BERNOULLI’S EQUATION
Fluid Flow
where:
Q
= heat (Btu)
U
= internal energy (Btu)
PE = potential energy (ft-lbf)
KE = kinetic energy (ft-lbf)
P
= pressure (lbf/ft2)
V
= volume (ft3)
W = work (ft-lbf)
Simplified Bernoulli Equation
Bernoulli’s equation results from the application of the general energy equation and the first law
of thermodynamics to a steady flow system in which no work is done on or by the fluid, no heat
is transferred to or from the fluid, and no change occurs in the internal energy (i.e., no
temperature change) of the fluid. Under these conditions, the general energy equation is
simplified to Equation 3-9.
(PE + KE + PV)1 = (PE + KE + PV)2
(3-9)
Substituting appropriate expressions for the potential energy and kinetic energy, Equation 3-9 can
be rewritten as Equation 3-10.
(3-10)
mgz1
gc
mv2
1
2gc
P1V1
mgz2
gc
mv2
2
2gc
P2V2
where:
m = mass (lbm)
z = height above reference (ft)
v = average velocity (ft/sec)
g = acceleration due to gravity (32.17 ft/sec2)
gc = gravitational constant, (32.17 ft-lbm/lbf-sec2)
Note: The factor gc is only required when the English System of measurement is used and mass
is measured in pound mass. It is essentially a conversion factor needed to allow the units
to come out directly. No factor is necessary if mass is measured in slugs or if the metric
system of measurement is used.
Each term in Equation 3-10 represents a form of energy possessed by a moving fluid (potential,
kinetic, and pressure related energies). In essence, the equation physically represents a balance
of the KE, PE, PV energies so that if one form of energy increases, one or more of the others
will decrease to compensate and vice versa.
HT-03
Page 22
Rev. 0
