Settling Velocity of Spherical Particle given Coefficient of Drag Calculator

✖Unit weight of particle is defined as weight per unit volume of the particle.ⓘ Unit weight of particle [γ_s]			+10% -10%
✖Unit Weight of Liquid is the weight of water per unit volume of water.ⓘ Unit Weight of Liquid [γ_w]			+10% -10%
✖Diameter of Partical is a straight line passing from side to side through the center of a partical, especially a circle or sphere.ⓘ Diameter of Partical [D_p]			+10% -10%
✖Water Density is mass per unit of water.ⓘ Water Density [ρ_water]			+10% -10%
✖Coefficient of Drag is a dimensionless quantity that is used to quantify the drag or resistance of an object in a fluid environment, such as air or water.ⓘ Coefficient of Drag [C_d]			+10% -10%

✖Settling velocity is defined as the terminal velocity of a particle in still fluid.ⓘ Settling Velocity of Spherical Particle given Coefficient of Drag [v_s]

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Formula

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Settling Velocity of Spherical Particle given Coefficient of Drag

Formula

`"v"_{"s"} = sqrt(((4/3)*("γ"_{"s"}-"γ"_{"w"})*"D"_{"p"})/("ρ"_{"water"}*"C"_{"d"}))`

Example

`"0.159164m/s"=sqrt(((4/3)*("10kN/m³"-"9810N/m³")*"0.01m")/("1000kg/m³"*"0.1"))`

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Settling Velocity of Spherical Particle given Coefficient of Drag Solution

STEP 0: Pre-Calculation Summary

Formula Used

Settling Velocity = sqrt(((4/3)*(Unit weight of particle-Unit Weight of Liquid)*Diameter of Partical)/(Water Density*Coefficient of Drag))
v_s = sqrt(((4/3)*(γ_s-γ_w)*D_p)/(ρ_water*C_d))
This formula uses 1 Functions, 6 Variables

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Settling Velocity - (Measured in Meter per Second) - Settling velocity is defined as the terminal velocity of a particle in still fluid.
Unit weight of particle - (Measured in Newton per Cubic Meter) - Unit weight of particle is defined as weight per unit volume of the particle.
Unit Weight of Liquid - (Measured in Newton per Cubic Meter) - Unit Weight of Liquid is the weight of water per unit volume of water.
Diameter of Partical - (Measured in Meter) - Diameter of Partical is a straight line passing from side to side through the center of a partical, especially a circle or sphere.
Water Density - (Measured in Kilogram per Cubic Meter) - Water Density is mass per unit of water.
Coefficient of Drag - Coefficient of Drag is a dimensionless quantity that is used to quantify the drag or resistance of an object in a fluid environment, such as air or water.

STEP 1: Convert Input(s) to Base Unit

Unit weight of particle: 10 Kilonewton per Cubic Meter --> 10000 Newton per Cubic Meter (Check conversion here)
Unit Weight of Liquid: 9810 Newton per Cubic Meter --> 9810 Newton per Cubic Meter No Conversion Required
Diameter of Partical: 0.01 Meter --> 0.01 Meter No Conversion Required
Water Density: 1000 Kilogram per Cubic Meter --> 1000 Kilogram per Cubic Meter No Conversion Required
Coefficient of Drag: 0.1 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

v_s = sqrt(((4/3)*(γ_s-γ_w)*D_p)/(ρ_water*C_d)) --> sqrt(((4/3)*(10000-9810)*0.01)/(1000*0.1))

Evaluating ... ...

v_s = 0.159164485150844

STEP 3: Convert Result to Output's Unit

0.159164485150844 Meter per Second --> No Conversion Required

FINAL ANSWER

0.159164485150844 ≈ 0.159164 Meter per Second <-- Settling Velocity

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Environmental Engineering » Treatment of Sewage » Theory of Type -1 Settling » Settling Velocity of Particle » Settling Velocity of Spherical Particle given Coefficient of Drag

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Created by Suraj Kumar

Birsa Institute of Technology (BIT), Sindri

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Verified by Ishita Goyal

Meerut Institute of Engineering and Technology (MIET), Meerut

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< 9 Settling Velocity of Particle Calculators

Settling Velocity of Spherical Particle given Coefficient of Drag

Go Settling Velocity = sqrt(((4/3)*(Unit weight of particle-Unit Weight of Liquid)*Diameter of Partical)/(Water Density*Coefficient of Drag))

Settling Velocity given Specific Gravity of Particle

Go Settling Velocity = sqrt(((4/3)*Acceleration due to Gravity*(Specific gravity of sediment-1)*Diameter of Partical)/Coefficient of Drag)

Settling Velocity with respect to Diameter of Particle

Go Settling Velocity = ((Acceleration due to Gravity*(Specific gravity of sediment-1)*(Diameter of Partical)^(1.6))/(13.88*(Kinematic Viscosity)^(0.6)))^(0.714)

Settling Velocity of Spherical Particle

Go Settling Velocity = (Acceleration due to Gravity/18)*(Specific gravity of sediment-1)*((Diameter of Partical)^2/Kinematic Viscosity)

