Bernoulli's Principle Visualization

Bernoulli's principle states that as the speed of a fluid increases, the pressure within the fluid decreases. This principle is fundamental to understanding how fire sprinkler systems work. This interactive visualization demonstrates how water velocity increases and pressure decreases when flowing through a constricted pipe section.

Flow Rate

Key Points About Bernoulli's Principle in Fire Sprinkler Systems:

Conservation of Energy: Bernoulli's principle is based on the conservation of energy in fluid flow. The total energy at any point in a fluid system remains constant (in the absence of friction).
Pressure-Velocity Relationship: When water flows through a narrower pipe section, its velocity increases and its pressure decreases. Conversely, when water flows into a wider pipe section, its velocity decreases and its pressure increases.
Practical Applications: This principle affects pressure loss calculations in sprinkler systems, especially at fittings, valves, and changes in pipe diameter.
K-Factor Formula: The discharge from sprinkler heads is based on this principle, where flow is proportional to the square root of pressure (Q = K√P).
System Design: Understanding this principle helps engineers design systems that maintain adequate pressure at all points, ensuring proper sprinkler operation.

Bernoulli’s Equation Explorer | Pyrometrics

Bernoulli’s Equation Explorer

Pressure (P): Use a pressure gauge at the point of interest. Expressed in psi. If unknown, rearrange Bernoulli’s equation to solve for it.

Velocity (v): Use the flow rate and cross-sectional area:
v = Q / A where Q = flow rate (ft³/s), A = area (ft²).

Elevation (z): Measured vertically from a common datum (e.g., ground level). Point 1 and Point 2 must use the same reference level.

Bernoulli’s Equation:
P/γ + v²/(2g) + z = constant
where:
γ = specific weight (62.4 lb/ft³ for water)
g = 32.2 ft/s²

Pressure at Point 1 (psi) Velocity at Point 1 (ft/s) Elevation at Point 1 (ft) Pressure at Point 2 (psi) Velocity at Point 2 (ft/s) Elevation at Point 2 (ft)

What Is Bernoulli's Equation?

Bernoulli's Equation expresses the conservation of mechanical energy for incompressible, frictionless fluid along a streamline:

P/γ + v²/2g + z = constant

This means that the sum of pressure head, velocity head, and elevation head is constant between two points. This calculator helps you verify this relationship and understand energy conservation in flow systems.

Example Scenario

Point 1: Pressure = 50 psi, Velocity = 10 ft/s, Elevation = 0 ft

Point 2: Pressure = 45 psi, Velocity = 15 ft/s, Elevation = 10 ft

This example simulates water flowing from a pipe at ground level up a slope. You can edit the values to explore how energy is redistributed among pressure, velocity, and height.