1. What is a Pressure Calculator from Flow Rate?

Definition: This calculator determines the pressure difference required to maintain a given flow rate through a pipe using Poiseuille's Law.

Purpose: It helps engineers and physicists analyze fluid dynamics in pipes and understand the relationship between flow rate and pressure.

2. How Does the Calculator Work?

The calculator uses Poiseuille's Law:

Where:

• \( \Delta P \) — Pressure difference (Pascals)
• \( \mu \) — Dynamic viscosity (Pa·s)
• \( L \) — Length of pipe (meters)
• \( Q \) — Volumetric flow rate (m³/s)
• \( r \) — Pipe radius (meters)

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

3. Importance of Pressure-Flow Calculations

Details: Accurate pressure calculations are crucial for designing efficient piping systems, medical devices (like IVs), and understanding blood flow in circulatory systems.

4. Using the Calculator

Tips: Enter viscosity (default 0.001 Pa·s for water at 20°C), pipe length, flow rate, and pipe radius. All values must be > 0. Radius has the most significant impact on results.

5. Frequently Asked Questions (FAQ)

Q1: What viscosity value should I use for water?
A: Water at 20°C has viscosity of about 0.001 Pa·s. For other fluids, consult viscosity tables.

Q2: Why does radius have such a large effect?
A: Because of the r⁴ term in the denominator - small changes in radius dramatically affect the pressure needed.

Q3: What are the limitations of this formula?
A: It assumes laminar flow, Newtonian fluids, constant viscosity, and straight circular pipes with no obstructions.

Q4: How does temperature affect the results?
A: Temperature changes viscosity - higher temperature usually means lower viscosity for liquids.

Q5: Can I use this for blood flow calculations?
A: It provides a basic approximation, but blood is non-Newtonian and vessels are elastic, so specialized models are better.