Poiseuille's Formula Calculator

✖Pressure changes is the difference between the pressure inside the liquid droplet and atmospheric pressure.ⓘ Pressure Changes [Δp]			+10% -10%
✖Pipe Radius is a radial line from the focus to any point of a curve.ⓘ Pipe Radius [r_pipe]			+10% -10%
✖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%
✖Length is the measurement or extent of something from end to end.ⓘ Length [L]			+10% -10%

✖The Volumetric Flow Rate of Feed to Reactor gives the volume of the reactants stream being fed to the reactor per unit time.ⓘ Poiseuille's Formula [Q_v]

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Poiseuille's Formula

Formula

`"Q"_{"v"} = "Δp"*pi/8*("r"_{"pipe"}^4)/("μ"_{"viscosity"}*"L")`

Example

`"10.00588m³/s"="3.21Pa"*pi/8*(("2.22m")^4)/("1.02Pa*s"*"3m")`

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Poiseuille's Formula Solution

STEP 0: Pre-Calculation Summary

Formula Used

Volumetric Flow Rate of Feed to Reactor = Pressure Changes*pi/8*(Pipe Radius^4)/(Dynamic Viscosity*Length)
Q_v = Δp*pi/8*(r_pipe^4)/(μ_viscosity*L)
This formula uses 1 Constants, 5 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Volumetric Flow Rate of Feed to Reactor - (Measured in Cubic Meter per Second) - The Volumetric Flow Rate of Feed to Reactor gives the volume of the reactants stream being fed to the reactor per unit time.
Pressure Changes - (Measured in Pascal) - Pressure changes is the difference between the pressure inside the liquid droplet and atmospheric pressure.
Pipe Radius - (Measured in Meter) - Pipe Radius is a radial line from the focus to any point of a curve.
Dynamic Viscosity - (Measured in Pascal Second) - Dynamic Viscosity of a fluid is the measure of its resistance to flow when an external force is applied.
Length - (Measured in Meter) - Length is the measurement or extent of something from end to end.

STEP 1: Convert Input(s) to Base Unit

Pressure Changes: 3.21 Pascal --> 3.21 Pascal No Conversion Required
Pipe Radius: 2.22 Meter --> 2.22 Meter No Conversion Required
Dynamic Viscosity: 1.02 Pascal Second --> 1.02 Pascal Second No Conversion Required
Length: 3 Meter --> 3 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Q_v = Δp*pi/8*(r_pipe^4)/(μ_viscosity*L) --> 3.21*pi/8*(2.22^4)/(1.02*3)

Evaluating ... ...

Q_v = 10.0058822882867

STEP 3: Convert Result to Output's Unit

10.0058822882867 Cubic Meter per Second --> No Conversion Required

FINAL ANSWER

10.0058822882867 ≈ 10.00588 Cubic Meter per Second <-- Volumetric Flow Rate of Feed to Reactor

(Calculation completed in 00.004 seconds)

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National Institute of Technology (NIT), Jamshedpur

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< 9 Hydrodynamics Basics Calculators

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Poiseuille's Formula

Go Volumetric Flow Rate of Feed to Reactor = Pressure Changes*pi/8*(Pipe Radius^4)/(Dynamic Viscosity*Length)

Power Developed by Turbine

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Metacentric Height given Time Period of Rolling

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Reynolds Number

Go Reynolds Number = (Density of Liquid*Fluid Velocity*Pipe Diameter)/Dynamic Viscosity

Reynolds Number given Length

Go Reynolds Number = Density of Liquid*Velocity*Length/Kinematic Viscosity

Power Required to Overcome Frictional Resistance in Laminar Flow

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Power

Go Power Generated = Force on Fluid Element*Change in Velocity

Reynolds Number given Frictional Factor of Laminar Flow

Go Reynolds Number = 64/Friction Factor

Poiseuille's Formula Formula

Volumetric Flow Rate of Feed to Reactor = Pressure Changes*pi/8*(Pipe Radius^4)/(Dynamic Viscosity*Length)
Q_v = Δp*pi/8*(r_pipe^4)/(μ_viscosity*L)

What are Conditions in Poiseuille's Equation?

The assumptions of the equation are that the fluid is incompressible and Newtonian; the flow is laminar through a pipe of constant circular cross-section that is substantially longer than its diameter; and there is no acceleration of fluid in the pipe. For velocities and pipe diameters above a threshold, actual fluid flow is not laminar but turbulent, leading to larger pressure drops than calculated by the Hagen–Poiseuille equation.

How to Calculate Poiseuille's Formula?

Poiseuille's Formula calculator uses Volumetric Flow Rate of Feed to Reactor = Pressure Changes*pi/8*(Pipe Radius^4)/(Dynamic Viscosity*Length) to calculate the Volumetric Flow Rate of Feed to Reactor, Poiseuille's Formula is an equation that gives the pressure drop in an incompressible and Newtonian fluid in laminar flow flowing through a long cylindrical pipe of constant cross section. Volumetric Flow Rate of Feed to Reactor is denoted by Q_v symbol.

How to calculate Poiseuille's Formula using this online calculator? To use this online calculator for Poiseuille's Formula, enter Pressure Changes (Δp), Pipe Radius (r_pipe), Dynamic Viscosity (μ_viscosity) & Length (L) and hit the calculate button. Here is how the Poiseuille's Formula calculation can be explained with given input values -> 10.47345 = 3.21*pi/8*(2.22^4)/(1.02*3).

FAQ

What is Poiseuille's Formula?

Poiseuille's Formula is an equation that gives the pressure drop in an incompressible and Newtonian fluid in laminar flow flowing through a long cylindrical pipe of constant cross section and is represented as Q_v = Δp*pi/8*(r_pipe^4)/(μ_viscosity*L) or Volumetric Flow Rate of Feed to Reactor = Pressure Changes*pi/8*(Pipe Radius^4)/(Dynamic Viscosity*Length). Pressure changes is the difference between the pressure inside the liquid droplet and atmospheric pressure, Pipe Radius is a radial line from the focus to any point of a curve, Dynamic Viscosity of a fluid is the measure of its resistance to flow when an external force is applied & Length is the measurement or extent of something from end to end.

How to calculate Poiseuille's Formula?

Poiseuille's Formula is an equation that gives the pressure drop in an incompressible and Newtonian fluid in laminar flow flowing through a long cylindrical pipe of constant cross section is calculated using Volumetric Flow Rate of Feed to Reactor = Pressure Changes*pi/8*(Pipe Radius^4)/(Dynamic Viscosity*Length). To calculate Poiseuille's Formula, you need Pressure Changes (Δp), Pipe Radius (r_pipe), Dynamic Viscosity (μ_viscosity) & Length (L). With our tool, you need to enter the respective value for Pressure Changes, Pipe Radius, Dynamic Viscosity & Length 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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