Hose Flow Rate Calculator Based on Pressure

Flow Rate Formula (Hagen-Poiseuille Equation):

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

Hose Radius:

meters

Pressure Difference:

Pascals (Pa)

Fluid Viscosity:

Pa·s

Hose Length:

meters

Flow Rate (m³/s):

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1. What is a Hose Flow Rate Calculator Based on Pressure?

Definition: This calculator estimates the volumetric flow rate through a hose or pipe using the Hagen-Poiseuille equation for laminar flow conditions.

Purpose: It helps engineers, plumbers, and fluid system designers determine flow rates in piping systems under pressure differences.

2. How Does the Calculator Work?

The calculator uses the Hagen-Poiseuille equation:

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

Where:

\( Q \) — Volumetric flow rate (m³/s)
\( r \) — Inner radius of the hose (m)
\( \Delta P \) — Pressure difference between ends (Pa)
\( \mu \) — Dynamic viscosity of fluid (Pa·s)
\( L \) — Length of the hose (m)

Explanation: The equation describes laminar flow through a cylindrical pipe, showing that flow rate is highly sensitive to pipe radius (to the 4th power).

3. Importance of Flow Rate Calculation

Details: Accurate flow rate prediction ensures proper system design, adequate fluid delivery, and efficient pump sizing for various applications.

4. Using the Calculator

Tips: Enter the hose radius in meters, pressure difference in Pascals, fluid viscosity (default 0.001 Pa·s for water at 20°C), and hose length in meters. All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What flow regime does this equation apply to?
A: The Hagen-Poiseuille equation is valid only for laminar flow (typically Re < 2100). For turbulent flow, other equations like Darcy-Weisbach are needed.

Q2: 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 temperature.

Q3: How does radius affect flow rate?
A: Flow rate is proportional to radius to the 4th power - doubling the radius increases flow rate 16 times!

Q4: What units should I use?
A: Use consistent SI units: meters for dimensions, Pascals for pressure, and Pa·s for viscosity.

Q5: Does this account for fittings and bends?
A: No, this calculates flow for straight pipe sections only. For complex systems, additional loss factors must be considered.