Page 196 - Standard Handbook Of Petroleum & Natural Gas Engineering

Fluid Mechanics 181

Example 2-1 6
Assume 100 ft3/min of water is to be pumped through a nozzle with a throat
diameter of 3/4 in. What pressure drop should be expected?

100
=
Q = - 1.67 ftg/s
60

y = 62.4 lb/ft3

Assume C = 0.95; then

(1.67*)( 62.4)
AP = = 2,210 psia
2( 32.2)(0.95*)( 3.068 x lo-')*( 144)
To analyze compressible flow through chokes it is assumed that the entropy of the fluid
remains constant. The equation of isentropic flow is

p,v; = P,Vi (2-64)
where PI and VI are the pressure and specific volume of the fluid at point 1,
immediately upstream of the choke, and P, and V, are the pressure and specific
volume immediately downstream of the choke. Equation 2-64 can be combined with
the ideal gas law to provide an estimate for the temperature drop across the choke
( rlii

T, =T, 2 (2-65)

where T, and T, are temperatures in OR. Furthermore, the first law of thermodynamics
can also be imposed, yielding the following equation for the volumetric flowrate:

(2-66)

where Q is the volumetric flow rate in scfm, C is a discharge coefficient that accounts
for friction and velocity of approach (see Figure 2-24). A is the choke area in square
inches, PI is the inlet pressure in pounds per square inch absolute (psia), P, is the
outlet pressure in psia, TI is the inlet temperature in OR, and S is the specific gravity
of the gas.
Equations 2-65 and 2-66 apply only as long as the fluid velocity at the throat of the
choke is subsonic. Sonic velocity is the speed of a pressure wave in a fluid. Once sonic
velocity is achieved, the effects of the downstream pressure can no longer be transmitted
to the upstream side of the choke.