Bernoulli's Theorem

p

1

500.

A

1

0.9

v

1

0.5

h

1

2.5

Δx

1

0.25

A

2

0.5

h

2

1

t

0.2

Bernoulli's theorem is implied by the conservation of mass and energy in fluid flow. Consider a nonviscous, incompressible fluid flowing through a pipe with cross-sectional area

A

1

and pressure

p

1

, such that an element

Δm

is moved a distance

Δx

. The theorem states that the sum of the pressure, the potential, and kinetic energy per unit volume is equal to a fixed constant at any point of a fluid.