1. 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

2. 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

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

4. Total energy E possessed by fluid

5. Consider Continuity 2 1

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

8. 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).

9. Example Calculate

10. 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

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

13. 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)

14. 1
At the reservoir, p1=0
u1=0 2
So total head = H = z1

17. Varying Diameters