^(1/6))^2

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