Terminal Fall Velocity Solution

STEP 0: Pre-Calculation Summary
Formula Used
Terminal Velocity = ((Diameter of Sphere^2)/(18*Dynamic Viscosity))*(Specific Weight of Liquid-Specific Weight of Liquid in Piezometer)
Vterminal = ((DS^2)/(18*μviscosity))*(γf-S)
This formula uses 5 Variables
Variables Used
Terminal Velocity - (Measured in Meter per Second) - Terminal velocity is the maximum velocity attainable by an object as it falls through a fluid (air is the most common example).
Diameter of Sphere - (Measured in Meter) - Diameter of Sphere is the longest line that is inside the sphere and that passes through the center of the sphere.
Dynamic Viscosity - (Measured in Pascal Second) - The Dynamic Viscosity of a fluid is the measure of its resistance to flow when an external force is applied.
Specific Weight of Liquid - (Measured in Kilonewton per Cubic Meter) - Specific Weight of Liquid represents the force exerted by gravity on a unit volume of a fluid.
Specific Weight of Liquid in Piezometer - (Measured in Kilonewton per Cubic Meter) - Specific Weight of Liquid in Piezometer is the ratio of a body’s weight P to its volume V.
STEP 1: Convert Input(s) to Base Unit
Diameter of Sphere: 10 Meter --> 10 Meter No Conversion Required
Dynamic Viscosity: 10.2 Poise --> 1.02 Pascal Second (Check conversion here)
Specific Weight of Liquid: 9.81 Kilonewton per Cubic Meter --> 9.81 Kilonewton per Cubic Meter No Conversion Required
Specific Weight of Liquid in Piezometer: 0.75 Kilonewton per Cubic Meter --> 0.75 Kilonewton per Cubic Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Vterminal = ((DS^2)/(18*μviscosity))*(γf-S) --> ((10^2)/(18*1.02))*(9.81-0.75)
Evaluating ... ...
Vterminal = 49.3464052287582
STEP 3: Convert Result to Output's Unit
49.3464052287582 Meter per Second --> No Conversion Required
FINAL ANSWER
49.3464052287582 49.34641 Meter per Second <-- Terminal Velocity
(Calculation completed in 00.004 seconds)

Credits

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National Institute of Technology Karnataka (NITK), Surathkal
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18 Laminar Flow around a Sphere– Stokes’ Law Calculators

Coefficient of Drag given Drag Force
Go Coefficient of Drag = Drag Force/(Cross Sectional Area of Pipe*Mean Velocity*Mean Velocity*Density of Fluid*0.5)
Density of Fluid given Drag Force
Go Density of Fluid = Drag Force/(Cross Sectional Area of Pipe*Mean Velocity*Mean Velocity*Coefficient of Drag*0.5)
Projected Area given Drag Force
Go Cross Sectional Area of Pipe = Drag Force/(Coefficient of Drag*Mean Velocity*Mean Velocity*Density of Fluid*0.5)
Drag Force given Coefficient of Drag
Go Drag Force = Coefficient of Drag*Cross Sectional Area of Pipe*Mean Velocity*Mean Velocity*Density of Fluid*0.5
Coefficient of Drag given density
Go Coefficient of Drag = (24*Drag Force*Dynamic Viscosity)/(Density of Fluid*Mean Velocity*Diameter of Sphere)
Dynamic Viscosity of fluid given Terminal Fall Velocity
Go Dynamic Viscosity = ((Diameter of Sphere^2)/(18*Terminal Velocity))*(Specific Weight of Liquid-Specific Weight of Liquid in Piezometer)
Terminal Fall Velocity
Go Terminal Velocity = ((Diameter of Sphere^2)/(18*Dynamic Viscosity))*(Specific Weight of Liquid-Specific Weight of Liquid in Piezometer)
Velocity of Sphere given Drag Force
Go Mean Velocity = sqrt(Drag Force/(Cross Sectional Area of Pipe*Coefficient of Drag*Density of Fluid*0.5))
Velocity of Sphere given Coefficient of Drag
Go Mean Velocity = (24*Dynamic Viscosity)/(Density of Fluid*Coefficient of Drag*Diameter of Sphere)
Diameter of Sphere given Coefficient of Drag
Go Diameter of Sphere = (24*Dynamic Viscosity)/(Density of Fluid*Mean Velocity*Coefficient of Drag)
Diameter of Sphere for given Fall Velocity
Go Diameter of Sphere = sqrt((Mean Velocity*18*Dynamic Viscosity)/(Specific Weight of Liquid))
Dynamic Viscosity of fluid given Resistance Force on Spherical Surface
Go Dynamic Viscosity = Resistance Force/(3*pi*Diameter of Sphere*Mean Velocity)
Velocity of Sphere given Resistance Force on Spherical Surface
Go Mean Velocity = Resistance Force/(3*pi*Dynamic Viscosity*Diameter of Sphere)
Diameter of Sphere given Resistance Force on Spherical Surface
Go Diameter of Sphere = Resistance Force/(3*pi*Dynamic Viscosity*Mean Velocity)
Resistance Force on Spherical Surface
Go Resistance Force = 3*pi*Dynamic Viscosity*Mean Velocity*Diameter of Sphere
Resistance Force on Spherical Surface given Specific Weights
Go Resistance Force = (pi/6)*(Diameter of Sphere^3)*(Specific Weight of Liquid)
Reynolds Number given Coefficient of Drag
Go Reynolds Number = 24/Coefficient of Drag
Coefficient of Drag given Reynolds Number
Go Coefficient of Drag = 24/Reynolds Number

