Question 1

What is Bernoulli's theorem?

Accepted Answer

Bernoulli's theorem states that for an inviscid, incompressible, steady flow along a streamline, the sum of static pressure, dynamic pressure (½ρv²), and hydrostatic pressure (ρgh) remains constant: P₁ + ½ρv₁² + ρgz₁ = P₂ + ½ρv₂² + ρgz₂. It implies that where velocity increases, pressure decreases — the principle behind venturi meters, aircraft lift, and carburetors.

Question 2

How does the continuity equation relate to Bernoulli's theorem?

Accepted Answer

The continuity equation for incompressible flow states A₁v₁ = A₂v₂ (mass conservation). It determines the outlet velocity from the inlet velocity and area ratio. Combined with Bernoulli's theorem, you can solve for both velocity and pressure at any cross-section of the pipe.

Question 3

What is dynamic pressure and how does it differ from static pressure?

Accepted Answer

Static pressure (P) is the thermodynamic pressure of the fluid, measurable by a pressure tap flush with the wall. Dynamic pressure (½ρv²) represents the kinetic energy per unit volume — it increases with velocity. Total pressure = static + dynamic, measured by a pitot tube. Bernoulli's theorem (for flat elevation) says total pressure is conserved along a streamline.

Question 4

How can this tool be used in CFD and piping design?

Accepted Answer

Key applications include: (1) pre-CFD hand-calculation to verify OpenFOAM or ANSYS Fluent results, (2) venturi meter and orifice plate design, (3) initial pressure drop estimates for HVAC and cooling systems, (4) pump sizing by knowing the required pressure head. Note that real pipelines also require friction loss correction via the Darcy-Weisbach equation.

Bernoulli's Theorem — Pipe Flow Visualizer

Theory