Settling Velocity for Turbulent Settling

Go Settling Velocity = (1.8*sqrt(Acceleration due to Gravity*(Specific gravity of sediment-1)*Diameter of Partical))

Settling Velocity for Modified Hazen's Equation

Go Settling Velocity = (60.6*Diameter of Partical*(Specific gravity of sediment-1)*(((3*Temperature)+70)/100))

Settling Velocity of Spherical Particle given Reynold Number

Go Settling Velocity = (Reynolds Number*Kinematic Viscosity)/Diameter

Settling Velocity for Organic Matter

Go Settling velocity for organic solids = 0.12*Diameter of Partical*((3*Temperature)+70)

Settling Velocity for Inorganic Solids

Go Settling velocity for inorganic solids = (Diameter of Partical*((3*Temperature)+70))

Settling Velocity of Spherical Particle given Coefficient of Drag Formula

Settling Velocity = sqrt(((4/3)*(Unit weight of particle-Unit Weight of Liquid)*Diameter of Partical)/(Water Density*Coefficient of Drag))
v_s = sqrt(((4/3)*(γ_s-γ_w)*D_p)/(ρ_water*C_d))

What is settling velocity ?

The settling velocity (also referred to as the “sedimentation velocity”) is defined as the terminal velocity of a particle in still fluid

How to Calculate Settling Velocity of Spherical Particle given Coefficient of Drag?

Settling Velocity of Spherical Particle given Coefficient of Drag calculator uses Settling Velocity = sqrt(((4/3)*(Unit weight of particle-Unit Weight of Liquid)*Diameter of Partical)/(Water Density*Coefficient of Drag)) to calculate the Settling Velocity, Settling Velocity of Spherical Particle given Coefficient of Drag is defined as speed at which particle falls through still fluid. Settling Velocity is denoted by v_s symbol.

How to calculate Settling Velocity of Spherical Particle given Coefficient of Drag using this online calculator? To use this online calculator for Settling Velocity of Spherical Particle given Coefficient of Drag, enter Unit weight of particle (γ_s), Unit Weight of Liquid (γ_w), Diameter of Partical (D_p), Water Density (ρ_water) & Coefficient of Drag (C_d) and hit the calculate button. Here is how the Settling Velocity of Spherical Particle given Coefficient of Drag calculation can be explained with given input values -> 0.159164 = sqrt(((4/3)*(10000-9810)*0.01)/(1000*0.1)).

FAQ

What is Settling Velocity of Spherical Particle given Coefficient of Drag?

Settling Velocity of Spherical Particle given Coefficient of Drag is defined as speed at which particle falls through still fluid and is represented as v_s = sqrt(((4/3)*(γ_s-γ_w)*D_p)/(ρ_water*C_d)) or Settling Velocity = sqrt(((4/3)*(Unit weight of particle-Unit Weight of Liquid)*Diameter of Partical)/(Water Density*Coefficient of Drag)). Unit weight of particle is defined as weight per unit volume of the particle, Unit Weight of Liquid is the weight of water per unit volume of water, Diameter of Partical is a straight line passing from side to side through the center of a partical, especially a circle or sphere, Water Density is mass per unit of water & Coefficient of Drag is a dimensionless quantity that is used to quantify the drag or resistance of an object in a fluid environment, such as air or water.

How to calculate Settling Velocity of Spherical Particle given Coefficient of Drag?

Settling Velocity of Spherical Particle given Coefficient of Drag is defined as speed at which particle falls through still fluid is calculated using Settling Velocity = sqrt(((4/3)*(Unit weight of particle-Unit Weight of Liquid)*Diameter of Partical)/(Water Density*Coefficient of Drag)). To calculate Settling Velocity of Spherical Particle given Coefficient of Drag, you need Unit weight of particle (γ_s), Unit Weight of Liquid (γ_w), Diameter of Partical (D_p), Water Density (ρ_water) & Coefficient of Drag (C_d). With our tool, you need to enter the respective value for Unit weight of particle, Unit Weight of Liquid, Diameter of Partical, Water Density & Coefficient of Drag 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 Settling Velocity?

In this formula, Settling Velocity uses Unit weight of particle, Unit Weight of Liquid, Diameter of Partical, Water Density & Coefficient of Drag. We can use 6 other way(s) to calculate the same, which is/are as follows -

Settling Velocity = (Acceleration due to Gravity/18)*(Specific gravity of sediment-1)*((Diameter of Partical)^2/Kinematic Viscosity)
Settling Velocity = (Reynolds Number*Kinematic Viscosity)/Diameter
Settling Velocity = sqrt(((4/3)*Acceleration due to Gravity*(Specific gravity of sediment-1)*Diameter of Partical)/Coefficient of Drag)
Settling Velocity = ((Acceleration due to Gravity*(Specific gravity of sediment-1)*(Diameter of Partical)^(1.6))/(13.88*(Kinematic Viscosity)^(0.6)))^(0.714)
Settling Velocity = (1.8*sqrt(Acceleration due to Gravity*(Specific gravity of sediment-1)*Diameter of Partical))
Settling Velocity = (60.6*Diameter of Partical*(Specific gravity of sediment-1)*(((3*Temperature)+70)/100))

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