1. By Woo Chang Chung Bernoulli’s Principle and Simple Fluid Dynamics

6. Bernoulli’s Equation Where p is the pressure, ρ is the density, v is the velocity, h is elevation, and g is gravitational acceleration

8. Derivation of Bernoulli’s Equation Consider the change in total energy of the fluid as it moves from the inlet to the outlet. Δ E total = W done on fluid - W done by fluid Δ E total = ( 1 / 2 mv 2 2 + mgh 1 ) – ( 1 / 2 mv 1 2 + mgh 2 ) W done on fluid - W done by fluid = ( 1 / 2 mv 2 2 + mgh 1 ) – ( 1 / 2 mv 1 2 + mgh 2 ) P 2 V 2 - P 1 V 1 = ( 1 / 2 mv 2 2 + mgh 1 ) – ( 1 / 2 mv 1 2 + mgh 2 ) P 2 – P 1 = ( 1 / 2 ρ v 1 2 + ρ gh 1 ) – ( 1 / 2 ρ v 1 2 + ρ gh 1 ) E total = 1 / 2 mv 2 + mgh W = F / A *A*d = PV P 2 + 1 / 2 ρ v 1 2 + ρ gh 1 = P 1 + 1 / 2 ρ v 1 2 + ρ gh 1 ∴