Distance of Element from Center Line given Velocity at any point in Cylindrical Element Calculator

✖The Pipe Radius is the radius of the pipe through which the fluid is flowing.ⓘ Pipe Radius [R]			+10% -10%
✖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%
✖Fluid Velocity in Pipe is the volume of fluid flowing in the given vessel per unit cross sectional area.ⓘ Fluid Velocity in Pipe [u_Fluid]			+10% -10%
✖Pressure Gradient is the change in pressure with respect to radial distance of element.ⓘ Pressure Gradient [dp\|dr]			+10% -10%

✖Radial distance is defined as distance between whisker sensor's pivot point to whisker-object contact point.ⓘ Distance of Element from Center Line given Velocity at any point in Cylindrical Element [d_radial]

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Distance of Element from Center Line given Velocity at any point in Cylindrical Element

Formula

`"d"_{"radial"} = sqrt(("R"^2)-(-4*"μ"_{"viscosity"}*"u"_{"Fluid"}/"dp|dr"))`

Example

`"8.486403m"=sqrt((("138mm")^2)-(-4*"10.2P"*"300m/s"/"17N/m³"))`

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Distance of Element from Center Line given Velocity at any point in Cylindrical Element Solution

STEP 0: Pre-Calculation Summary

Formula Used

Radial Distance = sqrt((Pipe Radius^2)-(-4*Dynamic Viscosity*Fluid Velocity in Pipe/Pressure Gradient))
d_radial = sqrt((R^2)-(-4*μ_viscosity*u_Fluid/dp|dr))
This formula uses 1 Functions, 5 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

Radial Distance - (Measured in Meter) - Radial distance is defined as distance between whisker sensor's pivot point to whisker-object contact point.
Pipe Radius - (Measured in Meter) - The Pipe Radius is the radius of the pipe through which the fluid is flowing.
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.
Fluid Velocity in Pipe - (Measured in Meter per Second) - Fluid Velocity in Pipe is the volume of fluid flowing in the given vessel per unit cross sectional area.
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

Pipe Radius: 138 Millimeter --> 0.138 Meter (Check conversion here)
Dynamic Viscosity: 10.2 Poise --> 1.02 Pascal Second (Check conversion here)
Fluid Velocity in Pipe: 300 Meter per Second --> 300 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

d_radial = sqrt((R^2)-(-4*μ_viscosity*u_Fluid/dp|dr)) --> sqrt((0.138^2)-(-4*1.02*300/17))

Evaluating ... ...

d_radial = 8.48640347850607

STEP 3: Convert Result to Output's Unit

8.48640347850607 Meter --> No Conversion Required

FINAL ANSWER

8.48640347850607 ≈ 8.486403 Meter <-- Radial Distance

(Calculation completed in 00.004 seconds)

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< 12 Steady Laminar Flow in Circular Pipes – Hagen Poiseuille Law Calculators

Distance of Element from Center Line given Velocity at any point in Cylindrical Element

Go Radial Distance = sqrt((Pipe Radius^2)-(-4*Dynamic Viscosity*Fluid Velocity in Pipe/Pressure Gradient))

Velocity at any point in Cylindrical Element

Go Fluid Velocity in Pipe = -(1/(4*Dynamic Viscosity))*Pressure Gradient*((Pipe Radius^2)-(Radial Distance^2))

Shear Stress at any Cylindrical Element given Head Loss

Go Shear Stress = (Specific Weight of Liquid*Head Loss due to Friction*Radial Distance)/(2*Length of Pipe)

Distance of Element from Center Line given Head Loss

Go Radial Distance = 2*Shear Stress*Length of Pipe/(Head Loss due to Friction*Specific Weight of Liquid)

Discharge through Pipe given Pressure Gradient

Go Discharge in pipe = (pi/(8*Dynamic Viscosity))*(Pipe Radius^4)*Pressure Gradient

Velocity Gradient given Pressure Gradient at Cylindrical Element

Go Velocity Gradient = (1/(2*Dynamic Viscosity))*Pressure Gradient*Radial Distance

Distance of Element from Center Line given Velocity Gradient at Cylindrical Element

