WORLD FOR CIVIL

Bernoulli Equation

For fluid energy, the law of conservation of energy is represented by the Bernoulli equation(for ideal fluid only):

Z₁+p₁/w+V₁²/2g=Z₂+p₂/w+V₂²/2g

where

Z₁= elevation, ft (m), at any point 1 of flowing fluid above an arbitrary datum

Z₂= elevation, ft (m), at downstream point in fluid above same datum

p₁= pressure at 1, lb/ft2 (kPa)

p₂= pressure at 2, lb/ft2 (kPa)

w= specific weight of fluid, lb/ft3 (kg/m3)

V₁= velocity of fluid at 1, ft/s (m/s)

V₂= velocity of fluid at 2, ft/s (m/s)

g= acceleration due to gravity, 32.2 ft /s2 (9.81 m/s2)

The left side of the equation sums the total energy per unit weight of fluid at 1, and the right side, the total energy per unit weight at 2. The equation for real fluid consist of a value due to head loss due to friction.

This is given below

Z₁+p₁/w+V₁²/2g=Z₂+p₂/w+V₂²/2g+h_f

The term P/W is called pressure head and V*V/2 is called velocity head.