Poiseuille’s Law Calculator
System Results
What Is a Poiseuille’s Law Calculator?
A Poiseuille’s Law Calculator uses the Hagen-Poiseuille equation to estimate fluid flow through a rigid circular pipe under ideal laminar-flow conditions. It can calculate volumetric flow rate from a known pressure drop. It can also rearrange the equation to calculate the pressure drop needed for a known flow rate.
A Poiseuille’s law calculator finds flow rate or pressure drop from pipe radius, pipe length, dynamic viscosity, and one known driving value. It is useful for quick technical estimates when a Newtonian, incompressible fluid moves steadily through a straight pipe with a constant circular cross-section.
The calculator converts each supported unit into SI units before applying the formula. The main answer appears in your selected flow or pressure unit. It also displays average fluid velocity in meters per second and cross-sectional area in square meters.
How the Hagen-Poiseuille Formula Works
In flow rate mode, the calculator uses the Hagen-Poiseuille equation:
In pressure drop mode, it rearranges the same equation:
- Q is volumetric flow rate in cubic meters per second before output conversion.
- ΔP is the pressure drop between the pipe inlet and outlet, measured internally in pascals.
- r is the pipe’s internal radius in meters.
- μ is dynamic viscosity in pascal-seconds.
- L is the pipe length in meters.
Worked flow rate example
Suppose a pipe has a radius of 5 millimeters, a length of 10 meters, and carries a fluid with a dynamic viscosity of 1 centipoise. The pressure drop is 5,000 pascals.
- Convert the radius: 5 mm = 0.005 m.
- Convert viscosity: 1 cP = 0.001 Pa·s.
- Substitute the values: Q = [π × (0.005)4 × 5,000] ÷ [8 × 0.001 × 10].
- The result is about 0.0001227185 m³/s.
- Converted to liters per minute, the calculator displays about 7.3631 L/min.
For the same example, the pipe area is about 0.00007854 m², and average velocity is 1.5625 m/s. These results assume steady laminar flow in a rigid, straight pipe. Zero, negative, or missing values are rejected because radius, length, viscosity, pressure drop, and flow rate must be greater than zero.
How to Use the Poiseuille’s Law Calculator: Step by Step
- Select what you want to calculate. Choose Volumetric Flow Rate (Q) or Pressure Drop (ΔP).
- Enter the pipe’s internal radius. Select meters, centimeters, millimeters, or inches as the radius unit.
- Enter the pipe length. Available units are meters, centimeters, and feet.
- Enter the fluid’s dynamic viscosity. Choose centipoise, pascal-seconds, or poise.
- For flow rate mode, enter the known pressure drop. You can use pascals, kilopascals, PSI, bar, or mmHg.
- For pressure drop mode, enter the known flow rate. Supported units are liters per minute, milliliters per minute, U.S. gallons per minute, and cubic meters per second.
- Select the unit in which you want the main result displayed.
- Select Calculate to view the result, average fluid velocity, and pipe cross-sectional area. Use Reset to restore the default entries.
The main result is either the estimated volumetric flow rate or pressure drop. Average velocity shows how quickly the fluid moves through the pipe. The area value is based on πr². A caution message appears when calculated average velocity exceeds 5 m/s, since high velocity may indicate that the laminar-flow assumption is not suitable.
What to Check Before Using This Poiseuille’s Law Calculator
Use the internal radius, not the diameter
The calculator requires pipe radius. If you only know the internal diameter, divide it by two before entering the value. Small radius errors can cause large result errors because radius is raised to the fourth power. Doubling the radius increases the calculated flow rate by a factor of 16 when all other inputs stay unchanged.
Enter dynamic viscosity in the correct unit
Dynamic viscosity describes a fluid’s resistance to flowing. A larger viscosity produces a lower flow rate for the same pressure drop. In pressure drop mode, a more viscous fluid requires more pressure to maintain the same flow. The calculator accepts cP, Pa·s, and P, then converts the entry to Pa·s.
| Input factor | Effect in flow rate mode | Effect in pressure drop mode |
|---|---|---|
| Pipe radius | Flow changes with r4 | Pressure drop changes with 1/r4 |
| Pipe length | Longer pipe lowers flow | Longer pipe raises pressure drop |
| Dynamic viscosity | Higher viscosity lowers flow | Higher viscosity raises pressure drop |
| Pressure drop or flow rate | More pressure raises flow | More flow raises pressure drop |
Confirm that the flow is laminar
Hagen-Poiseuille’s law applies to steady, laminar flow of an incompressible Newtonian fluid through a straight, rigid pipe with a constant circular cross-section. It does not model pipe fittings, bends, changing diameters, flexible walls, entrance losses, or turbulent flow. Under turbulent conditions, it may overestimate flow or underestimate pressure drop.
The calculator does not calculate Reynolds number because it does not ask for fluid density. Its high-velocity notice is only a caution based on velocity exceeding 5 m/s. It is not a direct test for turbulence. For critical engineering work, confirm the flow regime and account for all system losses separately.
Frequently Asked Questions
What does a Poiseuille’s law calculator calculate?
A Poiseuille’s law calculator estimates either volumetric flow rate or pressure drop in a circular pipe. It uses pipe radius, pipe length, dynamic viscosity, and one known flow or pressure value. This calculator also displays the calculated pipe area and average fluid velocity.
How do I calculate flow rate using Poiseuille’s law?
Choose volumetric flow rate mode, then enter the pipe radius, length, dynamic viscosity, and pressure drop. Select the correct unit beside each value and choose an output flow unit. The calculator applies Q = πr⁴ΔP ÷ 8μL and converts the result into your selected unit.
Can this calculator find the required pressure drop?
Yes. Select pressure drop mode and enter the desired flow rate along with radius, length, and dynamic viscosity. The tool calculates ΔP = 8μLQ ÷ πr⁴. You can display the answer in pascals, kilopascals, PSI, bar, or millimeters of mercury.
Why does pipe radius have such a large effect on flow rate?
Pipe radius has a large effect because the Hagen-Poiseuille equation uses the fourth power of radius. A modest radius change can therefore produce a much larger change in calculated flow. Accurate internal measurements are important, especially for narrow tubing where a small measurement error can strongly affect the result.
Is centipoise the same as pascal-seconds?
Centipoise and pascal-seconds both measure dynamic viscosity, but they use different scales. One centipoise equals 0.001 Pa·s. The calculator handles this conversion automatically when you select cP. It also accepts poise, where one poise equals 0.1 Pa·s.
Does the calculator determine whether flow is turbulent?
No. The calculator does not compute Reynolds number or directly classify the flow regime because fluid density is not an input. It only displays a caution when average velocity exceeds 5 m/s. You must independently confirm that the flow is laminar before relying on the Poiseuille result.
How accurate is a Poiseuille’s law calculator?
It is accurate to the equation when the entered values and Poiseuille assumptions are valid. Real systems may differ because of turbulence, bends, fittings, pipe roughness, changing diameter, flexible walls, compressibility, or non-Newtonian fluid behavior. Treat the result as an idealized technical estimate rather than a full system model.