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Pressure Gradient given Flow Velocity Formula

GoPressure Gradient given Shear Stress 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{(V mean \cdot \frac{R}{w}) - V f}{(\frac{0.5 \cdot (w \cdot R - R^{2})}{μ})}

dp|dr - Pressure Gradient?V_mean - Mean Velocity?R - Horizontal Distance?w - Width?V_f - Flow velocity?μ - Dynamic Viscosity?

Pressure Gradient given Flow Velocity Example

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Here is how the Pressure Gradient given Flow Velocity equation looks like with Values.

Here is how the Pressure Gradient given Flow Velocity equation looks like with Units.

Here is how the Pressure Gradient given Flow Velocity equation looks like.

8.6963 = \frac{(10.1 \cdot \frac{4}{2.29}) - 46.8}{(\frac{0.5 \cdot (2.29 \cdot 4 - 4^{2})}{10.2})}

8.6963N/m³ = \frac{(10.1m/s \cdot \frac{4m}{2.29m}) - 46.8m/s}{(\frac{0.5 \cdot (2.29m \cdot 4m - {4m}^{2})}{10.2P})}

8.6963 = \frac{(10.1 \cdot \frac{4}{2.29}) - 46.8}{(\frac{0.5 \cdot (2.29 \cdot 4 - 4^{2})}{10.2})}

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Pressure Gradient given Flow Velocity Solution

Follow our step by step solution on how to calculate Pressure Gradient given Flow Velocity?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

dp|dr = \frac{(10.1m/s \cdot \frac{4m}{2.29m}) - 46.8m/s}{(\frac{0.5 \cdot (2.29m \cdot 4m - {4m}^{2})}{10.2P})}

Next Step Convert Units

∴

dp|dr = \frac{(10.1m/s \cdot \frac{4m}{2.29m}) - 46.8m/s}{(\frac{0.5 \cdot (2.29m \cdot 4m - {4m}^{2})}{1.02Pa*s})}

Next Step Prepare to Evaluate

∴

dp|dr = \frac{(10.1 \cdot \frac{4}{2.29}) - 46.8}{(\frac{0.5 \cdot (2.29 \cdot 4 - 4^{2})}{1.02})}

Next Step Evaluate

∴

dp|dr = 8.69626905692178N/m³

LAST Step Rounding Answer

∴

dp|dr = 8.6963N/m³

Pressure Gradient given Flow Velocity 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

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

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

Width

The Width refers to the measurement or extent of something from side to side.

Symbol: w

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Width

Flow velocity

Flow Velocity is the velocity of the flow of any fluid.

Symbol: V_f

Measurement: SpeedUnit: m/s

Note: Value can be positive or negative.

Formulas to find Flow velocity

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

Other Formulas to find Pressure Gradient

Go Pressure Gradient given Shear Stress

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

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 Flow Velocity?

Pressure Gradient given Flow Velocity evaluator uses Pressure Gradient = ((Mean Velocity*Horizontal Distance/Width)-Flow velocity)/(((0.5*(Width*Horizontal Distance-Horizontal Distance^2))/Dynamic Viscosity)) to evaluate the Pressure Gradient, The Pressure Gradient given Flow Velocity formula is defined as the change in pressure per unit distance along the flow direction, it drives fluid flow from high to low pressure. Pressure Gradient is denoted by dp|dr symbol.

How to evaluate Pressure Gradient given Flow Velocity using this online evaluator? To use this online evaluator for Pressure Gradient given Flow Velocity, enter Mean Velocity (V_mean), Horizontal Distance (R), Width (w), Flow velocity (V_f) & Dynamic Viscosity (μ) and hit the calculate button.

FAQs on Pressure Gradient given Flow Velocity

What is the formula to find Pressure Gradient given Flow Velocity?

The formula of Pressure Gradient given Flow Velocity is expressed as Pressure Gradient = ((Mean Velocity*Horizontal Distance/Width)-Flow velocity)/(((0.5*(Width*Horizontal Distance-Horizontal Distance^2))/Dynamic Viscosity)). Here is an example- 17 = ((10.1*4/2.29)-46.8)/(((0.5*(2.29*4-4^2))/1.02)).

How to calculate Pressure Gradient given Flow Velocity?

With Mean Velocity (V_mean), Horizontal Distance (R), Width (w), Flow velocity (V_f) & Dynamic Viscosity (μ) we can find Pressure Gradient given Flow Velocity using the formula - Pressure Gradient = ((Mean Velocity*Horizontal Distance/Width)-Flow velocity)/(((0.5*(Width*Horizontal Distance-Horizontal Distance^2))/Dynamic Viscosity)).

What are the other ways to Calculate Pressure Gradient?

Here are the different ways to Calculate Pressure Gradient-

Pressure Gradient=((Dynamic Viscosity*Mean Velocity/Distance between plates)-Shear Stress)/(0.5*Distance between plates-Horizontal Distance)

Can the Pressure Gradient given Flow Velocity be negative?

No, the Pressure Gradient given Flow Velocity, measured in Pressure Gradient cannot be negative.

Which unit is used to measure Pressure Gradient given Flow Velocity?

Pressure Gradient given Flow Velocity 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 Flow Velocity can be measured.

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: Value
: Unit

Pressure Gradient given Flow Velocity Formula

​GoPressure Gradient given Shear Stress Formula

Pressure Gradient given Flow Velocity Example

Pressure Gradient given Flow Velocity Solution

Pressure Gradient given Flow Velocity 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 Flow Velocity?

FAQs on Pressure Gradient given Flow Velocity

Variable Name

GoPressure Gradient given Shear Stress Formula