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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^4))
ΔP = (8*μ*Lc*Q)/(pi*(r^4))
This formula uses 1 Constants, 4 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Variables Used
Viscosity of Blood - 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. (Measured in Centipoise)
Length of the Capillary Tube - 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. (Measured in Meter)
Blood Flow - The blood Flow involves a cyclic series of steps that move blood trough the heart and to the lungs to be oxygenated. (Measured in Milliliter per Sec)
Radius - Radius is a radial line from the focus to any point of a curve. (Measured in Meter)
STEP 1: Convert Input(s) to Base Unit
Viscosity of Blood: 10 Centipoise --> 0.01 Pascal Second (Check conversion here)
Length of the Capillary Tube: 8 Meter --> 8 Meter No Conversion Required
Blood Flow: 10 Milliliter per Sec --> 1E-05 Meter³ per Second (Check conversion here)
Radius: 10 Meter --> 10 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
ΔP = (8*μ*Lc*Q)/(pi*(r^4)) --> (8*0.01*8*1E-05)/(pi*(10^4))
Evaluating ... ...
ΔP = 2.03718327157626E-10
STEP 3: Convert Result to Output's Unit
2.03718327157626E-10 Pascal -->2.03718327157626E-15 Bar (Check conversion here)
FINAL ANSWER
2.03718327157626E-15 Bar <-- Difference in pressure
(Calculation completed in 00.016 seconds)

10+ Hemodynamics Calculators

Poiseuille's Equation for Blood Flow
blood_flow = ((Final Pressure of System-Initial Pressure of System)*pi*(Radius^4)/(8*Length of the Capillary Tube*Density)) Go
Pulse wave velocity using Moens-Korteweg equation
pulse_wave_velocity = sqrt((The elastic (tangent) modulus at blood pressure P*Thickness of the artery)/(2*Blood Density*Radius of the artery)) Go
Elastic (Tangent) Modulus using Hughes equation
the_elastic_tangent_modulus_at_blood_pressure_P = Elastic Modulus at Zero Blood Pressure*exp(Material Coefficient of the Artery*Blood Pressure) Go
Pressure Drop using Hagen-Poiseuille equation
difference_in_pressure = (8*Viscosity of Blood*Length of the Capillary Tube*Blood Flow)/(pi*(Radius^4)) Go
Frank Bramwell-Hill equation for Pulse Wave Velocity
pulse_wave_velocity = sqrt((Volume*Change in pressure)/(Density of Blood*Change in Volume)) Go
Reynolds Number of Blood in the Vessel
reynolds_number = (Density of Blood*Mean Velocity of Blood*Diameter)/Viscosity of Blood Go
Mean Arterial Pressure
mean_arterial_pressure = Diastolic Blood Pressure+((1/3)*(Systolic Blood Pressure-Diastolic Blood Pressure)) Go
Pulsatility Index
pulsatility_index = (Peak Systolic Velocity-Minimum Diastolic Velocity)/Average Velocity 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) Go

Pressure Drop using Hagen-Poiseuille equation Formula

difference_in_pressure = (8*Viscosity of Blood*Length of the Capillary Tube*Blood Flow)/(pi*(Radius^4))
ΔP = (8*μ*Lc*Q)/(pi*(r^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^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 (r) and hit the calculate button. Here is how the Pressure Drop using Hagen-Poiseuille equation calculation can be explained with given input values -> 2.037E-15 = (8*0.01*8*1E-05)/(pi*(10^4)).

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*(r^4)) or difference_in_pressure = (8*Viscosity of Blood*Length of the Capillary Tube*Blood Flow)/(pi*(Radius^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 & Radius is a radial line from the focus to any point of a curve.
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^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 (r). With our tool, you need to enter the respective value for Viscosity of Blood, Length of the Capillary Tube, Blood Flow & Radius 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 Difference in pressure?
In this formula, Difference in pressure uses Viscosity of Blood, Length of the Capillary Tube, Blood Flow & Radius. We can use 10 other way(s) to calculate the same, which is/are as follows -
  • mean_arterial_pressure = Diastolic Blood Pressure+((1/3)*(Systolic Blood Pressure-Diastolic Blood Pressure))
  • pulse_pressure = 3*(Mean Arterial Pressure-Diastolic Blood Pressure)
  • pulse_wave_velocity = sqrt((The elastic (tangent) modulus at blood pressure P*Thickness of the artery)/(2*Blood Density*Radius of the artery))
  • the_elastic_tangent_modulus_at_blood_pressure_P = Elastic Modulus at Zero Blood Pressure*exp(Material Coefficient of the Artery*Blood Pressure)
  • blood_flow = (Blood Velocity*Cross sectional area)
  • pulse_wave_velocity = sqrt((Volume*Change in pressure)/(Density of Blood*Change in Volume))
  • pulsatility_index = (Peak Systolic Velocity-Minimum Diastolic Velocity)/Average Velocity
  • blood_flow = ((Final Pressure of System-Initial Pressure of System)*pi*(Radius^4)/(8*Length of the Capillary Tube*Density))
  • difference_in_pressure = (8*Viscosity of Blood*Length of the Capillary Tube*Blood Flow)/(pi*(Radius^4))
  • reynolds_number = (Density of Blood*Mean Velocity of Blood*Diameter)/Viscosity of Blood
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