Page 119 - Chemical Process Equipment - Selection and Design

6

FLOW OF FLUIDS

he transfer of fluids through piping and equipment is rates. In this chapter, the concepts and theory of fluid
accompanied by friction and may result in changes mechanics bearing on these topics will be reviewed briefly
in pressure, velocity, and elevarion. These effects and practical and empirical methods of sizing hes and
requ,ire input of energy to maintain flow at desired auxiliary equipment will be emphasized.

6.1. PRQPERTES AND UNITS For nonideal gases a general relation is
The basis of flow relations is Newton’s relation between force,
mass, and acceleration, which is p = MP/zRT, (6.4)
where the compressibility factor z is correlated empirically in terms
F = (m/s,)a. (6.1) of reduced properties TIT, and P/P, and the acentric factor. This
subject is treated for example by Reid et al. (1977, p. 26) and Walas
When F and a are in lb units, the numerical value of the coefficient (1985, pp. 17, 70). Many PVT equations of state are available. That
is gc = 32.174 Ib ft/’lbfsec2. In some other units, of Redlich and Kwong may be written in the form
kg m/sec” g cm/sec* kg m/sec*
g =I--= 1 ~- -9.ao6-. V = b + RT/(P + a/fiV2), (6.5)
N dw kg,
which is suitable for solution by direct iteration as used in Example
Since the common engineering units for both mass and force are 6.1.
llb, it is essential to retain g, in all force-mass relations. The Flow rates are expressible as linear velocities or in volumetric,
interconversions may be illustrated with the example of viscosity mass, or weight units. Symbols for and relations between the
whose basic definition is force/(velocity)(distance). Accordingly the several modes are summarized in Table 6.1.
viscosity in various units relative to that in SI units is The several variables on which fluid fiow depends may be
gathered into a smaller number of dimensionless groups, of which
1
1 Ws/mz = __ kg, s/m2 = 10 g/(cm)(s) the Reynolds number and friction factor are of particular
9.806 importance. They are defined and written in the common kinds of
= 10 P = 0.0672 lb/(ft)(sec) units also in Table 6.1. Other dimensionless groups occur less
frequently and will be mentioned as they occur in this chapter; a
-- 0‘0672 Ibf sec/ft’ = 0.0020189 lbf sec/ft2
-
32.174 long list is given in Perry’s Chemical Engineers Handbook
(McGraw-Hill, New York, 1984, p. 5.62).
In data book’s, viscosity may be recorded either in force or mass
units. The particular merit of SI units (kg, m, s, N) is that g, = 1 and
much confusion can be avoided by consistent use of that system.
Some numbeIs of frequent use in fluid Wow problems are
EXAMPLE 6.1
Viscosity: 1 cPoise = 0.001 N s/m2 = 0.41134 Ib/(ft)(hr). Density of a Nonideal Gas from Its Equation of State
Density: 1 g m/crn3 = 1000 kg/m3 = 62.43 lb/ft3. The Redlich-Kwong equation of carbon dioxide is
Specific weight: 62.43 Ibf/cuft = 1000 kg,/m3.
Pressure: 1 afm = 0.10125 MPa = 0.10125(106) N/m2 = 1.0125 bar. (P + 63.72(106)/fiV2)(V - 29.664) = 82.05T
Data of densities of liquids are empirical in nature, but the with P in atm, V in mL/g mol and Tin K. The density will be found
effects of temperature, pressure, and composition can be estimated; at P = 20 and T = 400. Rearrange the equation to
suitable methods are described by Reid et al. (Properties of Gases
and Liquids, McGraw Hill, New Yorlr, 1977), the APZ Refining V = 29.664 + (82.05)(400)/(20 + 63.72(1O6)/$$%V2).
Data Book (American Petroleum Institute, Washington, DC, 1983),
and the AlChE Data Prediction Manual (1984-date). The densities Substitute the ideal gas volume on the right, V = 1641; then find V
of gases are represented by equations of state of which the simplest on the left; substitute that value on the right, and continue. The
is that of ideal gases; from this the density is given by: successive values of V are

p = 1/V = MP/RT, massfvolume (6.2) V = 1641, 1579, 1572.1, 1571.3, 1571.2, . . . mL/g mol
where A4 is the molecular weight. For air, for example, with P in and converge at 1571.2. Therefore, the density is
atm and T in “R,
p = 1/V = 1/1571.2, or 0.6365 g mol/L or 28.00 g/L.
29p Ib/cuft. (6.3)
p=m’