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Pressure Gradient given Shear Stress Formula

GoPressure Gradient given Flow Velocity Formula

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The Pressure Gradient refers to the rate of change of pressure in a particular direction indicating how quickly the pressure increases or decreases around a specific location. Check FAQs

dp|dr = \frac{(μ \cdot \frac{V mean}{D}) - 𝜏}{0.5 \cdot D - R}

dp|dr - Pressure Gradient?μ - Dynamic Viscosity?V_mean - Mean Velocity?D - Distance between plates?𝜏 - Shear Stress?R - Horizontal Distance?

Pressure Gradient given Shear Stress Example

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Here is how the Pressure Gradient given Shear Stress equation looks like with Values.

Here is how the Pressure Gradient given Shear Stress equation looks like with Units.

Here is how the Pressure Gradient given Shear Stress equation looks like.

16.6069 = \frac{(10.2 \cdot \frac{10.1}{2.9}) - 45.9}{0.5 \cdot 2.9 - 4}

16.6069N/m³ = \frac{(10.2P \cdot \frac{10.1m/s}{2.9}) - 45.9Pa}{0.5 \cdot 2.9 - 4m}

16.6069 = \frac{(10.2 \cdot \frac{10.1}{2.9}) - 45.9}{0.5 \cdot 2.9 - 4}

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Pressure Gradient given Shear Stress Solution

Follow our step by step solution on how to calculate Pressure Gradient given Shear Stress?

FIRST Step Consider the formula

dp|dr = \frac{(μ \cdot \frac{V mean}{D}) - 𝜏}{0.5 \cdot D - R}

Next Step Substitute values of Variables

∴

dp|dr = \frac{(10.2P \cdot \frac{10.1m/s}{2.9}) - 45.9Pa}{0.5 \cdot 2.9 - 4m}

Next Step Convert Units

∴

dp|dr = \frac{(1.02Pa*s \cdot \frac{10.1m/s}{2.9}) - 45.9Pa}{0.5 \cdot 2.9 - 4m}

Next Step Prepare to Evaluate

∴

dp|dr = \frac{(1.02 \cdot \frac{10.1}{2.9}) - 45.9}{0.5 \cdot 2.9 - 4}

Next Step Evaluate

∴

dp|dr = 16.6068965517241N/m³

LAST Step Rounding Answer

∴

dp|dr = 16.6069N/m³

Pressure Gradient given Shear Stress Formula Elements

Variables

Pressure Gradient

The Pressure Gradient refers to the rate of change of pressure in a particular direction indicating how quickly the pressure increases or decreases around a specific location.

Symbol: dp|dr

Measurement: Pressure GradientUnit: N/m³

Note: Value should be greater than 0.

Formulas to find Pressure Gradient

Dynamic Viscosity

The Dynamic Viscosity refers to the internal resistance of a fluid to flow when a force is applied.

Symbol: μ

Measurement: Dynamic ViscosityUnit: P

Note: Value should be greater than 0.

Formulas to find Dynamic Viscosity

Mean Velocity

Mean velocity is defined as the average velocity of a fluid at a point and over an arbitrary time T.

Symbol: V_mean

Measurement: SpeedUnit: m/s

Note: Value can be positive or negative.

Formulas to find Mean Velocity

Distance between plates

Distance between plates is the length of the space between two points.

Symbol: D

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Distance between plates

Shear Stress

Shear Stress is force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress.

Symbol: 𝜏

Measurement: StressUnit: Pa

Note: Value should be greater than 0.

Formulas to find Shear Stress

Horizontal Distance

Horizontal Distance denotes the instantaneous horizontal distance cover by an object in a projectile motion.

