How to Calculate Hydraulic Head (Bernoulli)

Hydraulic Head Formula (Bernoulli Equation):

\[ h = \frac{P}{\rho \cdot g} + \frac{v^2}{2 \cdot g} + z \]

Pressure (P):

Density (ρ):

kg/m³

Velocity (v):

m/s

Elevation (z):

Hydraulic Head (h): m

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1. What is Hydraulic Head (Bernoulli Equation)?

Definition: Hydraulic head represents the total energy per unit weight of fluid, consisting of pressure head, velocity head, and elevation head.

Purpose: It's used in fluid mechanics to analyze fluid flow systems, including water distribution, hydrology, and pipeline design.

2. How Does the Calculator Work?

The calculator uses the Bernoulli equation:

\[ h = \frac{P}{\rho \cdot g} + \frac{v^2}{2 \cdot g} + z \]

Where:

\( h \) — Total hydraulic head (meters)
\( P \) — Fluid pressure (Pascals)
\( \rho \) — Fluid density (kg/m³)
\( g \) — Gravitational acceleration (9.81 m/s²)
\( v \) — Fluid velocity (m/s)
\( z \) — Elevation head (meters)

Explanation: The equation sums three components:

Pressure head: Energy from fluid pressure
Velocity head: Energy from fluid motion
Elevation head: Potential energy from height

3. Importance of Hydraulic Head

Details: Hydraulic head determines flow direction and rate in fluid systems. It's crucial for designing pipelines, pumps, and understanding groundwater movement.

4. Using the Calculator

Tips:

Enter pressure in Pascals (1 psi ≈ 6895 Pa)
Water density is typically 1000 kg/m³
For stationary fluids, velocity can be 0
Elevation is relative to your reference point

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between head and pressure?
A: Head expresses energy as height equivalent, while pressure is force per area. They're related through density and gravity.

Q2: When can I neglect the velocity head term?
A: In slow-moving fluids (v < 1 m/s) or when analyzing static systems, velocity head is often negligible.

Q3: What are typical values for water systems?
A: Municipal water systems often operate at 30-80 m head. Household pressure is typically 20-60 m head.

Q4: How does elevation affect hydraulic head?
A: Each meter of elevation adds 1 m to the total head, representing potential energy.

Q5: Can I use this for other fluids besides water?
A: Yes, but you must use the correct density (e.g., 800 kg/m³ for gasoline, 13600 kg/m³ for mercury).