Flow to Pressure Calculator

Pressure Difference Formula:

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

Viscosity (μ):

Pa·s

Length (L):

Flow Rate (Q):

m³/s

Radius (r):

Pressure Difference (ΔP):

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1. What is a Flow to Pressure Calculator?

Definition: This calculator determines the pressure difference required to maintain a given flow rate through a pipe using the Hagen-Poiseuille equation.

Purpose: It helps engineers and fluid system designers understand the relationship between flow rate and pressure drop in cylindrical pipes.

2. How Does the Calculator Work?

The calculator uses the Hagen-Poiseuille equation:

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

Where:

\( \Delta P \) — Pressure difference (Pascals)
\( \mu \) — Dynamic viscosity (Pascal-seconds)
\( L \) — Length of pipe (meters)
\( Q \) — Volumetric flow rate (cubic meters/second)
\( r \) — Pipe radius (meters)

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

3. Importance of Pressure Difference Calculation

Details: Accurate pressure drop calculations are essential for designing efficient fluid systems, selecting appropriate pumps, and ensuring proper flow rates in pipelines.

4. Using the Calculator

Tips: Enter the fluid viscosity, pipe length, desired flow rate, and pipe radius. All values must be > 0. The radius has a particularly strong effect on the result.

5. Frequently Asked Questions (FAQ)

Q1: What fluids is this calculator valid for?
A: The equation applies to Newtonian fluids in laminar flow through straight, circular pipes of constant diameter.

Q2: How does pipe radius affect the pressure drop?
A: Pressure drop is inversely proportional to r⁴, meaning small changes in radius have large effects on pressure requirements.

Q3: What's a typical viscosity value for water?
A: Water at 20°C has a viscosity of about 0.001 Pa·s. Viscosity decreases with increasing temperature.

Q4: Can I use this for turbulent flow?
A: No, this equation is only valid for laminar flow (Re < 2100). Different equations are needed for turbulent flow.

Q5: How do I convert the result to other pressure units?
A: 1 Pa = 0.000145 psi, or 1 bar = 100,000 Pa. You may need to convert based on your preferred units.