Symbol: R

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Horizontal Distance

Other Formulas to find Pressure Gradient

Go Pressure Gradient given Flow Velocity

dp|dr = \frac{(V mean \cdot \frac{R}{w}) - V f}{(\frac{0.5 \cdot (w \cdot R - R^{2})}{μ})}

Other formulas in Laminar Flow between Parallel Flat Plates, one plate moving and other at rest, Couette Flow category

Go Flow Velocity of Section

V f = (V mean \cdot \frac{R}{w}) - \frac{0.5 \cdot dp|dr \cdot (D \cdot R - R^{2})}{μ}

Go Mean Velocity of Flow given Flow Velocity

V f = (V mean \cdot \frac{R}{w}) - \frac{0.5 \cdot dp|dr \cdot (w \cdot R - R^{2})}{μ}

Go Dynamic Viscosity given Flow Velocity

μ = \frac{(0.5 \cdot dp|dr \cdot (D \cdot R - R^{2}))}{(V mean \cdot \frac{R}{w}) - V f}

Go Flow Velocity given No Pressure Gradient

V f = (V mean \cdot R)

How to Evaluate Pressure Gradient given Shear Stress?

Pressure Gradient given Shear Stress evaluator uses Pressure Gradient = ((Dynamic Viscosity*Mean Velocity/Distance between plates)-Shear Stress)/(0.5*Distance between plates-Horizontal Distance) to evaluate the Pressure Gradient, The Pressure Gradient given Shear Stress is defined as change in pressure with respect to length of pipe in the horizontal distance. Pressure Gradient is denoted by dp|dr symbol.

How to evaluate Pressure Gradient given Shear Stress using this online evaluator? To use this online evaluator for Pressure Gradient given Shear Stress, enter Dynamic Viscosity (μ), Mean Velocity (V_mean), Distance between plates (D), Shear Stress (𝜏) & Horizontal Distance (R) and hit the calculate button.

FAQs on Pressure Gradient given Shear Stress

What is the formula to find Pressure Gradient given Shear Stress?

The formula of Pressure Gradient given Shear Stress is expressed as Pressure Gradient = ((Dynamic Viscosity*Mean Velocity/Distance between plates)-Shear Stress)/(0.5*Distance between plates-Horizontal Distance). Here is an example- 16.6069 = ((1.02*10.1/2.9)-45.9)/(0.5*2.9-4).

How to calculate Pressure Gradient given Shear Stress?

With Dynamic Viscosity (μ), Mean Velocity (V_mean), Distance between plates (D), Shear Stress (𝜏) & Horizontal Distance (R) we can find Pressure Gradient given Shear Stress using the formula - Pressure Gradient = ((Dynamic Viscosity*Mean Velocity/Distance between plates)-Shear Stress)/(0.5*Distance between plates-Horizontal Distance).

What are the other ways to Calculate Pressure Gradient?

Here are the different ways to Calculate Pressure Gradient-

Pressure Gradient=((Mean Velocity*Horizontal Distance/Width)-Flow velocity)/(((0.5*(Width*Horizontal Distance-Horizontal Distance^2))/Dynamic Viscosity))

Can the Pressure Gradient given Shear Stress be negative?

No, the Pressure Gradient given Shear Stress, measured in Pressure Gradient cannot be negative.

Which unit is used to measure Pressure Gradient given Shear Stress?

Pressure Gradient given Shear Stress is usually measured using the Newton per Cubic Meter[N/m³] for Pressure Gradient. Newton per Cubic Inch[N/m³], Kilonewton per Cubic Kilometer[N/m³], Newton per Cubic Kilometer[N/m³] are the few other units in which Pressure Gradient given Shear Stress can be measured.

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Pressure Gradient given Shear Stress Formula

​GoPressure Gradient given Flow Velocity Formula

Pressure Gradient given Shear Stress Example

Pressure Gradient given Shear Stress Solution

Pressure Gradient given Shear Stress Formula Elements

Other Formulas to find Pressure Gradient

Other formulas in Laminar Flow between Parallel Flat Plates, one plate moving and other at rest, Couette Flow category

How to Evaluate Pressure Gradient given Shear Stress?

FAQs on Pressure Gradient given Shear Stress

Variable Name

GoPressure Gradient given Flow Velocity Formula