Distance between Plates given Mean Velocity of Flow with Pressure Gradient Solution

STEP 0: Pre-Calculation Summary
Formula Used
Width = sqrt((12*Dynamic Viscosity*Mean Velocity)/Pressure Gradient)
w = sqrt((12*μviscosity*Vmean)/dp|dr)
This formula uses 1 Functions, 4 Variables
Functions Used
sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)
Variables Used
Width - (Measured in Meter) - Width is the measurement or extent of something from side to side.
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.
Pressure Gradient - (Measured in Newton per Cubic Meter) - Pressure Gradient is the change in pressure with respect to radial distance of element.
STEP 1: Convert Input(s) to Base Unit
Dynamic Viscosity: 10.2 Poise --> 1.02 Pascal Second (Check conversion here)
Mean Velocity: 32.4 Meter per Second --> 32.4 Meter per Second No Conversion Required
Pressure Gradient: 17 Newton per Cubic Meter --> 17 Newton per Cubic Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
w = sqrt((12*μviscosity*Vmean)/dp|dr) --> sqrt((12*1.02*32.4)/17)
Evaluating ... ...
w = 4.82990683139955
STEP 3: Convert Result to Output's Unit
4.82990683139955 Meter --> No Conversion Required
FINAL ANSWER
4.82990683139955 4.829907 Meter <-- Width
(Calculation completed in 00.004 seconds)

Credits

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National Institute of Technology Karnataka (NITK), Surathkal
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20 Laminar Flow between Parallel Plates, both plates at rest Calculators

Distance between Plates given Pressure Head Drop
Go Width = sqrt((12*Dynamic Viscosity*Length of Pipe*Mean Velocity)/(Specific Weight of Liquid*Head Loss due to Friction))
Length of Pipe given Pressure Head Drop
Go Length of Pipe = (Specific Weight of Liquid*Width*Width*Head Loss due to Friction)/(12*Dynamic Viscosity*Mean Velocity)
Velocity Distribution Profile
Go Velocity of Liquid = -(1/(2*Dynamic Viscosity))*Pressure Gradient*(Width*Horizontal Distance-(Horizontal Distance^2))
Distance between Plates using Velocity Distribution Profile
Go Width = (((-Velocity of Liquid*2*Dynamic Viscosity)/Pressure Gradient)+(Horizontal Distance^2))/Horizontal Distance
Length of Pipe given Pressure Difference
Go Length of Pipe = (Pressure Difference*Width*Width)/(Dynamic Viscosity*12*Mean Velocity)
Distance between Plates given Pressure Difference
Go Width = sqrt(12*Mean Velocity*Dynamic Viscosity*Length of Pipe/Pressure Difference)
Pressure Head Drop
Go Head Loss due to Friction = (12*Dynamic Viscosity*Length of Pipe*Mean Velocity)/(Specific Weight of Liquid)
Pressure Difference
Go Pressure Difference = 12*Dynamic Viscosity*Mean Velocity*Length of Pipe/(Width^2)
Distance between Plates given Maximum Velocity between Plates
Go Width = sqrt((8*Dynamic Viscosity*Maximum Velocity)/(Pressure Gradient))
Distance between Plates given Mean Velocity of Flow with Pressure Gradient
Go Width = sqrt((12*Dynamic Viscosity*Mean Velocity)/Pressure Gradient)
Distance between Plates given Discharge
Go Width = ((Discharge in Laminar Flow*12*Dynamic Viscosity)/Pressure Gradient)^(1/3)
Discharge given Viscosity
Go Discharge in Laminar Flow = Pressure Gradient*(Width^3)/(12*Dynamic Viscosity)
Maximum Velocity between Plates
Go Maximum Velocity = ((Width^2)*Pressure Gradient)/(8*Dynamic Viscosity)
Distance between Plates given Shear Stress Distribution Profile
Go Width = 2*(Horizontal Distance-(Shear Stress/Pressure Gradient))
Shear Stress Distribution Profile
Go Shear Stress = -Pressure Gradient*(Width/2-Horizontal Distance)
Horizontal Distance given Shear Stress Distribution Profile
Go Horizontal Distance = Width/2+(Shear Stress/Pressure Gradient)
Maximum Shear Stress in fluid
Go Maximum Shear Stress in Shaft = 0.5*Pressure Gradient*Width
Distance between Plates given Mean Velocity of Flow
Go Width = Discharge in Laminar Flow/Mean Velocity
Discharge given Mean Velocity of Flow
Go Discharge in Laminar Flow = Width*Mean Velocity
Maximum Velocity given Mean Velocity of Flow
Go Maximum Velocity = 1.5*Mean Velocity

