Velocity at any point in Cylindrical Element Calculator

✖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%
✖Pressure Gradient is the change in pressure with respect to radial distance of element.ⓘ Pressure Gradient [dp\|dr]			+10% -10%
✖The Pipe Radius is the radius of the pipe through which the fluid is flowing.ⓘ Pipe Radius [R]			+10% -10%
✖Radial distance is defined as distance between whisker sensor's pivot point to whisker-object contact point.ⓘ Radial Distance [d_radial]			+10% -10%

✖Fluid Velocity in Pipe is the volume of fluid flowing in the given vessel per unit cross sectional area.ⓘ Velocity at any point in Cylindrical Element [u_Fluid]

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Formula

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Velocity at any point in Cylindrical Element

Formula

`"u"_{"Fluid"} = -(1/(4*"μ"_{"viscosity"}))*"dp|dr"*(("R"^2)-("d"_{"radial"}^2))`

Example

`"352.5873m/s"=-(1/(4*"10.2P"))*"17N/m³"*((("138mm")^2)-(("9.2m")^2))`

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Velocity at any point in Cylindrical Element Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Variables Used

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.
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.
Pressure Gradient - (Measured in Newton per Cubic Meter) - Pressure Gradient is the change in pressure with respect to radial distance of element.
Pipe Radius - (Measured in Meter) - The Pipe Radius is the radius of the pipe through which the fluid is flowing.
Radial Distance - (Measured in Meter) - Radial distance is defined as distance between whisker sensor's pivot point to whisker-object contact point.

STEP 1: Convert Input(s) to Base Unit

Dynamic Viscosity: 10.2 Poise --> 1.02 Pascal Second (Check conversion here)
Pressure Gradient: 17 Newton per Cubic Meter --> 17 Newton per Cubic Meter No Conversion Required
Pipe Radius: 138 Millimeter --> 0.138 Meter (Check conversion here)
Radial Distance: 9.2 Meter --> 9.2 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

u_Fluid = -(1/(4*μ_viscosity))*dp|dr*((R^2)-(d_radial^2)) --> -(1/(4*1.02))*17*((0.138^2)-(9.2^2))

Evaluating ... ...

u_Fluid = 352.587316666667

STEP 3: Convert Result to Output's Unit

352.587316666667 Meter per Second --> No Conversion Required

FINAL ANSWER

352.587316666667 ≈ 352.5873 Meter per Second <-- Fluid Velocity in Pipe

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Hydraulics and Waterworks » Laminar Flow » Steady Laminar Flow in Circular Pipes – Hagen Poiseuille Law » Velocity at any point in Cylindrical Element

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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

Velocity at any point in Cylindrical Element Formula

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

What is Hagen Poiseuille Law ?

Velocity of the steady flow of a fluid through a narrow tube (as a blood vessel or a catheter) varies directly as the pressure and the fourth power of the radius of the tube and inversely as the length of the tube and the coefficient of viscosity.

How to Calculate Velocity at any point in Cylindrical Element?

Velocity at any point in Cylindrical Element calculator uses Fluid Velocity in Pipe = -(1/(4*Dynamic Viscosity))*Pressure Gradient*((Pipe Radius^2)-(Radial Distance^2)) to calculate the Fluid Velocity in Pipe, The Velocity at any point in Cylindrical Element is defined as rate at which fluid into the pipe forming a parabolic profile. Fluid Velocity in Pipe is denoted by u_Fluid symbol.

How to calculate Velocity at any point in Cylindrical Element using this online calculator? To use this online calculator for Velocity at any point in Cylindrical Element, enter Dynamic Viscosity (μ_viscosity), Pressure Gradient (dp|dr), Pipe Radius (R) & Radial Distance (d_radial) and hit the calculate button. Here is how the Velocity at any point in Cylindrical Element calculation can be explained with given input values -> 352.5 = -(1/(4*1.02))*17*((0.138^2)-(9.2^2)).

FAQ

What is Velocity at any point in Cylindrical Element?

The Velocity at any point in Cylindrical Element is defined as rate at which fluid into the pipe forming a parabolic profile and is represented as u_Fluid = -(1/(4*μ_viscosity))*dp|dr*((R^2)-(d_radial^2)) or Fluid Velocity in Pipe = -(1/(4*Dynamic Viscosity))*Pressure Gradient*((Pipe Radius^2)-(Radial Distance^2)). The Dynamic Viscosity of a fluid is the measure of its resistance to flow when an external force is applied, Pressure Gradient is the change in pressure with respect to radial distance of element, The Pipe Radius is the radius of the pipe through which the fluid is flowing & Radial distance is defined as distance between whisker sensor's pivot point to whisker-object contact point.

How to calculate Velocity at any point in Cylindrical Element?

The Velocity at any point in Cylindrical Element is defined as rate at which fluid into the pipe forming a parabolic profile is calculated using Fluid Velocity in Pipe = -(1/(4*Dynamic Viscosity))*Pressure Gradient*((Pipe Radius^2)-(Radial Distance^2)). To calculate Velocity at any point in Cylindrical Element, you need Dynamic Viscosity (μ_viscosity), Pressure Gradient (dp|dr), Pipe Radius (R) & Radial Distance (d_radial). With our tool, you need to enter the respective value for Dynamic Viscosity, Pressure Gradient, Pipe Radius & Radial Distance and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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