1. What is the Pressure Gradient Formula?

Definition: This formula describes how pressure changes in a fluid due to gravity and height differences, part of the Navier-Stokes equations.

Purpose: It's fundamental for understanding fluid flow, designing piping systems, and analyzing pressure distributions in various engineering applications.

2. How Does the Formula Work?

The formula is:

Where:

• \( \nabla P \) — Pressure gradient (Pa/m)
• \( \rho \) — Fluid density (kg/m³)
• \( g \) — Gravitational acceleration (m/s²)
• \( \nabla h \) — Height gradient (dimensionless)

Explanation: The negative sign indicates pressure decreases with height. Viscous terms are omitted in this simplified calculator.

3. Importance in Fluid Mechanics

Details: The pressure gradient drives fluid flow and is crucial for designing pumps, piping systems, and understanding natural phenomena like weather patterns.

4. Using the Calculator

Tips: Enter fluid density (water ≈ 1000 kg/m³), gravity (9.81 m/s² on Earth), and height gradient (1 for vertical column). All values must be valid numbers.

5. Frequently Asked Questions (FAQ)

Q1: What are the viscous terms?
A: They account for fluid friction and are important in detailed flow analysis, but often negligible for simple hydrostatic calculations.

Q2: What's a typical water density?
A: Pure water at 4°C is 1000 kg/m³, but varies with temperature and impurities.

Q3: When would height gradient not be 1?
A: For non-vertical flows or inclined pipes, use the sine of the angle relative to horizontal.

Q4: How does this relate to Bernoulli's equation?
A: This is essentially the hydrostatic term in Bernoulli's principle for stationary fluids.

Q5: What about gases?
A: For gases, density varies with pressure and temperature, requiring more complex calculations.