Page 122 - Chemical Process Equipment - Selection and Design

94 FLOW OF FLUIDS

EXAMPLE 6.3 = 364.6 -, J ,
Nm
Units of the Energy Balance 364.6 -
kg
In a certain process the changes in stored energy and the friction are Nm kgf kg m kgf
~,=364.6--=37.19---.
AE = -135 ft lbf/lb kg 9.806N kg
wf = 13 ft lbf/lb.
At sea level, numerically lbf = lb and kgf = kg.
Accordingly,
The net work will be found in several kinds of units:
ft lbf lb kgf m - 37.19 - kgf m
W, = -(AE + w~) 122 ft lbf/lb, w, = 122-----
=
ft lbf 4.448N2.204 lb m lb lbf kg 3.28ft kg ’
w, = 122----
lb Ibf kg 3.28ft as before.

and the simpler form of the energy balance becomes diameter
AE + Wf = - W,. (6.17) Dh = 4(cross section)/wetted perimeter.

The units of every term in these energy balances are For an annular space, Dh = D, - D,.
alternately: In laminar flow the friction is given by the theoretical Poiseuille
equation
ft lb$lb with g, = 32.174 and g in ft/sec2 (32.174 at sea level).
N m/kg = J/kg with g, = 1 and g in m/sec2 (1.000 at sea level). f = 64/Nr,, NRe < 2100, approximately. (6.19)
kg, m/kg with g, = 9.806 and g in m/sec2 (9.806 at sea level).
At higher Reynolds numbers, the friction factor is affected by the
roughness of the surface, measured as the ratio E/D of projections
Example 6.3 is an exercise in conversion of units of the energy on the surface to the diameter of the pipe. Values of E are as
balances. follows; glass and plastic pipe essentially have E = 0.
The sign convention is that work input is a negative quantity
and consequently results in an increase of the terms on the left of
Eq. (6.17). Similarly, work is produced by the flowing fluid only if E (ft) E (mm)
the stored energy AE is reduced. Riveted steel 0.003-0.03 0.9-9.0
Concrete 0.001-0.01 0.3-3.0
6.3. LIQUIDS Wood stave 0.0006-0.003 0.18-0.9
Cast iron 0.00085 0.25
Velocities in pipe lines are limited in practice because of Galvanized iron 0.0005 0.15
Asphalted cast iron 0.0004 0.12
1. the occurrence of erosion. Commercial steel or 0.00015 0.046
wrought iron
2. economic balance between cost of piping and equipment and the Drawn tubing 0.000005 0.0015
cost of power loss because of friction which increases sharply
with velocity. The equation of Colebrook [J. Inst. Ciu. Eng. London, 11, pp.
133-156 (1938-1939)] is based on experimental data of Nikuradze
Although erosion is not serious in some cases at velocities as high as [Ver. Dtsch. Ing. Forschungsh. 356 (1932)l.
10-15 ft/sec, conservative practice in the absence of specific
knowledge limits velocities to 5-6 ft/sec. 1
Economic optimum design of piping will be touched on later, v7 -+- NR,>2100. (6.20)
-= 1.14-0.869111 (i ;e?$),
but the rules of Table 6.2 of typical linear velocities and pressure
drops provide a rough guide for many situations. Other equations equivalent to this one but explicit in f have been
The correlations of friction in lines that will be presented are devised. A literature review and comparison with more recent
for new and clean pipes. Usually a factor of safety of 20-40% is experimental data are made by Olujic [Chem. Eng., 91-94, (14
advisable because pitting or deposits may develop over the years. Dec. 198l)l. Two of the simpler but adequate equations are
There are no recommended fouling factors for friction as there are
for heat transfer, but instances are known of pressure drops to f =1.6364 [ In (,.,,E +- 6.5)]-’
~
double in water lines over a period of 10 years or so. NRe (6.21)
In lines of circular cross section, the pressure drop is
represented by [Round, Can. J. Chern. Eng. 58, 122 (1980)],
+
(6.18) 0 8686 In - 2.1802 In -
-
={- ’ [3.;D (3.& ~ (6’22)
For other shapes and annular spaces, D is replaced by the hydraulic [Schacham, Znd. Eng. Chem. Fundam. 19(5), 228 (1980)l. These