Pressure Gradient given Velocity at any point in Cylindrical Element Solution

STEP 0: Pre-Calculation Summary
Formula Used
Pressure Gradient = Fluid Velocity in Pipe/((1/(4*Dynamic Viscosity))*((Pipe Radius^2)-(Radial Distance^2)))
dp|dr = uFluid/((1/(4*μviscosity))*((R^2)-(dradial^2)))
This formula uses 5 Variables
Variables Used
Pressure Gradient - (Measured in Newton per Cubic Meter) - Pressure Gradient is the change in pressure with respect to radial distance of element.
Fluid Velocity in Pipe - (Measured in Meter per Second) - Fluid Velocity in Pipe is the volume of fluid flowing in the given vessel per unit cross sectional area.
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.
Pipe Radius - (Measured in Meter) - The Pipe Radius is the radius of the pipe through which the fluid is flowing.
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
Fluid Velocity in Pipe: 300 Meter per Second --> 300 Meter per Second No Conversion Required
Dynamic Viscosity: 10.2 Poise --> 1.02 Pascal Second (Check conversion here)
Pipe Radius: 138 Millimeter --> 0.138 Meter (Check conversion here)
Radial Distance: 9.2 Meter --> 9.2 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
dp|dr = uFluid/((1/(4*μviscosity))*((R^2)-(dradial^2))) --> 300/((1/(4*1.02))*((0.138^2)-(9.2^2)))
Evaluating ... ...
dp|dr = -14.4645021500348
STEP 3: Convert Result to Output's Unit
-14.4645021500348 Newton per Cubic Meter --> No Conversion Required
FINAL ANSWER
-14.4645021500348 -14.464502 Newton per Cubic Meter <-- Pressure Gradient
(Calculation completed in 00.004 seconds)

Credits

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National Institute of Technology Karnataka (NITK), Surathkal
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7 Pressure Gradient Calculators

Pressure Gradient given Velocity at any point in Cylindrical Element
Go Pressure Gradient = Fluid Velocity in Pipe/((1/(4*Dynamic Viscosity))*((Pipe Radius^2)-(Radial Distance^2)))
Pressure Gradient given Discharge through Pipe
Go Pressure Gradient = Discharge in pipe/((pi/(8*Dynamic Viscosity))*(Pipe Radius^4))
Pressure Gradient given Velocity Gradient at Cylindrical Element
Go Pressure Gradient = 2*Dynamic Viscosity*Velocity Gradient/Radial Distance
Pressure Gradients given Mean Velocity of Flow
Go Pressure Gradient = 8*Mean Velocity*Dynamic Viscosity/(Pipe Radius^2)
Pressure Gradient given Maximum Shear Stress at Cylindrical Element
Go Pressure Gradient = (2*Maximum Shear Stress on Shaft)/Pipe Radius
Pressure Gradient given Maximum Velocity at Axis of Cylindrical Element
Go Pressure Gradient = (4*Dynamic Viscosity)/(Pipe Radius^2)
Pressure Gradient given Shear Stress at any Cylindrical Element
Go Pressure Gradient = 2*Shear Stress/Radial Distance

Pressure Gradient given Velocity at any point in Cylindrical Element Formula

Pressure Gradient = Fluid Velocity in Pipe/((1/(4*Dynamic Viscosity))*((Pipe Radius^2)-(Radial Distance^2)))
dp|dr = uFluid/((1/(4*μviscosity))*((R^2)-(dradial^2)))

What is Pressure Gradient ?

Pressure gradient is a physical quantity that describes in which direction and at what rate the pressure increases the most rapidly around a particular location. The pressure gradient is a dimensional quantity expressed in units of pascals per metre.

How to Calculate Pressure Gradient given Velocity at any point in Cylindrical Element?

Pressure Gradient given Velocity at any point in Cylindrical Element calculator uses Pressure Gradient = Fluid Velocity in Pipe/((1/(4*Dynamic Viscosity))*((Pipe Radius^2)-(Radial Distance^2))) to calculate the Pressure Gradient, The Pressure Gradient given Velocity at any point in Cylindrical Element is defined as the variation of pressure with respect to the length of the pipe. Pressure Gradient is denoted by dp|dr symbol.

How to calculate Pressure Gradient given Velocity at any point in Cylindrical Element using this online calculator? To use this online calculator for Pressure Gradient given Velocity at any point in Cylindrical Element, enter Fluid Velocity in Pipe (uFluid), Dynamic Viscosity viscosity), Pipe Radius (R) & Radial Distance (dradial) and hit the calculate button. Here is how the Pressure Gradient given Velocity at any point in Cylindrical Element calculation can be explained with given input values -> -14.464502 = 300/((1/(4*1.02))*((0.138^2)-(9.2^2))).

FAQ

What is Pressure Gradient given Velocity at any point in Cylindrical Element?
The Pressure Gradient given Velocity at any point in Cylindrical Element is defined as the variation of pressure with respect to the length of the pipe and is represented as dp|dr = uFluid/((1/(4*μviscosity))*((R^2)-(dradial^2))) or Pressure Gradient = Fluid Velocity in Pipe/((1/(4*Dynamic Viscosity))*((Pipe Radius^2)-(Radial Distance^2))). Fluid Velocity in Pipe is the volume of fluid flowing in the given vessel per unit cross sectional area, The Dynamic Viscosity of a fluid is the measure of its resistance to flow when an external force is applied, The Pipe Radius is the radius of the pipe through which the fluid is flowing & Radial distance is defined as distance between whisker sensor's pivot point to whisker-object contact point.
How to calculate Pressure Gradient given Velocity at any point in Cylindrical Element?
The Pressure Gradient given Velocity at any point in Cylindrical Element is defined as the variation of pressure with respect to the length of the pipe is calculated using Pressure Gradient = Fluid Velocity in Pipe/((1/(4*Dynamic Viscosity))*((Pipe Radius^2)-(Radial Distance^2))). To calculate Pressure Gradient given Velocity at any point in Cylindrical Element, you need Fluid Velocity in Pipe (uFluid), Dynamic Viscosity viscosity), Pipe Radius (R) & Radial Distance (dradial). With our tool, you need to enter the respective value for Fluid Velocity in Pipe, Dynamic Viscosity, Pipe Radius & Radial Distance 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 Pressure Gradient?
In this formula, Pressure Gradient uses Fluid Velocity in Pipe, Dynamic Viscosity, Pipe Radius & Radial Distance. We can use 6 other way(s) to calculate the same, which is/are as follows -
  • Pressure Gradient = 2*Shear Stress/Radial Distance
  • Pressure Gradient = (2*Maximum Shear Stress on Shaft)/Pipe Radius
  • Pressure Gradient = 2*Dynamic Viscosity*Velocity Gradient/Radial Distance
  • Pressure Gradient = (4*Dynamic Viscosity)/(Pipe Radius^2)
  • Pressure Gradient = Discharge in pipe/((pi/(8*Dynamic Viscosity))*(Pipe Radius^4))
  • Pressure Gradient = 8*Mean Velocity*Dynamic Viscosity/(Pipe Radius^2)
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