Velocity Distribution Profile Calculator

✖The Dynamic Viscosity of a fluid is the measure of its resistance to flow when an external force is applied.ⓘ Dynamic Viscosity [μ_viscosity]			+10% -10%
✖Pressure Gradient is the change in pressure with respect to radial distance of element.ⓘ Pressure Gradient [dp\|dr]			+10% -10%
✖Width is the measurement or extent of something from side to side.ⓘ Width [w]			+10% -10%
✖Horizontal Distance denotes the instantaneous horizontal distance cover by an object in a projectile motion.ⓘ Horizontal Distance [R]			+10% -10%

✖Velocity of Liquid is a vector quantity (it has both magnitude and direction) and is the rate of change of the position of an object with respect to time.ⓘ Velocity Distribution Profile [v]

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Formula

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Velocity Distribution Profile

Formula

`"v" = -(1/(2*"μ"_{"viscosity"}))*"dp|dr"*("w"*"R"-("R"^2))`

Example

`"224.25m/s"=-(1/(2*"10.2P"))*"17N/m³"*("3m"*"6.9m"-(("6.9m")^2))`

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Download Laminar Flow between Parallel Plates, both plates at rest Formulas PDF PDF Image

Velocity Distribution Profile Solution

STEP 0: Pre-Calculation Summary

Formula Used

Velocity of Liquid = -(1/(2*Dynamic Viscosity))*Pressure Gradient*(Width*Horizontal Distance-(Horizontal Distance^2))
v = -(1/(2*μ_viscosity))*dp|dr*(w*R-(R^2))
This formula uses 5 Variables

Variables Used

Velocity of Liquid - (Measured in Meter per Second) - Velocity of Liquid is a vector quantity (it has both magnitude and direction) and is the rate of change of the position of an object with respect to time.
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.
Pressure Gradient - (Measured in Newton per Cubic Meter) - Pressure Gradient is the change in pressure with respect to radial distance of element.
Width - (Measured in Meter) - Width is the measurement or extent of something from side to side.
Horizontal Distance - (Measured in Meter) - Horizontal Distance denotes the instantaneous horizontal distance cover by an object in a projectile motion.

STEP 1: Convert Input(s) to Base Unit

Dynamic Viscosity: 10.2 Poise --> 1.02 Pascal Second (Check conversion here)
Pressure Gradient: 17 Newton per Cubic Meter --> 17 Newton per Cubic Meter No Conversion Required
Width: 3 Meter --> 3 Meter No Conversion Required
Horizontal Distance: 6.9 Meter --> 6.9 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

v = -(1/(2*μ_viscosity))*dp|dr*(w*R-(R^2)) --> -(1/(2*1.02))*17*(3*6.9-(6.9^2))

Evaluating ... ...

v = 224.25

STEP 3: Convert Result to Output's Unit

224.25 Meter per Second --> No Conversion Required

FINAL ANSWER

224.25 Meter per Second <-- Velocity of Liquid

(Calculation completed in 00.004 seconds)

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Created by Rithik Agrawal

National Institute of Technology Karnataka (NITK), Surathkal

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Meerut Institute of Engineering and Technology (MIET), Meerut

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< 20 Laminar Flow between Parallel Plates, both plates at rest Calculators

Distance between Plates given Pressure Head Drop

Go Width = sqrt((12*Dynamic Viscosity*Length of Pipe*Mean Velocity)/(Specific Weight of Liquid*Head Loss due to Friction))

Length of Pipe given Pressure Head Drop

Go Length of Pipe = (Specific Weight of Liquid*Width*Width*Head Loss due to Friction)/(12*Dynamic Viscosity*Mean Velocity)

Velocity Distribution Profile

Go Velocity of Liquid = -(1/(2*Dynamic Viscosity))*Pressure Gradient*(Width*Horizontal Distance-(Horizontal Distance^2))

Distance between Plates using Velocity Distribution Profile

Go Width = (((-Velocity of Liquid*2*Dynamic Viscosity)/Pressure Gradient)+(Horizontal Distance^2))/Horizontal Distance

Length of Pipe given Pressure Difference

Go Length of Pipe = (Pressure Difference*Width*Width)/(Dynamic Viscosity*12*Mean Velocity)

Distance between Plates given Pressure Difference

Go Width = sqrt(12*Mean Velocity*Dynamic Viscosity*Length of Pipe/Pressure Difference)

Pressure Head Drop

Go Head Loss due to Friction = (12*Dynamic Viscosity*Length of Pipe*Mean Velocity)/(Specific Weight of Liquid)

