Bernoulli's Equation
Proof of Bernoulli's Equation
Daniel Bernoulli (1700-1782)–where the v of a fluid is high, P is low
and where v is low, P is high
The pressure at point 2 is lower (since v is greater @
point 2 than at point 1 where v is smaller). (a)
High pressure would slow the fluid down.
To derive Bernoulli’s equation, assume flow is steady and
laminar, the fluid is incompressible and viscosity is small enough
to be ignored.
P1 + ½ ρv12 + ρgy1 = P2 + ½ ρv22 + ρgy2
P1 + ½ ρv12 + ρgy1 = CONSTANT @ every point in the fluid
Bernoulli's equation is an expression of the law of energy
conservation since we derived it from the work-energy principle.