Poiseuille's Equation For Blood Flow Calculator

Poiseuille's Equation:

\[ Q = \frac{(P_f - P_i) \times \pi \times R_0^4}{8 \times L_c \times \rho} \]

Final Pressure of System (P_f):

Pascal

Initial Pressure of Blood (P_i):

Pascal

Radius of Artery (R₀):

Meter

Length of Capillary Tube (L_c):

Meter

Density (ρ):

kg/m³

Blood Flow (Q):

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1. What is Poiseuille's Equation For Blood Flow?

Poiseuille's equation describes the flow of fluid through a cylindrical tube and is used to calculate blood flow in arteries and capillaries. It relates blood flow to pressure difference, vessel dimensions, and blood properties.

2. How Does the Calculator Work?

The calculator uses Poiseuille's equation:

\[ Q = \frac{(P_f - P_i) \times \pi \times R_0^4}{8 \times L_c \times \rho} \]

Where:

\( Q \) — Blood flow (m³/s)
\( P_f \) — Final pressure of system (Pascal)
\( P_i \) — Initial pressure of blood (Pascal)
\( R_0 \) — Radius of artery (Meter)
\( L_c \) — Length of capillary tube (Meter)
\( \rho \) — Density (kg/m³)
\( \pi \) — Archimedes' constant (3.14159)

Explanation: The equation shows that blood flow is proportional to the pressure difference and the fourth power of the radius, and inversely proportional to length and viscosity.

3. Importance of Blood Flow Calculation

Details: Accurate blood flow calculation is crucial for understanding cardiovascular function, diagnosing circulatory disorders, and planning medical interventions.

4. Using the Calculator

Tips: Enter all values in SI units. Pressure values in Pascal, dimensions in meters, and density in kg/m³. All values must be positive and non-zero.

5. Frequently Asked Questions (FAQ)

Q1: Why is radius raised to the fourth power?
A: The radius has a profound effect on flow resistance. Doubling the radius increases flow by 16 times (2⁴), making it the most significant factor in blood flow regulation.

Q2: What are typical blood flow values in human arteries?
A: Blood flow varies by vessel type. Aorta: ~5 L/min, large arteries: 1-2 L/min, capillaries: much smaller flows measured in mL/min or μL/min.

Q3: How does viscosity affect blood flow?
A: Higher viscosity increases resistance and decreases flow. Blood viscosity is affected by hematocrit, temperature, and plasma protein concentration.

Q4: What are the limitations of Poiseuille's equation for blood flow?
A: It assumes Newtonian fluid, steady flow, rigid tubes, and laminar flow. Blood is non-Newtonian, flow is pulsatile, vessels are elastic, and flow can become turbulent.

Q5: How is this equation used in medical practice?
A: It helps understand hemodynamics, design medical devices, calculate drug delivery rates, and interpret diagnostic tests like Doppler ultrasound.