Pressure Gradient given Shear Stress Solution

STEP 0: Pre-Calculation Summary
Formula Used
Pressure Gradient = ((Dynamic Viscosity*Mean Velocity/Distance between plates)-Shear Stress)/(0.5*Distance between plates-Horizontal Distance)
dp|dr = ((μviscosity*Vmean/D)-𝜏)/(0.5*D-R)
This formula uses 6 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.
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.
Distance between plates - Distance between plates is the length of the space between two points.
Shear Stress - (Measured in Pascal) - Shear Stress is force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress.
Horizontal Distance - (Measured in Meter) - Horizontal Distance denotes the instantaneous horizontal distance cover by an object in a projectile motion.
STEP 1: Convert Input(s) to Base Unit
Dynamic Viscosity: 10.2 Poise --> 1.02 Pascal Second (Check conversion here)
Mean Velocity: 10.1 Meter per Second --> 10.1 Meter per Second No Conversion Required
Distance between plates: 2.9 --> No Conversion Required
Shear Stress: 45.9 Pascal --> 45.9 Pascal No Conversion Required
Horizontal Distance: 4 Meter --> 4 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
dp|dr = ((μviscosity*Vmean/D)-𝜏)/(0.5*D-R) --> ((1.02*10.1/2.9)-45.9)/(0.5*2.9-4)
Evaluating ... ...
dp|dr = 16.6068965517241
STEP 3: Convert Result to Output's Unit
16.6068965517241 Newton per Cubic Meter --> No Conversion Required
FINAL ANSWER
16.6068965517241 16.6069 Newton per Cubic Meter <-- Pressure Gradient
(Calculation completed in 00.004 seconds)

Credits

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National Institute of Technology Karnataka (NITK), Surathkal
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12 Laminar Flow between Parallel Flat Plates, one plate moving and other at rest, Couette Flow Calculators

Dynamic Viscosity given Flow Velocity
Go Dynamic Viscosity = ((0.5*Pressure Gradient*(Distance between plates*Horizontal Distance-Horizontal Distance^2)))/((Mean Velocity*Horizontal Distance/Width)-Flow velocity)
Flow Velocity of Section
Go Flow velocity = (Mean Velocity*Horizontal Distance/Width)-(0.5*Pressure Gradient*(Distance between plates*Horizontal Distance-Horizontal Distance^2))/Dynamic Viscosity
Pressure Gradient given Flow Velocity
Go Pressure Gradient = ((Mean Velocity*Horizontal Distance/Width)-Flow velocity)/(((0.5*(Width*Horizontal Distance-Horizontal Distance^2))/Dynamic Viscosity))
Mean Velocity of Flow given Flow Velocity
Go Flow velocity = (Mean Velocity*Horizontal Distance/Width)-(0.5*Pressure Gradient*(Width*Horizontal Distance-Horizontal Distance^2))/Dynamic Viscosity
Mean Velocity of Flow given Shear Stress
Go Mean Velocity = (Shear Stress+Pressure Gradient*(0.5*Distance between plates-Horizontal Distance))*(Distance between plates/Dynamic Viscosity)
Pressure Gradient given Shear Stress
Go Pressure Gradient = ((Dynamic Viscosity*Mean Velocity/Distance between plates)-Shear Stress)/(0.5*Distance between plates-Horizontal Distance)
Shear Stress given Velocity
Go Shear Stress = (Dynamic Viscosity*Mean Velocity/Distance between plates)-Pressure Gradient*(0.5*Distance between plates-Horizontal Distance)
Dynamic Viscosity given Stress
Go Dynamic Viscosity = (Shear Stress+Pressure Gradient*(0.5*Distance between plates-Horizontal Distance))*(Width/Mean Velocity)
Distance between Plates given Flow Velocity with No Pressure Gradient
Go Distance between plates = Mean Velocity*Horizontal Distance/Flow velocity
Horizontal Distance given Flow Velocity with No Pressure Gradient
Go Horizontal Distance = Flow velocity*Width/Mean Velocity
Mean Velocity of Flow given Flow Velocity with No Pressure Gradient
Go Mean Velocity = Distance between plates*Horizontal Distance
Flow Velocity given No Pressure Gradient
Go Flow velocity = (Mean Velocity*Horizontal Distance)

Pressure Gradient given Shear Stress Formula

Pressure Gradient = ((Dynamic Viscosity*Mean Velocity/Distance between plates)-Shear Stress)/(0.5*Distance between plates-Horizontal Distance)
dp|dr = ((μviscosity*Vmean/D)-𝜏)/(0.5*D-R)

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 Shear Stress?

Pressure Gradient given Shear Stress calculator uses Pressure Gradient = ((Dynamic Viscosity*Mean Velocity/Distance between plates)-Shear Stress)/(0.5*Distance between plates-Horizontal Distance) to calculate 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 calculate Pressure Gradient given Shear Stress using this online calculator? To use this online calculator for Pressure Gradient given Shear Stress, enter Dynamic Viscosity viscosity), Mean Velocity (Vmean), Distance between plates (D), Shear Stress (𝜏) & Horizontal Distance (R) and hit the calculate button. Here is how the Pressure Gradient given Shear Stress calculation can be explained with given input values -> 16.6069 = ((1.02*10.1/2.9)-45.9)/(0.5*2.9-4).

FAQ

What is Pressure Gradient given Shear Stress?
The Pressure Gradient given Shear Stress is defined as change in pressure with respect to length of pipe in the horizontal distance and is represented as dp|dr = ((μviscosity*Vmean/D)-𝜏)/(0.5*D-R) or Pressure Gradient = ((Dynamic Viscosity*Mean Velocity/Distance between plates)-Shear Stress)/(0.5*Distance between plates-Horizontal Distance). The Dynamic Viscosity of a fluid is the measure of its resistance to flow when an external force is applied, Mean velocity is defined as the average velocity of a fluid at a point and over an arbitrary time T, Distance between plates is the length of the space between two points, Shear Stress is force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress & Horizontal Distance denotes the instantaneous horizontal distance cover by an object in a projectile motion.
How to calculate Pressure Gradient given Shear Stress?
The Pressure Gradient given Shear Stress is defined as change in pressure with respect to length of pipe in the horizontal distance is calculated using Pressure Gradient = ((Dynamic Viscosity*Mean Velocity/Distance between plates)-Shear Stress)/(0.5*Distance between plates-Horizontal Distance). To calculate Pressure Gradient given Shear Stress, you need Dynamic Viscosity viscosity), Mean Velocity (Vmean), Distance between plates (D), Shear Stress (𝜏) & Horizontal Distance (R). With our tool, you need to enter the respective value for Dynamic Viscosity, Mean Velocity, Distance between plates, Shear Stress & Horizontal 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, Mean Velocity, Distance between plates, Shear Stress & Horizontal Distance. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Pressure Gradient = ((Mean Velocity*Horizontal Distance/Width)-Flow velocity)/(((0.5*(Width*Horizontal Distance-Horizontal Distance^2))/Dynamic Viscosity))
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