Page 460 - Chemical process engineering design and economics

Design of Flow Systems 439

f 2gc( P l -p 2 )/p V /2
Q = Ao | ————————— | (8.13)

This formula is the same for frictionless flow through the venturi and nozzle me-
ters.
To account for friction and the approximate values of a used, multiplied
Equation 8.13 by a discharge coefficient, CD.

( 2 gc (p,-p 2 )/p V /2
Q = C D Aol —————————— I (8.14)
2
V [1-(A 0 /A) ] >/
The discharge coefficient is a function of the meter type and Reynolds number.
Using the orifice meter as an example, Example 8.2 illustrates the sizing
procedure. Calculating the orifice diameter requires assigning the pressure drop
across the orifice.

Example 8.2 Orifice-Meter Sizing _________________________

3
Size an orifice meter to meter 70 gal/min (0.265 m /min) of acetone at 15 °C. The
pipe size is a two-inch Schedule 40 pipe. The viscosity of acetone is 0.337 cp
4
(3.37xlO~ Pa-s), and its specific gravity is 0.792.
To size an orifice meter requires calculating the orifice diameter from Equa-
tion 8.14. After dividing and multiplying Equation 8.14 by A, substituting A= n
2
D /4, and letting P = DO/ D, where DO is the orifice diameter and D the inside pipe
diameter, we obtain
r2g (p,-p )/pi i/2
2
c
Q = C D —— p 2 ————————— I
4
4 L (1-P ) J
Because C = f (Re), first calculate the Reynolds number in the pipe. From
D
Table 8.2A, the inside diameter of a Schedule 40, two-inch pipe is 2.067 in (5.25
cm).

4Q 4 70.0 gal/min 1 1
= —— = _ ——————— ———— ——————— = 6. 692 ft/s (2.04 m/s)
v
2
re D 2 TI 7.48 gal/ft 3 60 s/min (2.067/12) ft 2
4
4
y. = 0.337 cp (6.72 x lO^lbw/ft-s-cp) = 2.265X10" lb M/ft-s (3.37X10" Pa-s)
p = 0.792 (62.4) = 49.42 lb M/ft 3

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