Pressure Gradients given Mean Velocity of Flow Calculator

✖Mean velocity is defined as the average velocity of a fluid at a point and over an arbitrary time T.ⓘ Mean Velocity [V_mean]			+10% -10%
✖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%
✖The Pipe Radius is the radius of the pipe through which the fluid is flowing.ⓘ Pipe Radius [R]			+10% -10%

✖Pressure Gradient is the change in pressure with respect to radial distance of element.ⓘ Pressure Gradients given Mean Velocity of Flow [dp|dr]

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Formula

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Pressure Gradients given Mean Velocity of Flow

Formula

`"dp|dr" = 8*"V"_{"mean"}*"μ"_{"viscosity"}/("R"^2)`

Example

`"4327.662N/m³"=8*"10.1m/s"*"10.2P"/(("138mm")^2)`

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Pressure Gradients given Mean Velocity of Flow Solution

STEP 0: Pre-Calculation Summary

Formula Used

Pressure Gradient = 8*Mean Velocity*Dynamic Viscosity/(Pipe Radius^2)
dp|dr = 8*V_mean*μ_viscosity/(R^2)
This formula uses 4 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.
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.
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

Mean Velocity: 10.1 Meter per Second --> 10.1 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 = 8*V_mean*μ_viscosity/(R^2) --> 8*10.1*1.02/(0.138^2)

Evaluating ... ...

dp|dr = 4327.66225582861

STEP 3: Convert Result to Output's Unit

4327.66225582861 Newton per Cubic Meter --> No Conversion Required

FINAL ANSWER

4327.66225582861 ≈ 4327.662 Newton per Cubic Meter <-- Pressure Gradient

(Calculation completed in 00.020 seconds)

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Home » Engineering » Civil » Hydraulics and Waterworks » Laminar Flow » Steady Laminar Flow in Circular Pipes – Hagen Poiseuille Law » Pressure Gradient » Pressure Gradients given Mean Velocity of Flow

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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 Gradients given Mean Velocity of Flow Formula

Pressure Gradient = 8*Mean Velocity*Dynamic Viscosity/(Pipe Radius^2)
dp|dr = 8*V_mean*μ_viscosity/(R^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 Gradients given Mean Velocity of Flow?

Pressure Gradients given Mean Velocity of Flow calculator uses Pressure Gradient = 8*Mean Velocity*Dynamic Viscosity/(Pipe Radius^2) to calculate the Pressure Gradient, The Pressure Gradients given Mean Velocity of Flow is defined as the rate at which pressure is changing with respect to radial distance from center. Pressure Gradient is denoted by dp|dr symbol.

How to calculate Pressure Gradients given Mean Velocity of Flow using this online calculator? To use this online calculator for Pressure Gradients given Mean Velocity of Flow, enter Mean Velocity (V_mean), Dynamic Viscosity (μ_viscosity) & Pipe Radius (R) and hit the calculate button. Here is how the Pressure Gradients given Mean Velocity of Flow calculation can be explained with given input values -> 4327.662 = 8*10.1*1.02/(0.138^2).

FAQ

What is Pressure Gradients given Mean Velocity of Flow?

The Pressure Gradients given Mean Velocity of Flow is defined as the rate at which pressure is changing with respect to radial distance from center and is represented as dp|dr = 8*V_mean*μ_viscosity/(R^2) or Pressure Gradient = 8*Mean Velocity*Dynamic Viscosity/(Pipe Radius^2). Mean velocity is defined as the average velocity of a fluid at a point and over an arbitrary time T, 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 Gradients given Mean Velocity of Flow?

The Pressure Gradients given Mean Velocity of Flow is defined as the rate at which pressure is changing with respect to radial distance from center is calculated using Pressure Gradient = 8*Mean Velocity*Dynamic Viscosity/(Pipe Radius^2). To calculate Pressure Gradients given Mean Velocity of Flow, you need Mean Velocity (V_mean), Dynamic Viscosity (μ_viscosity) & Pipe Radius (R). With our tool, you need to enter the respective value for Mean Velocity, 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 Mean Velocity, 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 = Discharge in pipe/((pi/(8*Dynamic Viscosity))*(Pipe Radius^4))

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