Distance between Plates given Mean Velocity of Flow with Pressure Gradient Formula

Width = sqrt((12*Dynamic Viscosity*Mean Velocity)/Pressure Gradient)
w = sqrt((12*μviscosity*Vmean)/dp|dr)

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 Distance between Plates given Mean Velocity of Flow with Pressure Gradient?

Distance between Plates given Mean Velocity of Flow with Pressure Gradient calculator uses Width = sqrt((12*Dynamic Viscosity*Mean Velocity)/Pressure Gradient) to calculate the Width, The Distance between Plates given Mean Velocity of Flow with Pressure Gradient is defined as the width of section of flow in the pipe. Width is denoted by w symbol.

How to calculate Distance between Plates given Mean Velocity of Flow with Pressure Gradient using this online calculator? To use this online calculator for Distance between Plates given Mean Velocity of Flow with Pressure Gradient, enter Dynamic Viscosity viscosity), Mean Velocity (Vmean) & Pressure Gradient (dp|dr) and hit the calculate button. Here is how the Distance between Plates given Mean Velocity of Flow with Pressure Gradient calculation can be explained with given input values -> 4.829907 = sqrt((12*1.02*32.4)/17).

FAQ

What is Distance between Plates given Mean Velocity of Flow with Pressure Gradient?
The Distance between Plates given Mean Velocity of Flow with Pressure Gradient is defined as the width of section of flow in the pipe and is represented as w = sqrt((12*μviscosity*Vmean)/dp|dr) or Width = sqrt((12*Dynamic Viscosity*Mean Velocity)/Pressure Gradient). 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 & Pressure Gradient is the change in pressure with respect to radial distance of element.
How to calculate Distance between Plates given Mean Velocity of Flow with Pressure Gradient?
The Distance between Plates given Mean Velocity of Flow with Pressure Gradient is defined as the width of section of flow in the pipe is calculated using Width = sqrt((12*Dynamic Viscosity*Mean Velocity)/Pressure Gradient). To calculate Distance between Plates given Mean Velocity of Flow with Pressure Gradient, you need Dynamic Viscosity viscosity), Mean Velocity (Vmean) & Pressure Gradient (dp|dr). With our tool, you need to enter the respective value for Dynamic Viscosity, Mean Velocity & Pressure Gradient 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 Width?
In this formula, Width uses Dynamic Viscosity, Mean Velocity & Pressure Gradient. We can use 7 other way(s) to calculate the same, which is/are as follows -
  • Width = (((-Velocity of Liquid*2*Dynamic Viscosity)/Pressure Gradient)+(Horizontal Distance^2))/Horizontal Distance
  • Width = sqrt((8*Dynamic Viscosity*Maximum Velocity)/(Pressure Gradient))
  • Width = ((Discharge in Laminar Flow*12*Dynamic Viscosity)/Pressure Gradient)^(1/3)
  • Width = Discharge in Laminar Flow/Mean Velocity
  • Width = sqrt(12*Mean Velocity*Dynamic Viscosity*Length of Pipe/Pressure Difference)
  • Width = sqrt((12*Dynamic Viscosity*Length of Pipe*Mean Velocity)/(Specific Weight of Liquid*Head Loss due to Friction))
  • Width = 2*(Horizontal Distance-(Shear Stress/Pressure Gradient))
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