Pressure Difference

Go Pressure Difference = 12*Dynamic Viscosity*Mean Velocity*Length of Pipe/(Width^2)

Distance between Plates given Maximum Velocity between Plates

Go Width = sqrt((8*Dynamic Viscosity*Maximum Velocity)/(Pressure Gradient))

Distance between Plates given Mean Velocity of Flow with Pressure Gradient

Go Width = sqrt((12*Dynamic Viscosity*Mean Velocity)/Pressure Gradient)

Distance between Plates given Discharge

Go Width = ((Discharge in Laminar Flow*12*Dynamic Viscosity)/Pressure Gradient)^(1/3)

Discharge given Viscosity

Go Discharge in Laminar Flow = Pressure Gradient*(Width^3)/(12*Dynamic Viscosity)

Maximum Velocity between Plates

Go Maximum Velocity = ((Width^2)*Pressure Gradient)/(8*Dynamic Viscosity)

Distance between Plates given Shear Stress Distribution Profile

Go Width = 2*(Horizontal Distance-(Shear Stress/Pressure Gradient))

Shear Stress Distribution Profile

Go Shear Stress = -Pressure Gradient*(Width/2-Horizontal Distance)

Horizontal Distance given Shear Stress Distribution Profile

Go Horizontal Distance = Width/2+(Shear Stress/Pressure Gradient)

Maximum Shear Stress in fluid

Go Maximum Shear Stress in Shaft = 0.5*Pressure Gradient*Width

Distance between Plates given Mean Velocity of Flow

Go Width = Discharge in Laminar Flow/Mean Velocity

Discharge given Mean Velocity of Flow

Go Discharge in Laminar Flow = Width*Mean Velocity

Maximum Velocity given Mean Velocity of Flow

Go Maximum Velocity = 1.5*Mean Velocity

Velocity Distribution Profile Formula

Velocity of Liquid = -(1/(2*Dynamic Viscosity))*Pressure Gradient*(Width*Horizontal Distance-(Horizontal Distance^2))
v = -(1/(2*μ_viscosity))*dp|dr*(w*R-(R^2))

What is Velocity?

The velocity of an object is the rate of change of its position with respect to a frame of reference, and is a function of time. Velocity is equivalent to a specification of an object's speed and direction of motion.

How to Calculate Velocity Distribution Profile?

Velocity Distribution Profile calculator uses Velocity of Liquid = -(1/(2*Dynamic Viscosity))*Pressure Gradient*(Width*Horizontal Distance-(Horizontal Distance^2)) to calculate the Velocity of Liquid, The Velocity Distribution Profile is defined as the velocity with respect to plate in the direction of flow in the stream. Velocity of Liquid is denoted by v symbol.

How to calculate Velocity Distribution Profile using this online calculator? To use this online calculator for Velocity Distribution Profile, enter Dynamic Viscosity (μ_viscosity), Pressure Gradient (dp|dr), Width (w) & Horizontal Distance (R) and hit the calculate button. Here is how the Velocity Distribution Profile calculation can be explained with given input values -> 224.25 = -(1/(2*1.02))*17*(3*6.9-(6.9^2)).

FAQ

What is Velocity Distribution Profile?

The Velocity Distribution Profile is defined as the velocity with respect to plate in the direction of flow in the stream and is represented as v = -(1/(2*μ_viscosity))*dp|dr*(w*R-(R^2)) or Velocity of Liquid = -(1/(2*Dynamic Viscosity))*Pressure Gradient*(Width*Horizontal Distance-(Horizontal Distance^2)). The Dynamic Viscosity of a fluid is the measure of its resistance to flow when an external force is applied, Pressure Gradient is the change in pressure with respect to radial distance of element, Width is the measurement or extent of something from side to side & Horizontal Distance denotes the instantaneous horizontal distance cover by an object in a projectile motion.

How to calculate Velocity Distribution Profile?

The Velocity Distribution Profile is defined as the velocity with respect to plate in the direction of flow in the stream is calculated using Velocity of Liquid = -(1/(2*Dynamic Viscosity))*Pressure Gradient*(Width*Horizontal Distance-(Horizontal Distance^2)). To calculate Velocity Distribution Profile, you need Dynamic Viscosity (μ_viscosity), Pressure Gradient (dp|dr), Width (w) & Horizontal Distance (R). With our tool, you need to enter the respective value for Dynamic Viscosity, Pressure Gradient, Width & Horizontal Distance 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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