Page 135 - APPLIED PROCESS DESIGN FOR CHEMICAL AND PETROCHEMICAL PLANTS, Volume 1, 3rd Edition

Fluid Flow 119

3. If sonic velocity of step 2 is greater than calculated From Figure 2-38, Y = 0.97; from Figure 2-18.
velocity of step 1, calculate line pressure drop using
usual flow equations. If these velocities are equal,
then the pressure drop calculated will be the maxi- c' (assumed turbulent) (2-47)
mum for the line, using usual flow equations. If [l - (dof a, )-1 ]1;2
sonic velocity is less than the velocity of step 1, reas-
sume line size and repeat calculations. where Cd = orifice discharge coefficient, uncorrected for
velocity of approach
B. How to determine flow rate ( capacity) for a given line size
and fixed pressure drop. C' = 0.74 at est. Re� 2000
Temperature = 460 + 50 = 510°F
This is also a trial and error solution following the pat-
tern of (A), except capacities are assumed and the pres-
sure drops are calculated to find a match for the given D . 144P 144 (54.7)
conditions of inlet pressure, calculating back from the ensity = P = RT = (96.4) (510)
outlet pressure. = 0.1602 lb/cu ft

C. How to determine pressure at inlet of pipe system for fixed W = 1891 Y d/C (Af>p)1;2 (2-95)
pipe size and flow rate. W = 1891 (0.97) (0.750) 2 0.74 [(3) (0.1602)]112
W = 529.2 lbs/hr methane
1. Determine sonic velocity at outlet conditions and
check against a calculated velocity using flow rate. If Check assumed R., to verify turbulence; if not in rea-
sonic is the lower, it must be used as limiting, and capac- sonable agreement, recalculate C' and balance of solu-
ity is limited to that corresponding to this velocity.
2. Using the lower velocity, and corresponding capaci- tion, checking:
ty, calculate pressure drop by the usual equations.
For greater accuracy start at the outlet end of the Viscosity of methane = 0.0123 centipoise
line, divide it in sections using the physical proper- = 6.31 W/dµ
ties of the system at these points, backing up to the = 6.31 (502)/ (0.750) (0.0123)
inlet end of the line for the friction loss calculations. Re= 343,373
This procedure is recommended particularly for
steam turbine and similar equipment exhausting to This is turbulent and satisfactory for the assumption.
atmosphere or vacuum. The pressure at the inlet of For helpful quick reference for discharge of air through
the line is then the sum of the discharge or outlet an orifice, see Table 2-12B.
line pressure and all the incremental section pres-
sure losses. In the case of a turbine, this would set its Example 2-11: Sonic Velocity
outlet pressure, which would be higher than the
pressure in the condenser or exhaust system. Water vapor ( 4930 lbs/hr) is flowing in a 3-inch line at
730°F. The outlet pressure is less than one half the inlet
Example 2-10: Gas Flow Through Sharp-edged Orifice absolute pressure. What is maximum flow that can be
expected?
A l"-Schedule 40 pipe is flowing methane at 40 psig
and 50°F. The flange taps across the orifice (0.750 inch s,I c, = 1.30
diameter) show a 3 psi pressure differential. Determine
the flow rate through the orifice. MW vapor = 18.02
Solution:
CH 4; Sp Gr = Sg = 0.553 v, = [ ( 1.30) (32.2) (1544/18.02) (730 + 460)] 1
1 2
= 2,065 ft/sec
Gas constant = R = 96.4
Ratio Sp. ht. = k = 1.26 Cross section of 3-inch pipe = 0.0513 sq ft
Absolute system pressure = P = 40 + 14.7 = 54.7 psia
b.P/P 1 = 3.0/54.7 = 0.0549 Volume flow = (2,065) (0.0513) = 105.7 cu ft/sec
Pipe ID = 1.049 in.
d /d1 = 0.750/1.049 = 0.7149 Vapor density= 4930/(3600) (105.7) = 0.01295 lb/cu ft
0