Pressure Drop using Hagen-Poiseuille equation Solution

STEP 0: Pre-Calculation Summary
Formula Used
Difference in Pressure = (8*Viscosity of Blood*Length of the Capillary Tube*Blood Flow)/(pi*(Radius of Artery^4))
ΔP = (8*μ*Lc*Q)/(pi*(R0^4))
This formula uses 1 Constants, 5 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Variables Used
Difference in Pressure - (Measured in Pascal) - Difference in Pressure is the difference between the pressures.
Viscosity of Blood - (Measured in Pascal Second) - Viscosity of Blood is a measure of the resistance of blood to flow. It can also be described as the thickness and stickiness of blood.
Length of the Capillary Tube - (Measured in Meter) - Length of the Capillary Tube is the length of tube in which a liquid flows up into the tubes against gravity in a process called capillary action.
Blood Flow - (Measured in Cubic Meter per Second) - The blood Flow involves a cyclic series of steps that move blood trough the heart and to the lungs to be oxygenated.
Radius of Artery - (Measured in Meter) - The radius of artery is the radius of the blood vessel involved in circulatory system.
STEP 1: Convert Input(s) to Base Unit
Viscosity of Blood: 12.5 Centipoise --> 0.0125 Pascal Second (Check conversion here)
Length of the Capillary Tube: 8 Meter --> 8 Meter No Conversion Required
Blood Flow: 9 Milliliter per Second --> 9E-06 Cubic Meter per Second (Check conversion here)
Radius of Artery: 10.9 Meter --> 10.9 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
ΔP = (8*μ*Lc*Q)/(pi*(R0^4)) --> (8*0.0125*8*9E-06)/(pi*(10.9^4))
Evaluating ... ...
ΔP = 1.62359098778801E-10
STEP 3: Convert Result to Output's Unit
1.62359098778801E-10 Pascal --> No Conversion Required
FINAL ANSWER
1.62359098778801E-10 Pascal <-- Difference in Pressure
(Calculation completed in 00.087 seconds)

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Created by Soupayan banerjee
National University of Judicial Science (NUJS), Kolkata
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10+ Hemodynamics Calculators

Poiseuille's Equation for Blood Flow
Blood Flow = ((Final Pressure of System-Initial Pressure of System)*pi*(Radius of Artery^4)/(8*Length of the Capillary Tube*Density)) Go
Pulse Wave Velocity using Moens-Korteweg equation
Pulse Wave Velocity = sqrt((Elastic (tangent) Modulus at Blood Pressure P*Thickness of Artery)/(2*Blood Density*Radius of Artery)) Go
Pressure Drop using Hagen-Poiseuille equation
Difference in Pressure = (8*Viscosity of Blood*Length of the Capillary Tube*Blood Flow)/(pi*(Radius of Artery^4)) Go
Elastic (Tangent) Modulus using Hughes equation
Elastic (tangent) Modulus at Blood Pressure P = Elastic Modulus at Zero Blood Pressure*exp(Material Coefficient of Artery*Blood Pressure) Go
Frank Bramwell-Hill equation for Pulse Wave Velocity
Pulse Wave Velocity = sqrt((Volume*Change in Pressure)/(Blood Density*Change in Volume)) Go
Reynolds Number of Blood in Vessel
Reynolds Number = (Blood Density*Mean Velocity of Blood*Diameter of Artery)/Viscosity of Blood Go
Pulsatility Index
Pulsatility Index = (Peak Systolic Velocity-Minimum Diastolic Velocity)/Average Velocity in terms of Cardiac Cycle Go
Mean Arterial Pressure
Mean Arterial Pressure = Diastolic Blood Pressure+((1/3)*(Systolic Blood Pressure-Diastolic Blood Pressure)) Go
Pulse Pressure
Pulse Pressure = 3*(Mean Arterial Pressure-Diastolic Blood Pressure) Go
Rate of Mean Blood Flow
Blood Flow = (Blood Velocity*Cross Sectional Area of Artery) Go

Pressure Drop using Hagen-Poiseuille equation Formula

Difference in Pressure = (8*Viscosity of Blood*Length of the Capillary Tube*Blood Flow)/(pi*(Radius of Artery^4))
ΔP = (8*μ*Lc*Q)/(pi*(R0^4))

What is Hagen–Poiseuille equation?

It is a physical law that gives the pressure drop in an incompressible and Newtonian fluid in laminar flow flowing through a long cylindrical pipe of constant cross section. It can be successfully applied to air flow in lung alveoli, or the flow through a drinking straw or through a hypodermic needle.

How to Calculate Pressure Drop using Hagen-Poiseuille equation?

Pressure Drop using Hagen-Poiseuille equation calculator uses Difference in Pressure = (8*Viscosity of Blood*Length of the Capillary Tube*Blood Flow)/(pi*(Radius of Artery^4)) to calculate the Difference in Pressure, The Pressure Drop using Hagen-Poiseuille equation of Blood is defined as resistance which is related to vessel radius, vessel length, and blood viscosity. Difference in Pressure is denoted by ΔP symbol.

How to calculate Pressure Drop using Hagen-Poiseuille equation using this online calculator? To use this online calculator for Pressure Drop using Hagen-Poiseuille equation, enter Viscosity of Blood (μ), Length of the Capillary Tube (Lc), Blood Flow (Q) & Radius of Artery (R0) and hit the calculate button. Here is how the Pressure Drop using Hagen-Poiseuille equation calculation can be explained with given input values -> 1.6E-15 = (8*0.0125*8*9E-06)/(pi*(10.9^4)).

FAQ

What is Pressure Drop using Hagen-Poiseuille equation?
The Pressure Drop using Hagen-Poiseuille equation of Blood is defined as resistance which is related to vessel radius, vessel length, and blood viscosity and is represented as ΔP = (8*μ*Lc*Q)/(pi*(R0^4)) or Difference in Pressure = (8*Viscosity of Blood*Length of the Capillary Tube*Blood Flow)/(pi*(Radius of Artery^4)). Viscosity of Blood is a measure of the resistance of blood to flow. It can also be described as the thickness and stickiness of blood, Length of the Capillary Tube is the length of tube in which a liquid flows up into the tubes against gravity in a process called capillary action, The blood Flow involves a cyclic series of steps that move blood trough the heart and to the lungs to be oxygenated & The radius of artery is the radius of the blood vessel involved in circulatory system.
How to calculate Pressure Drop using Hagen-Poiseuille equation?
The Pressure Drop using Hagen-Poiseuille equation of Blood is defined as resistance which is related to vessel radius, vessel length, and blood viscosity is calculated using Difference in Pressure = (8*Viscosity of Blood*Length of the Capillary Tube*Blood Flow)/(pi*(Radius of Artery^4)). To calculate Pressure Drop using Hagen-Poiseuille equation, you need Viscosity of Blood (μ), Length of the Capillary Tube (Lc), Blood Flow (Q) & Radius of Artery (R0). With our tool, you need to enter the respective value for Viscosity of Blood, Length of the Capillary Tube, Blood Flow & Radius of Artery 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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