Mean Velocity of Fluid Flow Solution

STEP 0: Pre-Calculation Summary
Formula Used
Mean Velocity = (1/(8*Dynamic Viscosity))*Pressure Gradient*Pipe Radius^2
Vmean = (1/(8*μviscosity))*dp|dr*R^2
This formula uses 4 Variables
Variables Used
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 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.
Pipe Radius - (Measured in Meter) - The Pipe Radius is the radius of the pipe through which the fluid is flowing.
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
Pipe Radius: 138 Millimeter --> 0.138 Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Vmean = (1/(8*μviscosity))*dp|dr*R^2 --> (1/(8*1.02))*17*0.138^2
Evaluating ... ...
Vmean = 0.039675
STEP 3: Convert Result to Output's Unit
0.039675 Meter per Second --> No Conversion Required
FINAL ANSWER
0.039675 Meter per Second <-- Mean Velocity
(Calculation completed in 00.020 seconds)

Credits

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National Institute of Technology Karnataka (NITK), Surathkal
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12 Steady Laminar Flow in Circular Pipes – Hagen Poiseuille Law Calculators

Distance of Element from Center Line given Velocity at any point in Cylindrical Element
Go Radial Distance = sqrt((Pipe Radius^2)-(-4*Dynamic Viscosity*Fluid Velocity in Pipe/Pressure Gradient))
Velocity at any point in Cylindrical Element
Go Fluid Velocity in Pipe = -(1/(4*Dynamic Viscosity))*Pressure Gradient*((Pipe Radius^2)-(Radial Distance^2))
Shear Stress at any Cylindrical Element given Head Loss
Go Shear Stress = (Specific Weight of Liquid*Head Loss due to Friction*Radial Distance)/(2*Length of Pipe)
Distance of Element from Center Line given Head Loss
Go Radial Distance = 2*Shear Stress*Length of Pipe/(Head Loss due to Friction*Specific Weight of Liquid)
Discharge through Pipe given Pressure Gradient
Go Discharge in pipe = (pi/(8*Dynamic Viscosity))*(Pipe Radius^4)*Pressure Gradient
Velocity Gradient given Pressure Gradient at Cylindrical Element
Go Velocity Gradient = (1/(2*Dynamic Viscosity))*Pressure Gradient*Radial Distance
Distance of Element from Center Line given Velocity Gradient at Cylindrical Element
Go Radial Distance = 2*Dynamic Viscosity*Velocity Gradient/Pressure Gradient
Mean Velocity of Fluid Flow
Go Mean Velocity = (1/(8*Dynamic Viscosity))*Pressure Gradient*Pipe Radius^2
Distance of Element from Center line given Shear Stress at any Cylindrical Element
Go Radial Distance = 2*Shear Stress/Pressure Gradient
Shear Stress at any Cylindrical Element
Go Shear Stress = Pressure Gradient*Radial Distance/2
Mean Velocity of Flow given Maximum Velocity at Axis of Cylindrical Element
Go Mean Velocity = 0.5*Maximum Velocity
Maximum Velocity at Axis of Cylindrical Element given Mean Velocity of Flow
Go Maximum Velocity = 2*Mean Velocity

Mean Velocity of Fluid Flow Formula

Mean Velocity = (1/(8*Dynamic Viscosity))*Pressure Gradient*Pipe Radius^2
Vmean = (1/(8*μviscosity))*dp|dr*R^2

What is Mean Velocity of Flow ?

The time average of the velocity of a fluid at a fixed point, over a somewhat arbitrary time interval T counted from some fixed time t0.

How to Calculate Mean Velocity of Fluid Flow?

Mean Velocity of Fluid Flow calculator uses Mean Velocity = (1/(8*Dynamic Viscosity))*Pressure Gradient*Pipe Radius^2 to calculate the Mean Velocity, The Mean Velocity of Fluid Flow is defined as average velocity of stream flowing the pipe measured over the entire length. Mean Velocity is denoted by Vmean symbol.

How to calculate Mean Velocity of Fluid Flow using this online calculator? To use this online calculator for Mean Velocity of Fluid Flow, enter Dynamic Viscosity viscosity), Pressure Gradient (dp|dr) & Pipe Radius (R) and hit the calculate button. Here is how the Mean Velocity of Fluid Flow calculation can be explained with given input values -> 0.083333 = (1/(8*1.02))*17*0.138^2.

FAQ

What is Mean Velocity of Fluid Flow?
The Mean Velocity of Fluid Flow is defined as average velocity of stream flowing the pipe measured over the entire length and is represented as Vmean = (1/(8*μviscosity))*dp|dr*R^2 or Mean Velocity = (1/(8*Dynamic Viscosity))*Pressure Gradient*Pipe Radius^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 & The Pipe Radius is the radius of the pipe through which the fluid is flowing.
How to calculate Mean Velocity of Fluid Flow?
The Mean Velocity of Fluid Flow is defined as average velocity of stream flowing the pipe measured over the entire length is calculated using Mean Velocity = (1/(8*Dynamic Viscosity))*Pressure Gradient*Pipe Radius^2. To calculate Mean Velocity of Fluid Flow, you need Dynamic Viscosity viscosity), Pressure Gradient (dp|dr) & Pipe Radius (R). With our tool, you need to enter the respective value for Dynamic Viscosity, Pressure Gradient & Pipe Radius 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 Mean Velocity?
In this formula, Mean Velocity uses Dynamic Viscosity, Pressure Gradient & Pipe Radius. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Mean Velocity = 0.5*Maximum Velocity
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