It is customary to express the
energy contained in a fluid in terms of the potential energy
contained in an equivalent height or "head" of a column of the
fluid. Using this convention, Bernoulli's theorem breaks down
the total energy at a point in terms of:
1.
The head due to its
elevation above an arbitrary datum of zero potential energy.
2.
A pressure head due to
the potential energy contained in the pressure in the fluid at
that point.
3.
A velocity head due to
the kinetic energy contained within the fluid
Assuming that no energy is added to the fluid by a pump or
compressor, and that the fluid is not performing work as in a
steam turbine, the law of conservation of energy requires that
the energy at point "2" in the piping system downstream of point
"1" must equal the energy at point "1" minus the energy loss to
friction and change in elevation. Thus, Bernoulli's theorem may
be written:
Or
where:
Z =
elevation head, ft
P =
pressure, psi
p =
density, lb/ft3
V =
velocity, ft/sec
g =
gravitation constant
HL =
friction head loss, ft
Darcy's Equation
This equation, which is also
sometimes called the Weisbach equation or the DarcyWeisbach
equation, states that the friction head loss between two points
in a completely filled, circular cross section pipe is
proportional to the velocity head and the length of pipe and
inversely proportional to the pipe diameter. This can be
written:
where:
L=
length of pipe, ft
D =
pipe diameter, ft
f =
factor of proportionality
Equations 1 and 2 can be used
to calculate the pressure at any point in a piping system if the
pressure, flow velocity, pipe diameter, and elevation are known
at any other point. Conversely, if the pressure, pipe diameter,
and elevations are known at two points, the flow velocity can be
calculated.
In most production facility piping systems the head differences
due to elevation and velocity changes between two points can be
neglected. In this case Equation 2 can be reduced to:
where
∆P
= loss in pressure between points 1 and 2,
in psi
