Pressure Gradient given Velocity Gradient at Cylindrical Element Calculator

✖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%
✖Velocity Gradient is the difference in velocity between the adjacent layers of the fluid.ⓘ Velocity Gradient [VG]			+10% -10%
✖Radial distance is defined as distance between whisker sensor's pivot point to whisker-object contact point.ⓘ Radial Distance [d_radial]			+10% -10%

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

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Formula

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Pressure Gradient given Velocity Gradient at Cylindrical Element

Formula

`"dp|dr" = 2*"μ"_{"viscosity"}*"VG"/"d"_{"radial"}`

Example

`"16.98522N/m³"=2*"10.2P"*"76.6m/s"/"9.2m"`

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Pressure Gradient given Velocity Gradient at Cylindrical Element Solution

STEP 0: Pre-Calculation Summary

Formula Used

Pressure Gradient = 2*Dynamic Viscosity*Velocity Gradient/Radial Distance
dp|dr = 2*μ_viscosity*VG/d_radial
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.
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.
Velocity Gradient - (Measured in Meter per Second) - Velocity Gradient is the difference in velocity between the adjacent layers of the fluid.
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)
Velocity Gradient: 76.6 Meter per Second --> 76.6 Meter per Second No Conversion Required
Radial Distance: 9.2 Meter --> 9.2 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

dp|dr = 2*μ_viscosity*VG/d_radial --> 2*1.02*76.6/9.2

Evaluating ... ...

dp|dr = 16.9852173913043

STEP 3: Convert Result to Output's Unit

16.9852173913043 Newton per Cubic Meter --> No Conversion Required

FINAL ANSWER

16.9852173913043 ≈ 16.98522 Newton per Cubic Meter <-- Pressure Gradient

(Calculation completed in 00.004 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 Gradient given Velocity Gradient at Cylindrical Element

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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 Gradient at Cylindrical Element Formula

Pressure Gradient = 2*Dynamic Viscosity*Velocity Gradient/Radial Distance
dp|dr = 2*μ_viscosity*VG/d_radial

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 Gradient at Cylindrical Element?

Pressure Gradient given Velocity Gradient at Cylindrical Element calculator uses Pressure Gradient = 2*Dynamic Viscosity*Velocity Gradient/Radial Distance to calculate the Pressure Gradient, The Pressure Gradient given Velocity Gradient at Cylindrical Element is defined as the variation of pressure through the length of the pipe. Pressure Gradient is denoted by dp|dr symbol.

How to calculate Pressure Gradient given Velocity Gradient at Cylindrical Element using this online calculator? To use this online calculator for Pressure Gradient given Velocity Gradient at Cylindrical Element, enter Dynamic Viscosity (μ_viscosity), Velocity Gradient (VG) & Radial Distance (d_radial) and hit the calculate button. Here is how the Pressure Gradient given Velocity Gradient at Cylindrical Element calculation can be explained with given input values -> 16.98522 = 2*1.02*76.6/9.2.

FAQ

What is Pressure Gradient given Velocity Gradient at Cylindrical Element?

The Pressure Gradient given Velocity Gradient at Cylindrical Element is defined as the variation of pressure through the length of the pipe and is represented as dp|dr = 2*μ_viscosity*VG/d_radial or Pressure Gradient = 2*Dynamic Viscosity*Velocity Gradient/Radial Distance. The Dynamic Viscosity of a fluid is the measure of its resistance to flow when an external force is applied, Velocity Gradient is the difference in velocity between the adjacent layers of the fluid & Radial distance is defined as distance between whisker sensor's pivot point to whisker-object contact point.

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

The Pressure Gradient given Velocity Gradient at Cylindrical Element is defined as the variation of pressure through the length of the pipe is calculated using Pressure Gradient = 2*Dynamic Viscosity*Velocity Gradient/Radial Distance. To calculate Pressure Gradient given Velocity Gradient at Cylindrical Element, you need Dynamic Viscosity (μ_viscosity), Velocity Gradient (VG) & Radial Distance (d_radial). With our tool, you need to enter the respective value for Dynamic Viscosity, Velocity Gradient & 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 Dynamic Viscosity, Velocity Gradient & 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 = 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))
Pressure Gradient = 8*Mean Velocity*Dynamic Viscosity/(Pipe Radius^2)

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