Conservation of Energy/Bernoulli’s Equation Energy can neither be created nor destroyed. It can only be transferred from one form to another. Conservation of Energy In fluid mechanics three forms of energy exist. Consider fluid flow through a pipe. v z Element of fluid Reference level L Direction of flow

Potential energy: relative to some reference level. Kinetic Energy: Due to velocity Pressure Energy: Also known as flow energy or flow work. (1) (2) (3) Work necessary to move element against Pressure

Proof of work done Consider movement of fluid element a distance L

Total energy E possessed by fluid

Consider Continuity 2 1

Dividing by , Each term represents a form of Energy per unit weight which is or “head” Bernoulli’s Equation

Restrictions in the application of the Bernoulli’s equation Flow is steady; Density is constant (which also means the fluid is incompressible); Friction losses are negligible. The equation relates the states at two points along a single streamline, (not on two different streamlines).

Example Calculate

Assumptions for solving Exposed to air Soln. Assumptions for solving Exposed to air Large Volume Find known: Point A) Area is very large so assume Point F) It is below point A Bernoulli’s equation for points A and F

Pressure at For B write eqn. For pts A and B

Note: Unlike fluid statics, Pressure at the same elevation is NOT the same when fluid is moving. It is possible to have a negative pressure lower that the vapor pressure which leads to gas Bubbles formation (Cavitations)

1 At the reservoir, p1=0 u1=0 2 So total head = H = z1

Varying Diameters