Pressure Gradient given Discharge through Pipe Solution

STEP 0: Pre-Calculation Summary
Formula Used
Pressure Gradient = Discharge in pipe/((pi/(8*Dynamic Viscosity))*(Pipe Radius^4))
dp|dr = Q/((pi/(8*μviscosity))*(R^4))
This formula uses 1 Constants, 4 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Variables Used
Pressure Gradient - (Measured in Newton per Cubic Meter) - Pressure Gradient is the change in pressure with respect to radial distance of element.
Discharge in pipe - (Measured in Cubic Meter per Second) - Discharge in pipe is the rate of flow of a liquid.
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.
STEP 1: Convert Input(s) to Base Unit
Discharge in pipe: 1.000001 Cubic Meter per Second --> 1.000001 Cubic 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)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
dp|dr = Q/((pi/(8*μviscosity))*(R^4)) --> 1.000001/((pi/(8*1.02))*(0.138^4))
Evaluating ... ...
dp|dr = 7161.8360484234
STEP 3: Convert Result to Output's Unit
7161.8360484234 Newton per Cubic Meter --> No Conversion Required
FINAL ANSWER
7161.8360484234 7161.836 Newton per Cubic Meter <-- Pressure Gradient
(Calculation completed in 00.004 seconds)

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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 Discharge through Pipe Formula

Pressure Gradient = Discharge in pipe/((pi/(8*Dynamic Viscosity))*(Pipe Radius^4))
dp|dr = Q/((pi/(8*μviscosity))*(R^4))

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 Discharge through Pipe?

Pressure Gradient given Discharge through Pipe calculator uses Pressure Gradient = Discharge in pipe/((pi/(8*Dynamic Viscosity))*(Pipe Radius^4)) to calculate the Pressure Gradient, The Pressure Gradient given Discharge through Pipe 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 Discharge through Pipe using this online calculator? To use this online calculator for Pressure Gradient given Discharge through Pipe, enter Discharge in pipe (Q), Dynamic Viscosity viscosity) & Pipe Radius (R) and hit the calculate button. Here is how the Pressure Gradient given Discharge through Pipe calculation can be explained with given input values -> 7161.836 = 1.000001/((pi/(8*1.02))*(0.138^4)).

FAQ

What is Pressure Gradient given Discharge through Pipe?
The Pressure Gradient given Discharge through Pipe is defined as the variation of pressure with respect to the length of the pipe and is represented as dp|dr = Q/((pi/(8*μviscosity))*(R^4)) or Pressure Gradient = Discharge in pipe/((pi/(8*Dynamic Viscosity))*(Pipe Radius^4)). Discharge in pipe is the rate of flow of a liquid, 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.
How to calculate Pressure Gradient given Discharge through Pipe?
The Pressure Gradient given Discharge through Pipe is defined as the variation of pressure with respect to the length of the pipe is calculated using Pressure Gradient = Discharge in pipe/((pi/(8*Dynamic Viscosity))*(Pipe Radius^4)). To calculate Pressure Gradient given Discharge through Pipe, you need Discharge in pipe (Q), Dynamic Viscosity viscosity) & Pipe Radius (R). With our tool, you need to enter the respective value for Discharge in pipe, Dynamic Viscosity & 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 Pressure Gradient?
In this formula, Pressure Gradient uses Discharge in pipe, Dynamic Viscosity & Pipe Radius. 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 = Fluid Velocity in Pipe/((1/(4*Dynamic Viscosity))*((Pipe Radius^2)-(Radial Distance^2)))
  • Pressure Gradient = (4*Dynamic Viscosity)/(Pipe Radius^2)
  • Pressure Gradient = 8*Mean Velocity*Dynamic Viscosity/(Pipe Radius^2)
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