Terminal Fall Velocity Formula

Terminal Velocity = ((Diameter of Sphere^2)/(18*Dynamic Viscosity))*(Specific Weight of Liquid-Specific Weight of Liquid in Piezometer)
Vterminal = ((DS^2)/(18*μviscosity))*(γf-S)

What is Terminal Fall Velocity?

Terminal velocity is the maximum velocity attainable by an object as it falls through a fluid (air is the most common example). It occurs when the sum of the drag force (Fd) and the buoyancy is equal to the downward force of gravity (FG) acting on the object. Since the net force on the object is zero, the object has zero acceleration.

How to Calculate Terminal Fall Velocity?

Terminal Fall Velocity calculator uses Terminal Velocity = ((Diameter of Sphere^2)/(18*Dynamic Viscosity))*(Specific Weight of Liquid-Specific Weight of Liquid in Piezometer) to calculate the Terminal Velocity, The Terminal Fall Velocity formula is defined as the velocity with which object is moving in the fluid in the channel. Terminal Velocity is denoted by Vterminal symbol.

How to calculate Terminal Fall Velocity using this online calculator? To use this online calculator for Terminal Fall Velocity, enter Diameter of Sphere (DS), Dynamic Viscosity viscosity), Specific Weight of Liquid f) & Specific Weight of Liquid in Piezometer (S) and hit the calculate button. Here is how the Terminal Fall Velocity calculation can be explained with given input values -> 49.34641 = ((10^2)/(18*1.02))*(9810-750).

FAQ

What is Terminal Fall Velocity?
The Terminal Fall Velocity formula is defined as the velocity with which object is moving in the fluid in the channel and is represented as Vterminal = ((DS^2)/(18*μviscosity))*(γf-S) or Terminal Velocity = ((Diameter of Sphere^2)/(18*Dynamic Viscosity))*(Specific Weight of Liquid-Specific Weight of Liquid in Piezometer). Diameter of Sphere is the longest line that is inside the sphere and that passes through the center of the sphere, The Dynamic Viscosity of a fluid is the measure of its resistance to flow when an external force is applied, Specific Weight of Liquid represents the force exerted by gravity on a unit volume of a fluid & Specific Weight of Liquid in Piezometer is the ratio of a body’s weight P to its volume V.
How to calculate Terminal Fall Velocity?
The Terminal Fall Velocity formula is defined as the velocity with which object is moving in the fluid in the channel is calculated using Terminal Velocity = ((Diameter of Sphere^2)/(18*Dynamic Viscosity))*(Specific Weight of Liquid-Specific Weight of Liquid in Piezometer). To calculate Terminal Fall Velocity, you need Diameter of Sphere (DS), Dynamic Viscosity viscosity), Specific Weight of Liquid f) & Specific Weight of Liquid in Piezometer (S). With our tool, you need to enter the respective value for Diameter of Sphere, Dynamic Viscosity, Specific Weight of Liquid & Specific Weight of Liquid in Piezometer 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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