Calculator Inputs
Use Poiseuille mode for pressure-driven laminar flow or Velocity–Area mode when average speed is already known.
Plotly Graph
The graph changes with your selected method. Pressure-driven mode plots radius sensitivity. Speed-driven mode plots velocity sensitivity.
Example Data Table
These sample rows help verify the calculator structure and show typical output formatting for different scenarios.
| Scenario | Method | Radius | Length | Pressure | Viscosity | Density | Velocity | Flow | Reynolds | Regime |
|---|---|---|---|---|---|---|---|---|---|---|
| Artery Example | Poiseuille | 2.5 mm | 30 cm | 40 mmHg | 3.5 cP | 1060 kg/m³ | Auto | 4.675 L/min | 6008.58 | Turbulent tendency |
| Small Vessel | Poiseuille | 1.5 mm | 20 cm | 30 mmHg | 3.8 cP | 1060 kg/m³ | Auto | 0.628 L/min | 1238.64 | Laminar |
| Wide Vessel | Poiseuille | 4.0 mm | 50 cm | 25 mmHg | 4.0 cP | 1060 kg/m³ | Auto | 10.052 L/min | 7066.09 | Turbulent tendency |
| Continuity Case | Velocity–Area | 2.0 mm | 25 cm | Estimated | 3.5 cP | 1060 kg/m³ | 35 cm/s | 0.264 L/min | 424.00 | Laminar |
Formula Used
1. Cross-sectional area
Area is found from vessel radius. It is required for velocity-based flow and several derived metrics.
2. Volumetric flow from velocity
When average velocity is known, volumetric flow equals speed times cross-sectional area.
3. Poiseuille flow rate
This relation estimates laminar flow through a straight circular tube using pressure drop, radius, viscosity, and length.
4. Average velocity
If flow rate is known first, average velocity is obtained by dividing flow by area.
5. Reynolds number
This dimensionless value compares inertial and viscous effects. Here, diameter D equals 2r.
6. Wall shear stress
For laminar tube flow, wall shear stress can be derived from pressure gradient and vessel radius.
7. Estimated pressure drop in velocity mode
In Velocity–Area mode, the tool estimates the pressure difference needed to maintain the entered speed under laminar assumptions.
How to Use This Calculator
Step 1: Select a method
Choose Poiseuille when pressure difference is known, or choose Velocity–Area when average blood speed is known.
Step 2: Enter geometry
Provide vessel radius and length. The tool automatically converts units to SI values for the internal calculations.
Step 3: Enter fluid properties
Fill in dynamic viscosity and density. These values affect Reynolds number, mass flow, pressure behavior, and shear stress.
Step 4: Add duration
Enter a time interval to estimate how much total volume passes through the vessel during that period.
Step 5: Calculate and export
Click Calculate to show results above the form, inspect the graph, then download your output as CSV or PDF.
FAQs
1. What does this calculator estimate?
It estimates volumetric flow rate, average velocity, mass flow rate, Reynolds number, wall shear stress, transit time, delivered volume, and pressure-related behavior for a cylindrical vessel.
2. Which formulas are used here?
The calculator uses the continuity relation Q = vA and Poiseuille’s law for laminar tube flow. It also derives Reynolds number, wall shear stress, and pressure drop from the same inputs.
3. Why does radius matter so much?
In Poiseuille flow, rate depends on the fourth power of radius. Small radius changes can create large flow changes, which makes vessel narrowing highly significant in simplified physics models.
4. Is this suitable for medical diagnosis?
No. It is an educational and engineering-style estimator. Real circulation includes pulsatile flow, branching, vessel elasticity, non-Newtonian effects, and patient-specific physiology not captured here.
5. What viscosity value should I enter?
For many demonstration cases, blood viscosity is often entered around 3 to 4 cP. Use a value appropriate to your source, temperature, hematocrit assumption, or study conditions.
6. What does Reynolds number tell me?
Reynolds number compares inertial effects with viscous effects. Lower values usually support laminar assumptions, while larger values suggest transition or turbulence may reduce model accuracy.
7. Why are there two calculation modes?
Poiseuille mode starts from pressure drop, radius, viscosity, and length. Velocity–area mode starts from average speed and area, then estimates flow and the pressure drop needed under laminar assumptions.
8. Can I export my results?
Yes. The page includes CSV export for quick data capture and PDF export for sharing or archiving your current calculation summary and the main derived outputs.
Important Note
This calculator is for educational and analytical use. Real blood flow depends on pulsatility, branching, vessel elasticity, stenosis shape, temperature, and non-Newtonian behavior. Do not use it as a clinical decision tool.