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
and pressure ,
such that an element
is moved a distance .
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.

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In symbols
,
where
is the pressure,
is the density (of water, in this case),
is gravitational acceleration,
is the height, and
is the velocity. In the graphic, the subscript 1 denotes
quantities on the left and right sides of the pipe.

The arrow that represents
is drawn at one-tenth its real size because it grows too
much compared to .