Page 97 - APPLIED PROCESS DESIGN FOR CHEMICAL AND PETROCHEMICAL PLANTS, Volume 1, 3rd Edition

Fluid Flow 81

Piping Systems for 0 < 45°, as enlargements:

The K coefficient values for each of the items of pipe,
K2 = 2.6 [(sin 0/2) (l- �2)2]/�4 (2-38)
bends, valves, fittings, contractions, enlargements,
entrance/exits into z from vessels are additive as long as
they are on the same size basis (see Table 2-2 and Fig- for 0 < 45°, as contractions
ures 2-12A through 2-16). Thus the resistance equation
is applicable to calculate the head or pressure loss K 2 = [0.8 (sin 8/2) (l - �2)]/�4 (2-39)
through the specific system when the combined K value
is used.
For higher resistance valves, such as globes and angles,
hr = K (v 2 /2g) (2-27) the losses are less than sudden enlargements or contrac-
tions situations. For these reduced seat valves the resis-
or, hr= f (L/D) (v 2 /2g) (2-26) tance coefficient K, can be calculated as [3]:

where K = summation of all K values in a specific system, At 0 < 180, for sudden and gradual enlargements:
when all are on the same size (internal flow) basis. See dis-
cussion in "Common Denominator" section.
(2-40)
Resistance of Valves
At < 180, for gradual contraction:
Figure 2-J.2B and Table 2-2 present several typical
valves and connections, screwed and flanged, for a variety (2-41)
of sizes or internal diameters. These do not apply for mix-
tures of suspended solids in liquids; rather specific data
for this situation is required (see [2]). Reference [3] pre- The use of these equations requires some assumptions or
sents data for specific valves. judgment regarding the degree of opening for fluid flow.
Even so, this is better than assuming a wide open or full
Valves such as globes and angles generally are designed
with changes in flow direction internally, and thereby, flow condition, which would result in too low a resistance
to flow for the design situation.
exhibit relatively high flow resistances. These same types
of valves exhibit even greater resistances when they are
throttled down from the "wide open" position for control Flow Coefficients for Valves, C,.
of flow to a smaller internal flow path. For design purpos-
es, it is usually best to assume a % or ,!(, open position,
rather than wide open. Estimated K values can be deter- Flow coefficients (not resistance) for valves are gener-
mined [3] by reference to Figures 2-12A through 2-16 and ally available from the manufacturer. The C, coefficient of
Tables 2-2 and 2-3. a valve is defined as the flow of water at 60°F, in gallons
per minute, at a pressure drop of one pound per square
inch across the valve [3], regardless of whether the valve
where K; = refers to coefficient for smaller diameter ultimately will be flowing liquid or gases/vapors in the
K 2 = refers to coefficient for larger diameter plant process. It is expressed:
� = ratio of diameters of smaller Lo larger pipe size
e = angles of convergence or divergence in enlarge- 112
ments or contractions in pipe systems, degrees. C,. = 29.9 d 2/ (K) (2-42)

From Reference [3], K values for straight-through valves, c, = Q [p/(L'iPc) (62.4)] 1 2 (2-43)
1
such as gale and ball (wide open), can also be calculated.
These types of valves are not normally used to throttle Q = c, [Af'c (62.4/p)J 112 (2-44)
flow, but are either open or closed.
For sudden and gradual (Note: Sub l = smaller pipe; 1 2
Sub 2 = larger pipe) = 7.90 C, [L'iPc/Pl 1 (2-HA)

(2-37) L'iP = [Q/C,.]2 [p/62.4] (2-45)