Go Radial Distance = 2*Dynamic Viscosity*Velocity Gradient/Pressure Gradient

Mean Velocity of Fluid Flow

Go Mean Velocity = (1/(8*Dynamic Viscosity))*Pressure Gradient*Pipe Radius^2

Distance of Element from Center line given Shear Stress at any Cylindrical Element

Go Radial Distance = 2*Shear Stress/Pressure Gradient

Shear Stress at any Cylindrical Element

Go Shear Stress = Pressure Gradient*Radial Distance/2

Mean Velocity of Flow given Maximum Velocity at Axis of Cylindrical Element

Go Mean Velocity = 0.5*Maximum Velocity

Maximum Velocity at Axis of Cylindrical Element given Mean Velocity of Flow

Go Maximum Velocity = 2*Mean Velocity

Distance of Element from Center Line given Velocity at any point in Cylindrical Element Formula

Radial Distance = sqrt((Pipe Radius^2)-(-4*Dynamic Viscosity*Fluid Velocity in Pipe/Pressure Gradient))
d_radial = sqrt((R^2)-(-4*μ_viscosity*u_Fluid/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 of Element from Center Line given Velocity at any point in Cylindrical Element?

Distance of Element from Center Line given Velocity at any point in Cylindrical Element calculator uses Radial Distance = sqrt((Pipe Radius^2)-(-4*Dynamic Viscosity*Fluid Velocity in Pipe/Pressure Gradient)) to calculate the Radial Distance, The Distance of Element from Center Line given Velocity at any point in Cylindrical Element is defined as the radius of the elemental section. Radial Distance is denoted by d_radial symbol.

How to calculate Distance of Element from Center Line given Velocity at any point in Cylindrical Element using this online calculator? To use this online calculator for Distance of Element from Center Line given Velocity at any point in Cylindrical Element, enter Pipe Radius (R), Dynamic Viscosity (μ_viscosity), Fluid Velocity in Pipe (u_Fluid) & Pressure Gradient (dp|dr) and hit the calculate button. Here is how the Distance of Element from Center Line given Velocity at any point in Cylindrical Element calculation can be explained with given input values -> 8.487638 = sqrt((0.138^2)-(-4*1.02*300/17)).

FAQ

What is Distance of Element from Center Line given Velocity at any point in Cylindrical Element?

The Distance of Element from Center Line given Velocity at any point in Cylindrical Element is defined as the radius of the elemental section and is represented as d_radial = sqrt((R^2)-(-4*μ_viscosity*u_Fluid/dp|dr)) or Radial Distance = sqrt((Pipe Radius^2)-(-4*Dynamic Viscosity*Fluid Velocity in Pipe/Pressure Gradient)). The Pipe Radius is the radius of the pipe through which the fluid is flowing, The Dynamic Viscosity of a fluid is the measure of its resistance to flow when an external force is applied, Fluid Velocity in Pipe is the volume of fluid flowing in the given vessel per unit cross sectional area & Pressure Gradient is the change in pressure with respect to radial distance of element.

How to calculate Distance of Element from Center Line given Velocity at any point in Cylindrical Element?

The Distance of Element from Center Line given Velocity at any point in Cylindrical Element is defined as the radius of the elemental section is calculated using Radial Distance = sqrt((Pipe Radius^2)-(-4*Dynamic Viscosity*Fluid Velocity in Pipe/Pressure Gradient)). To calculate Distance of Element from Center Line given Velocity at any point in Cylindrical Element, you need Pipe Radius (R), Dynamic Viscosity (μ_viscosity), Fluid Velocity in Pipe (u_Fluid) & Pressure Gradient (dp|dr). With our tool, you need to enter the respective value for Pipe Radius, Dynamic Viscosity, Fluid Velocity in Pipe & 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 Radial Distance?

In this formula, Radial Distance uses Pipe Radius, Dynamic Viscosity, Fluid Velocity in Pipe & Pressure Gradient. We can use 3 other way(s) to calculate the same, which is/are as follows -

Radial Distance = 2*Shear Stress/Pressure Gradient
Radial Distance = 2*Shear Stress*Length of Pipe/(Head Loss due to Friction*Specific Weight of Liquid)
Radial Distance = 2*Dynamic Viscosity*Velocity Gradient/Pressure Gradient

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