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 Water is the ratio of total weight to the total volume of water.ⓘ Unit Weight of Water [γ_w]			+10% -10%
✖Diameter of Particle is the measurement of the size of individual particles in a soil or sediment sample.ⓘ Diameter of Particle [D_p]			+10% -10%
✖The Water Density refers to the measure of how much mass is contained in a given volume of water.ⓘ Water Density [ρ_water]			+10% -10%
✖The 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 of Particle given Coeff of Drag is the velocity at which a particle settles in a fluid, such as water or air, under the influence of gravity, considering coefficient of drag.ⓘ Settling Velocity of Spherical Particle given Coefficient of Drag [V_sc]

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Formula

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Settling Velocity of Spherical Particle given Coefficient of Drag

Formula

V sc = \sqrt{\frac{(\frac{4}{3}) \cdot (γ s - γ w) \cdot D p}{ρ water \cdot C D}}

Example

0.08165 m/s = \sqrt{\frac{(\frac{4}{3}) \cdot (10 kN/m³ - 9810 N/m³) \cdot 0.01 m}{1000 kg/m³ \cdot 0.38}}

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Settling Velocity of Spherical Particle given Coefficient of Drag Solution

STEP 0: Pre-Calculation Summary

Formula Used

Settling Velocity of Particle given Coeff of Drag = sqrt(((4/3)*(Unit Weight of Particle-Unit Weight of Water)*Diameter of Particle)/(Water Density*Coefficient of Drag))
V_sc = 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 of Particle given Coeff of Drag - (Measured in Meter per Second) - Settling Velocity of Particle given Coeff of Drag is the velocity at which a particle settles in a fluid, such as water or air, under the influence of gravity, considering coefficient of drag.
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 Water - (Measured in Newton per Cubic Meter) - Unit Weight of Water is the ratio of total weight to the total volume of water.
Diameter of Particle - (Measured in Meter) - Diameter of Particle is the measurement of the size of individual particles in a soil or sediment sample.
Water Density - (Measured in Kilogram per Cubic Meter) - The Water Density refers to the measure of how much mass is contained in a given volume of water.
Coefficient of Drag - The 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 Water: 9810 Newton per Cubic Meter --> 9810 Newton per Cubic Meter No Conversion Required
Diameter of Particle: 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: 0.38 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V_sc = sqrt(((4/3)*(γ_s-γ_w)*D_p)/(ρ_water*C_D)) --> sqrt(((4/3)*(10000-9810)*0.01)/(1000*0.38))

Evaluating ... ...

V_sc = 0.0816496580927726

STEP 3: Convert Result to Output's Unit

0.0816496580927726 Meter per Second --> No Conversion Required

FINAL ANSWER

0.0816496580927726 ≈ 0.08165 Meter per Second <-- Settling Velocity of Particle given Coeff of Drag

(Calculation completed in 00.020 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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Birsa Institute of Technology (BIT), Sindri

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< Settling Velocity of Particle Calculators

Settling Velocity of Spherical Particle given Coefficient of Drag

Go Settling Velocity of Particle given Coeff of Drag = sqrt(((4/3)*(Unit Weight of Particle-Unit Weight of Water)*Diameter of Particle)/(Water Density*Coefficient of Drag))

Settling Velocity given Specific Gravity of Particle

Go Settling Velocity given Specific Gravity = sqrt(((4/3)*Acceleration due to Gravity*(Specific Gravity of Sediment-1)*Diameter of Particle)/Coefficient of Drag)

Settling Velocity of Spherical Particle

Go Settling Velocity of Spherical Particle = (Acceleration due to Gravity/18)*(Specific Gravity of Sediment-1)*((Diameter of Particle)^2/Kinematic Viscosity)

Settling Velocity of Spherical Particle given Reynold Number

Go Settling Velocity of Particle given Reynold Number = (Reynolds Number of Particle*Kinematic Viscosity)/Diameter of Particle

Settling Velocity of Spherical Particle given Coefficient of Drag Formula

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 of Particle given Coeff of Drag = sqrt(((4/3)*(Unit Weight of Particle-Unit Weight of Water)*Diameter of Particle)/(Water Density*Coefficient of Drag)) to calculate the Settling Velocity of Particle given Coeff of Drag, The Settling Velocity of Spherical Particle given Coefficient of Drag formula is defined as the velocity at which a particle settles in a fluid, such as water or air, under the influence of gravity, considering coeff. of drag. Settling Velocity of Particle given Coeff of Drag is denoted by V_sc 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 Water (γ_w), Diameter of Particle (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 -> 0.08165 = sqrt(((4/3)*(10000-9810)*0.01)/(1000*0.38)).

FAQ

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

The Settling Velocity of Spherical Particle given Coefficient of Drag formula is defined as the velocity at which a particle settles in a fluid, such as water or air, under the influence of gravity, considering coeff. of drag and is represented as V_sc = sqrt(((4/3)*(γ_s-γ_w)*D_p)/(ρ_water*C_D)) or Settling Velocity of Particle given Coeff of Drag = sqrt(((4/3)*(Unit Weight of Particle-Unit Weight of Water)*Diameter of Particle)/(Water Density*Coefficient of Drag)). Unit Weight of Particle is defined as weight per unit volume of the particle, Unit Weight of Water is the ratio of total weight to the total volume of water, Diameter of Particle is the measurement of the size of individual particles in a soil or sediment sample, The Water Density refers to the measure of how much mass is contained in a given volume of water & The 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?

The Settling Velocity of Spherical Particle given Coefficient of Drag formula is defined as the velocity at which a particle settles in a fluid, such as water or air, under the influence of gravity, considering coeff. of drag is calculated using Settling Velocity of Particle given Coeff of Drag = sqrt(((4/3)*(Unit Weight of Particle-Unit Weight of Water)*Diameter of Particle)/(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 Water (γ_w), Diameter of Particle (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 Water, Diameter of Particle, 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.

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