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Diameter of Grain for given Friction Factor 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{{(v s)}^{2}}{\frac{8 \cdot [g] \cdot k \cdot (G - 1)}{f'}}

d^' - Diameter of Particle?v_s - Self Cleansing Velocity?k - Dimensional Constant?G - Specific Gravity of Sediment?f' - Friction Factor?[g] - Gravitational acceleration on Earth?

Diameter of Grain for given Friction Factor Example

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Here is how the Diameter of Grain for given Friction Factor equation looks like with Values.

Here is how the Diameter of Grain for given Friction Factor equation looks like with Units.

Here is how the Diameter of Grain for given Friction Factor equation looks like.

4.8039 = \frac{{(0.114)}^{2}}{\frac{8 \cdot 9.8066 \cdot 0.04 \cdot (1.3 - 1)}{0.348}}

4.8039mm = \frac{{(0.114m/s)}^{2}}{\frac{8 \cdot 9.8066m/s² \cdot 0.04 \cdot (1.3 - 1)}{0.348}}

4.8039 = \frac{{(0.114)}^{2}}{\frac{8 \cdot 9.8066 \cdot 0.04 \cdot (1.3 - 1)}{0.348}}

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Diameter of Grain for given Friction Factor Solution

Follow our step by step solution on how to calculate Diameter of Grain for given Friction Factor?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

d' = \frac{{(0.114m/s)}^{2}}{\frac{8 \cdot [g] \cdot 0.04 \cdot (1.3 - 1)}{0.348}}

Next Step Substitute values of Constants

∴

d' = \frac{{(0.114m/s)}^{2}}{\frac{8 \cdot 9.8066m/s² \cdot 0.04 \cdot (1.3 - 1)}{0.348}}

Next Step Prepare to Evaluate

∴

d' = \frac{{(0.114)}^{2}}{\frac{8 \cdot 9.8066 \cdot 0.04 \cdot (1.3 - 1)}{0.348}}

Next Step Evaluate

∴

d' = 0.00480393406514967m

Next Step Convert to Output's Unit

∴

d' = 4.80393406514967mm

LAST Step Rounding Answer

∴

d' = 4.8039mm

Diameter of Grain for given Friction Factor Formula Elements

Variables

Constants

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

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

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

Friction Factor

The Friction Factor quantifies resistance to flow in a pipe due to surface roughness, impacting energy loss and velocity.

Symbol: f'

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Friction Factor

Gravitational acceleration on Earth

Gravitational acceleration on Earth means that the velocity of an object in free fall will increase by 9.8 m/s2 every second.

Symbol: [g]

Value: 9.80665 m/s²

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 given Rugosity Coefficient

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

How to Evaluate Diameter of Grain for given Friction Factor?

Diameter of Grain for given Friction Factor evaluator uses Diameter of Particle = (Self Cleansing Velocity)^2/((8*[g]*Dimensional Constant*(Specific Gravity of Sediment-1))/Friction Factor) to evaluate the Diameter of Particle, The diameter of Grain for given Friction Factor 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 for given Friction Factor using this online evaluator? To use this online evaluator for Diameter of Grain for given Friction Factor, enter Self Cleansing Velocity (v_s), Dimensional Constant (k), Specific Gravity of Sediment (G) & Friction Factor (f') and hit the calculate button.

FAQs on Diameter of Grain for given Friction Factor

What is the formula to find Diameter of Grain for given Friction Factor?

The formula of Diameter of Grain for given Friction Factor is expressed as Diameter of Particle = (Self Cleansing Velocity)^2/((8*[g]*Dimensional Constant*(Specific Gravity of Sediment-1))/Friction Factor). Here is an example- 4803.934 = (0.114)^2/((8*[g]*0.04*(1.3-1))/0.348).

How to calculate Diameter of Grain for given Friction Factor?

With Self Cleansing Velocity (v_s), Dimensional Constant (k), Specific Gravity of Sediment (G) & Friction Factor (f') we can find Diameter of Grain for given Friction Factor using the formula - Diameter of Particle = (Self Cleansing Velocity)^2/((8*[g]*Dimensional Constant*(Specific Gravity of Sediment-1))/Friction Factor). This formula also uses Gravitational acceleration on Earth constant(s).

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=(1/(Dimensional Constant*(Specific Gravity of Sediment-1)))*((Self Cleansing Velocity*Rugosity Coefficient)/(Hydraulic Mean Depth)^(1/6))^2

Can the Diameter of Grain for given Friction Factor be negative?

No, the Diameter of Grain for given Friction Factor, measured in Length cannot be negative.

Which unit is used to measure Diameter of Grain for given Friction Factor?

Diameter of Grain for given Friction Factor 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 for given Friction Factor can be measured.

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Diameter of Grain for given Friction Factor Formula

​GoDiameter of Grain given Self Cleaning Invert Slope Formula

​GoDiameter of Grain given Self Cleansing velocity Formula

Diameter of Grain for given Friction Factor Example

Diameter of Grain for given Friction Factor Solution

Diameter of Grain for given Friction Factor Formula Elements

Other Formulas to find Diameter of Particle

How to Evaluate Diameter of Grain for given Friction Factor?

FAQs on Diameter of Grain for given Friction Factor

Variable Name

GoDiameter of Grain given Self Cleaning Invert Slope Formula

GoDiameter of Grain given Self Cleansing velocity Formula