The Bernoulli principle, first formulated by Daniel Bernoulli in 1738, is

one means of expressing Newton’s second law of physics, concerning

conservation of energy. Roughly stated, this principle demonstrates that

the sum of pressure and velocity through or over a device represents is

equal, neglecting the effects of losses due to friction and/or increases by

adding energy with external devices such as pumps. The basic concept of

Bernoulli’s principle can be observed in routine daily activities: A ship’s

sail can push a vessel into the wind; an airplane’s wing produces lift; a

pitcher induces spin on a baseball and generates high- and low-pressure

zones forcing the ball into a curved pattern. Bernoulli’s principle can also

be demonstrated in the flow of fluids through pipe.

Heavier-than-air flight was not achieved until a wing was developed

that engaged the Bernoulli principle. Airplane wings generate lift by

creating high- and low-pressure zones (Figure 1). Ignoring losses for

friction, the total energy at any point along the wing is equal to the sum

of the pressure (P) and the velocity (V). Pressure and velocity are equal

at points A and C, that is, P1+V1=P2+V2. Because aircraft wings are

curved on top, air travels farther and thus moves faster above the wing

than underneath it. Therefore, velocity at point B is greater above

the wing than below it. The law of conservation of energy indicates

that pressure is affected inversely: If V increases, then P decreases. This

creates a differential pressure, or ΔP: higher pressure beneath the wing

adds lift. As speed increases, so does lift.

## Relationship of Pressure, Velocity, and Head

Likewise, in piping systems, velocity and pressure are measured as fluid

flows internally in the pipe, rather than externally, as over a wing. Again

assuming that there is no friction loss and no energy added to the system

(e.g., pumps), the sum of pressure h, or head of fluid, and velocity will be

a constant at any point in the fluid. Consider an example with an ideal

fluid and frictionless pipe. Figure 2. shows the relationship between

pressure and velocity under steady flow conditions. Remember, ignore

losses caused by friction. Attaching manometers to the pipe will indicate

h, or head levels, at three points in the pipe. Pressure gauges will also

indicate the level of head. Notice that at points A and C, the levels of h

are equal, while at point B it is lower. This is because pipe size is reduced;

therefore, velocity (v) is higher. Once the pipe expands again, v will

decrease, and h will again increase. In actual practice, losses or energy

increases or decreases are encountered and must be included in the

Bernoulli equation.

This quantity is constant for all points within the pipe, and this is

Bernoulli’s theorem. Although it is not a new principle, it is an expression

of the law of conservation of mechanical energy in a convenient

form for fluid mechanics.