Fluid Flow
BERNOULLI’S EQUATION
Restrictions on the Simplified Bernoulli Equation
Practical applications of the simplified Bernoulli Equation to real piping systems is not possible
due to two restrictions. One serious restriction of the Bernoulli equation in its present form is
that no fluid friction is allowed in solving piping problems. Therefore, Equation 3-10 only
applies to ideal fluids. However, in reality, the total head possessed by the fluid cannot be
transferred completely from one point to another because of friction. Taking these losses of head
into account would provide a much more accurate description of what takes place physically.
This is especially true because one purpose of a pump in a fluid system is to overcome the losses
in pressure due to pipe friction.
The second restriction on Bernoulli’s equation is that no work is allowed to be done on or by the
fluid. This restriction prevents two points in a fluid stream from being analyzed if a pump exists
between the two points. Since most flow systems include pumps, this is a significant limitation.
Fortunately, the simplified Bernoulli equation can be modified in a manner that satisfactorily
deals with both head losses and pump work.
Extended Bernoulli
The Bernoulli equation can be modified to take into account gains and losses of head. The
resulting equation, referred to as the Extended Bernoulli equation, is very useful in solving most
fluid flow problems. In fact, the Extended Bernoulli equation is probably used more than any
other fluid flow equation. Equation 3-12 is one form of the Extended Bernoulli equation.
(3-12)
z1
v2
1
2g
P1n1
gc
g
Hp
z2
v2
2
2g
P2n2
gc
g
Hf
where:
z
= height above reference level (ft)
v
= average velocity of fluid (ft/sec)
P
= pressure of fluid (lbf/ft2)
n
= specific volume of fluid (ft3/lbm)
Hp
= head added by pump (ft)
Hf
= head loss due to fluid friction (ft)
g
= acceleration due to gravity (ft/sec2)
The head loss due to fluid friction (Hf) represents the energy used in overcoming friction caused
by the walls of the pipe. Although it represents a loss of energy from the standpoint of fluid
flow, it does not normally represent a significant loss of total energy of the fluid. It also does
not violate the law of conservation of energy since the head loss due to friction results in an
equivalent increase in the internal energy (u) of the fluid. These losses are greatest as the fluid
flows through entrances, exits, pumps, valves, fittings, and any other piping with rough inner
surfaces.
Rev. 0
Page 25
HT-03
