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Diameter of Grain given Rugosity Coefficient Formula

GoDiameter of Grain given Self Cleaning Invert Slope Formula

GoDiameter of Grain given Self Cleansing velocity Formula

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The Diameter of Particle is the straight-line distance across its widest point, typically measured in micrometers or millimeters. Check FAQs

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

d^' - Diameter of Particle?k - Dimensional Constant?G - Specific Gravity of Sediment?v_s - Self Cleansing Velocity?n - Rugosity Coefficient?m - Hydraulic Mean Depth?

Diameter of Grain given Rugosity Coefficient Example

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Here is how the Diameter of Grain given Rugosity Coefficient equation looks like with Values.

Here is how the Diameter of Grain given Rugosity Coefficient equation looks like with Units.

Here is how the Diameter of Grain given Rugosity Coefficient equation looks like.

0.1131 = (\frac{1}{0.04 \cdot (1.3 - 1)}) \cdot {(\frac{0.114 \cdot 0.015}{{(10)}^{\frac{1}{6}}})}^{2}

0.1131mm = (\frac{1}{0.04 \cdot (1.3 - 1)}) \cdot {(\frac{0.114m/s \cdot 0.015}{{(10m)}^{\frac{1}{6}}})}^{2}

0.1131 = (\frac{1}{0.04 \cdot (1.3 - 1)}) \cdot {(\frac{0.114 \cdot 0.015}{{(10)}^{\frac{1}{6}}})}^{2}

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Diameter of Grain given Rugosity Coefficient Solution

Follow our step by step solution on how to calculate Diameter of Grain given Rugosity Coefficient?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

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

Next Step Prepare to Evaluate

∴

d' = (\frac{1}{0.04 \cdot (1.3 - 1)}) \cdot {(\frac{0.114 \cdot 0.015}{{(10)}^{\frac{1}{6}}})}^{2}

Next Step Evaluate

∴

d' = 0.000113103915903059m

Next Step Convert to Output's Unit

∴

d' = 0.113103915903059mm

LAST Step Rounding Answer

∴

d' = 0.1131mm

Diameter of Grain given Rugosity Coefficient Formula Elements

Variables

Diameter of Particle

The Diameter of Particle is the straight-line distance across its widest point, typically measured in micrometers or millimeters.

Symbol: d^'

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Diameter of Particle

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).

Symbol: k

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Dimensional Constant

Specific Gravity of Sediment

Specific Gravity of Sediment is the ratio of sediment particle density to the density of water, indicating its heaviness.

Symbol: G

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Specific Gravity of Sediment

Self Cleansing Velocity

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.

Symbol: v_s

Measurement: SpeedUnit: m/s

Note: Value should be greater than 0.

Formulas to find Self Cleansing Velocity

Rugosity Coefficient

The Rugosity Coefficient, also known as the Manning's n, quantifies surface roughness in channels, affecting flow velocity and resistance.

Symbol: n

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Rugosity Coefficient

Hydraulic Mean Depth

The Hydraulic Mean Depth refers to the cross-sectional area of flow divided by the wetted perimeter, used to analyze fluid flow in channels.

Symbol: m

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Hydraulic Mean Depth

Other Formulas to find Diameter of Particle

Go Diameter of Grain given Self Cleaning Invert Slope

d' = \frac{sL I}{(\frac{k}{m}) \cdot (G - 1)}

Go Diameter of Grain given Self Cleansing velocity

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

Go Diameter of Grain for given Friction Factor

d' = \frac{{(v s)}^{2}}{\frac{8 \cdot [g] \cdot k \cdot (G - 1)}{f'}}

How to Evaluate Diameter of Grain given Rugosity Coefficient?

Diameter of Grain given Rugosity Coefficient evaluator uses Diameter of Particle = (1/(Dimensional Constant*(Specific Gravity of Sediment-1)))*((Self Cleansing Velocity*Rugosity Coefficient)/(Hydraulic Mean Depth)^(1/6))^2 to evaluate 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 evaluate Diameter of Grain given Rugosity Coefficient using this online evaluator? To use this online evaluator 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.

FAQs on Diameter of Grain given Rugosity Coefficient

What is the formula to find Diameter of Grain given Rugosity Coefficient?

The formula of Diameter of Grain given Rugosity Coefficient is expressed as Diameter of Particle = (1/(Dimensional Constant*(Specific Gravity of Sediment-1)))*((Self Cleansing Velocity*Rugosity Coefficient)/(Hydraulic Mean Depth)^(1/6))^2. Here is an example- 113.1039 = (1/(0.04*(1.3-1)))*((0.114*0.015)/(10)^(1/6))^2.

How to calculate Diameter of Grain given Rugosity Coefficient?

With Dimensional Constant (k), Specific Gravity of Sediment (G), Self Cleansing Velocity (v_s), Rugosity Coefficient (n) & Hydraulic Mean Depth (m) we can find Diameter of Grain given Rugosity Coefficient using the formula - Diameter of Particle = (1/(Dimensional Constant*(Specific Gravity of Sediment-1)))*((Self Cleansing Velocity*Rugosity Coefficient)/(Hydraulic Mean Depth)^(1/6))^2.

What are the other ways to Calculate Diameter of Particle?

Here are the different ways to Calculate Diameter of Particle-

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)

Can the Diameter of Grain given Rugosity Coefficient be negative?

No, the Diameter of Grain given Rugosity Coefficient, measured in Length cannot be negative.

Which unit is used to measure Diameter of Grain given Rugosity Coefficient?

Diameter of Grain given Rugosity Coefficient is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Diameter of Grain given Rugosity Coefficient can be measured.

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Diameter of Grain given Rugosity Coefficient Formula

​GoDiameter of Grain given Self Cleaning Invert Slope Formula

​GoDiameter of Grain given Self Cleansing velocity Formula

Diameter of Grain given Rugosity Coefficient Example

Diameter of Grain given Rugosity Coefficient Solution

Diameter of Grain given Rugosity Coefficient Formula Elements

Other Formulas to find Diameter of Particle

How to Evaluate Diameter of Grain given Rugosity Coefficient?

FAQs on Diameter of Grain given Rugosity Coefficient

Variable Name

GoDiameter of Grain given Self Cleaning Invert Slope Formula

GoDiameter of Grain given Self Cleansing velocity Formula