Diameter of Sphere for given Fall Velocity Solution

STEP 0: Pre-Calculation Summary
Formula Used
Diameter of Sphere = sqrt((Mean Velocity*18*Dynamic Viscosity)/(Specific Weight of Liquid))
DS = sqrt((Vmean*18*μviscosity)/(γf))
This formula uses 1 Functions, 4 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
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.
Mean Velocity - (Measured in Meter per Second) - Mean velocity is defined as the average velocity of a fluid at a point and over an arbitrary time T.
Dynamic Viscosity - (Measured in Kilopoise) - 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 Newton per Cubic Meter) - Specific Weight of Liquid represents the force exerted by gravity on a unit volume of a fluid.
STEP 1: Convert Input(s) to Base Unit
Mean Velocity: 10.1 Meter per Second --> 10.1 Meter per Second No Conversion Required
Dynamic Viscosity: 10.2 Poise --> 0.0102 Kilopoise (Check conversion here)
Specific Weight of Liquid: 9.81 Kilonewton per Cubic Meter --> 9810 Newton per Cubic Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
DS = sqrt((Vmean*18*μviscosity)/(γf)) --> sqrt((10.1*18*0.0102)/(9810))
Evaluating ... ...
DS = 0.0137487280479243
STEP 3: Convert Result to Output's Unit
0.0137487280479243 Meter --> No Conversion Required
FINAL ANSWER
0.0137487280479243 0.013749 Meter <-- Diameter of Sphere
(Calculation completed in 00.004 seconds)

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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

Diameter of Sphere for given Fall Velocity Formula

Diameter of Sphere = sqrt((Mean Velocity*18*Dynamic Viscosity)/(Specific Weight of Liquid))
DS = sqrt((Vmean*18*μviscosity)/(γf))

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 Diameter of Sphere for given Fall Velocity?

Diameter of Sphere for given Fall Velocity calculator uses Diameter of Sphere = sqrt((Mean Velocity*18*Dynamic Viscosity)/(Specific Weight of Liquid)) to calculate the Diameter of Sphere, The Diameter of Sphere for given Fall Velocity is defined as the width of the section of the sphere in the flow. Diameter of Sphere is denoted by DS symbol.

How to calculate Diameter of Sphere for given Fall Velocity using this online calculator? To use this online calculator for Diameter of Sphere for given Fall Velocity, enter Mean Velocity (Vmean), Dynamic Viscosity viscosity) & Specific Weight of Liquid f) and hit the calculate button. Here is how the Diameter of Sphere for given Fall Velocity calculation can be explained with given input values -> 0.013749 = sqrt((10.1*18*1.02)/(9810)).

FAQ

What is Diameter of Sphere for given Fall Velocity?
The Diameter of Sphere for given Fall Velocity is defined as the width of the section of the sphere in the flow and is represented as DS = sqrt((Vmean*18*μviscosity)/(γf)) or Diameter of Sphere = sqrt((Mean Velocity*18*Dynamic Viscosity)/(Specific Weight of Liquid)). Mean velocity is defined as the average velocity of a fluid at a point and over an arbitrary time T, 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.
How to calculate Diameter of Sphere for given Fall Velocity?
The Diameter of Sphere for given Fall Velocity is defined as the width of the section of the sphere in the flow is calculated using Diameter of Sphere = sqrt((Mean Velocity*18*Dynamic Viscosity)/(Specific Weight of Liquid)). To calculate Diameter of Sphere for given Fall Velocity, you need Mean Velocity (Vmean), Dynamic Viscosity viscosity) & Specific Weight of Liquid f). With our tool, you need to enter the respective value for Mean Velocity, Dynamic Viscosity & Specific Weight of Liquid 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 Diameter of Sphere?
In this formula, Diameter of Sphere uses Mean Velocity, Dynamic Viscosity & Specific Weight of Liquid. We can use 2 other way(s) to calculate the same, which is/are as follows -
  • Diameter of Sphere = Resistance Force/(3*pi*Dynamic Viscosity*Mean Velocity)
  • Diameter of Sphere = (24*Dynamic Viscosity)/(Density of Fluid*Mean Velocity*Coefficient of Drag)
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