Pressure Drop Using Hagen-Poiseuille Equation Calculator

Hagen-Poiseuille Equation:

\[ \Delta P = \frac{8 \times \mu \times L_c \times Q}{\pi \times R_0^4} \]

Viscosity of Blood (μ):

Pa·s

Length of the Capillary Tube (Lc):

Blood Flow (Q):

m³/s

Radius of Artery (R₀):

Difference in Pressure (ΔP):

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1. What is the Hagen-Poiseuille Equation?

The Hagen-Poiseuille equation describes the pressure drop in a fluid flowing through a long cylindrical pipe. It's particularly useful in hemodynamics for calculating pressure differences in blood vessels based on blood viscosity, vessel dimensions, and flow rate.

2. How Does the Calculator Work?

The calculator uses the Hagen-Poiseuille equation:

\[ \Delta P = \frac{8 \times \mu \times L_c \times Q}{\pi \times R_0^4} \]

Where:

\( \Delta P \) — Difference in Pressure (Pa)
\( \mu \) — Viscosity of Blood (Pa·s)
\( L_c \) — Length of the Capillary Tube (m)
\( Q \) — Blood Flow (m³/s)
\( R_0 \) — Radius of Artery (m)
\( \pi \) — Mathematical constant pi (≈3.1416)

Explanation: The equation demonstrates that pressure drop is directly proportional to viscosity, length, and flow rate, but inversely proportional to the fourth power of the radius.

3. Importance of Pressure Drop Calculation

Details: Calculating pressure drop is crucial in cardiovascular physiology for understanding blood flow dynamics, vascular resistance, and the energy requirements of the circulatory system.

4. Using the Calculator

Tips: Enter all values in SI units (Pa·s for viscosity, meters for length and radius, m³/s for flow rate). All values must be positive and non-zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical viscosity of blood?
A: Normal blood viscosity ranges from 0.0035 to 0.0045 Pa·s, though it can vary with hematocrit levels and temperature.

Q2: Why is radius raised to the fourth power?
A: The R⁴ relationship shows that small changes in vessel radius dramatically affect pressure drop and flow resistance.

Q3: What are the limitations of this equation?
A: The equation assumes laminar flow, Newtonian fluid behavior, and rigid cylindrical tubes, which may not perfectly represent real blood vessels.

Q4: How does this apply to arterial blood flow?
A: While arteries aren't perfect rigid cylinders, the equation provides a good approximation for pressure gradients in the circulatory system.

Q5: What factors affect blood viscosity?
A: Hematocrit level, plasma protein concentration, temperature, and shear rate all influence blood viscosity.