What is Bernoulli’s equation for an ideal fluid flowing between 2 sections of pipewith differing elevation, cross-sectional area and pressures?

Bernoulli's equation for an ideal fluid flowing between two sections of a pipe with differing elevation, cross-sectional area, and pressures is given by:

P₁ + ½ρv₁² + ρgh₁ = P₂ + ½ρv₂² + ρgh₂

Here's what each term represents:

• P₁ and P₂ are the pressures at the two points.
• v₁ and v₂ are the velocities of the fluid at the two points.
• h₁ and h₂ are the heights (elevations) of the two points above some reference level.
• ρ is the density of the fluid.
• g is the acceleration due to gravity.

This equation is a statement of the conservation of energy principle for flowing fluids. It accounts for gravitational potential energy, kinetic energy, and fluid pressure.