Bernoulli Equation Pipe Flow Calculator

Bernoulli Equation for Pipe Flow:

\[ \frac{P_1}{\rho g} + \frac{v_1^2}{2g} + h_1 = \frac{P_2}{\rho g} + \frac{v_2^2}{2g} + h_2 + h_L \]

P1 (Pressure at point 1):

ρ (Fluid density):

kg/m³

g (Gravity):

m/s²

v1 (Velocity at point 1):

m/s

h1 (Elevation at point 1):

P2 (Pressure at point 2):

v2 (Velocity at point 2):

m/s

h2 (Elevation at point 2):

hL (Head loss):

Equation Balanced:

Left Side Value:

Right Side Value:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Bernoulli Equation for Pipe Flow?

The Bernoulli equation is a statement of energy conservation for flowing fluids. It relates pressure, velocity, and elevation at two points along a streamline, accounting for energy losses (hL) in pipe flow systems.

2. How Does the Calculator Work?

The calculator verifies the Bernoulli equation:

\[ \frac{P_1}{\rho g} + \frac{v_1^2}{2g} + h_1 = \frac{P_2}{\rho g} + \frac{v_2^2}{2g} + h_2 + h_L \]

Where:

\( P \) — Pressure (Pa)
\( \rho \) — Fluid density (kg/m³)
\( g \) — Gravitational acceleration (m/s²)
\( v \) — Flow velocity (m/s)
\( h \) — Elevation head (m)
\( h_L \) — Head loss due to friction (m)

Explanation: The equation states that the total mechanical energy (pressure, kinetic, and potential) remains constant along a streamline, minus any energy losses.

3. Importance of Bernoulli Equation

Details: The Bernoulli principle is fundamental for analyzing pipe flow, pump systems, hydraulic engineering, and aerodynamics applications.

4. Using the Calculator

Tips: Enter all parameters in consistent SI units. The calculator checks if both sides of the equation balance (within 0.001 m tolerance). Head loss (hL) is typically positive.

5. Frequently Asked Questions (FAQ)

Q1: When is the Bernoulli equation valid?
A: For steady, incompressible, inviscid flow along a streamline. Real applications require accounting for viscosity (hence hL term).

Q2: What are typical head loss values?
A: Depends on pipe length, diameter, roughness, and flow rate. Can range from centimeters to meters per 100m of pipe.

Q3: How to estimate head loss?
A: Use Darcy-Weisbach or Hazen-Williams equations with friction factors.

Q4: What if my equation doesn't balance?
A: Check units and measurement accuracy. Significant imbalance suggests missing energy terms or measurement errors.

Q5: Can this be used for compressible flow?
A: No, this calculator is for incompressible flow only (constant density).