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Terminal Velocity Formula

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Terminal Velocity is the maximum velocity attainable by an object as it falls through a fluid (air is the most common example). Check FAQs

V terminal = \frac{2}{9} \cdot r^{2} \cdot (𝜌 1 - ρ 2) \cdot \frac{g}{μ viscosity}

V_terminal - Terminal Velocity?r - Radius?𝜌₁ - Density of the first phase?ρ₂ - Density of the second phase?g - Acceleration due to Gravity?μ_viscosity - Dynamic Viscosity?

Terminal Velocity Example

With values

With units

Only example

Here is how the Terminal Velocity equation looks like with Values.

Here is how the Terminal Velocity equation looks like with Units.

Here is how the Terminal Velocity equation looks like.

213.5076 = \frac{2}{9} \cdot {0.2}^{2} \cdot (8.5 - 6) \cdot \frac{9.8}{10.2}

213.5076m/s = \frac{2}{9} \cdot {0.2m}^{2} \cdot (8.5g/cm³ - 6g/cm³) \cdot \frac{9.8m/s²}{10.2P}

213.5076 = \frac{2}{9} \cdot {0.2}^{2} \cdot (8.5 - 6) \cdot \frac{9.8}{10.2}

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Terminal Velocity Solution

Follow our step by step solution on how to calculate Terminal Velocity?

FIRST Step Consider the formula

V terminal = \frac{2}{9} \cdot r^{2} \cdot (𝜌 1 - ρ 2) \cdot \frac{g}{μ viscosity}

Next Step Substitute values of Variables

∴

V terminal = \frac{2}{9} \cdot {0.2m}^{2} \cdot (8.5g/cm³ - 6g/cm³) \cdot \frac{9.8m/s²}{10.2P}

Next Step Convert Units

∴

V terminal = \frac{2}{9} \cdot {0.2m}^{2} \cdot (8500kg/m³ - 6000kg/m³) \cdot \frac{9.8m/s²}{1.02Pa*s}

Next Step Prepare to Evaluate

∴

V terminal = \frac{2}{9} \cdot {0.2}^{2} \cdot (8500 - 6000) \cdot \frac{9.8}{1.02}

Next Step Evaluate

∴

V terminal = 213.507625272331m/s

LAST Step Rounding Answer

∴

V terminal = 213.5076m/s

Terminal Velocity Formula Elements

Variables

Terminal Velocity

Terminal Velocity is the maximum velocity attainable by an object as it falls through a fluid (air is the most common example).

Symbol: V_terminal

Measurement: SpeedUnit: m/s

Note: Value can be positive or negative.

Formulas to find Terminal Velocity

Open Variable

Radius

Radius is a radial line from the focus to any point of a curve.

Symbol: r

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Radius

Open Variable

Density of the first phase

Density of the first phase in a two phase microstructure.

Symbol: 𝜌₁

Measurement: DensityUnit: g/cm³

Note: Value should be greater than 0.

Formulas to find Density of the first phase

Open Variable

Density of the second phase

Density of the second phase in a two phase microstructure.

Symbol: ρ₂

Measurement: DensityUnit: g/cm³

Note: Value should be greater than 0.

Formulas to find Density of the second phase

Open Variable

Acceleration due to Gravity

Acceleration due to Gravity is acceleration gained by an object because of gravitational force.

Symbol: g

Measurement: AccelerationUnit: m/s²

Note: Value should be greater than 0.

Formulas to find Acceleration due to Gravity

Open Variable

Dynamic Viscosity

The Dynamic Viscosity of a fluid is the measure of its resistance to flow when an external force is applied.

Symbol: μ_viscosity

Measurement: Dynamic ViscosityUnit: P

Note: Value should be greater than 0.

Formulas to find Dynamic Viscosity

Open Variable

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How to Evaluate Terminal Velocity?

Terminal Velocity evaluator uses Terminal Velocity = 2/9*Radius^2*(Density of the first phase-Density of the second phase)*Acceleration due to Gravity/Dynamic Viscosity to evaluate the Terminal Velocity, Terminal velocity is the maximum velocity attainable by an object as it falls through a fluid (air is the most common example). Terminal Velocity is denoted by V_terminal symbol.

How to evaluate Terminal Velocity using this online evaluator? To use this online evaluator for Terminal Velocity, enter Radius (r), Density of the first phase (𝜌₁), Density of the second phase (ρ₂), Acceleration due to Gravity (g) & Dynamic Viscosity (μ_viscosity) and hit the calculate button.

FAQs on Terminal Velocity

What is the formula to find Terminal Velocity?

The formula of Terminal Velocity is expressed as Terminal Velocity = 2/9*Radius^2*(Density of the first phase-Density of the second phase)*Acceleration due to Gravity/Dynamic Viscosity. Here is an example- 213.5076 = 2/9*0.2^2*(8500-6000)*9.8/1.02.

How to calculate Terminal Velocity?

With Radius (r), Density of the first phase (𝜌₁), Density of the second phase (ρ₂), Acceleration due to Gravity (g) & Dynamic Viscosity (μ_viscosity) we can find Terminal Velocity using the formula - Terminal Velocity = 2/9*Radius^2*(Density of the first phase-Density of the second phase)*Acceleration due to Gravity/Dynamic Viscosity.

Can the Terminal Velocity be negative?

Yes, the Terminal Velocity, measured in Speed can be negative.

Which unit is used to measure Terminal Velocity?

Terminal Velocity is usually measured using the Meter per Second[m/s] for Speed. Meter per Minute[m/s], Meter per Hour[m/s], Kilometer per Hour[m/s] are the few other units in which Terminal Velocity can be measured.

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