Velocity Gradient given Pressure Gradient at Cylindrical Element Solution

STEP 0: Pre-Calculation Summary
Formula Used
Velocity Gradient = (1/(2*Dynamic Viscosity))*Pressure Gradient*Radial Distance
VG = (1/(2*μviscosity))*dp|dr*dradial
This formula uses 4 Variables
Variables Used
Velocity Gradient - (Measured in Meter per Second) - Velocity Gradient is the difference in velocity between the adjacent layers of the fluid.
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.
Radial Distance - (Measured in Meter) - Radial distance is defined as distance between whisker sensor's pivot point to whisker-object contact point.
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
Radial Distance: 9.2 Meter --> 9.2 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
VG = (1/(2*μviscosity))*dp|dr*dradial --> (1/(2*1.02))*17*9.2
Evaluating ... ...
VG = 76.6666666666666
STEP 3: Convert Result to Output's Unit
76.6666666666666 Meter per Second --> No Conversion Required
FINAL ANSWER
76.6666666666666 76.66667 Meter per Second <-- Velocity Gradient
(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

Velocity Gradient given Pressure Gradient at Cylindrical Element Formula

Velocity Gradient = (1/(2*Dynamic Viscosity))*Pressure Gradient*Radial Distance
VG = (1/(2*μviscosity))*dp|dr*dradial

What is Velocity Gradient ?

The difference in velocity between adjacent layers of the fluid is known as a velocity gradient and is given by v/x, where v is the velocity difference and x is the distance between the layers.

How to Calculate Velocity Gradient given Pressure Gradient at Cylindrical Element?

Velocity Gradient given Pressure Gradient at Cylindrical Element calculator uses Velocity Gradient = (1/(2*Dynamic Viscosity))*Pressure Gradient*Radial Distance to calculate the Velocity Gradient, The Velocity Gradient given Pressure Gradient at Cylindrical Element is defined as variation of velocity with respect to radius of pipe. Velocity Gradient is denoted by VG symbol.

How to calculate Velocity Gradient given Pressure Gradient at Cylindrical Element using this online calculator? To use this online calculator for Velocity Gradient given Pressure Gradient at Cylindrical Element, enter Dynamic Viscosity viscosity), Pressure Gradient (dp|dr) & Radial Distance (dradial) and hit the calculate button. Here is how the Velocity Gradient given Pressure Gradient at Cylindrical Element calculation can be explained with given input values -> 76.66667 = (1/(2*1.02))*17*9.2.

FAQ

What is Velocity Gradient given Pressure Gradient at Cylindrical Element?
The Velocity Gradient given Pressure Gradient at Cylindrical Element is defined as variation of velocity with respect to radius of pipe and is represented as VG = (1/(2*μviscosity))*dp|dr*dradial or Velocity Gradient = (1/(2*Dynamic Viscosity))*Pressure Gradient*Radial Distance. 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 & Radial distance is defined as distance between whisker sensor's pivot point to whisker-object contact point.
How to calculate Velocity Gradient given Pressure Gradient at Cylindrical Element?
The Velocity Gradient given Pressure Gradient at Cylindrical Element is defined as variation of velocity with respect to radius of pipe is calculated using Velocity Gradient = (1/(2*Dynamic Viscosity))*Pressure Gradient*Radial Distance. To calculate Velocity Gradient given Pressure Gradient at Cylindrical Element, you need Dynamic Viscosity viscosity), Pressure Gradient (dp|dr) & Radial Distance (dradial). With our tool, you need to enter the respective value for Dynamic Viscosity, Pressure Gradient & Radial 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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