Page 87 - APPLIED PROCESS DESIGN FOR CHEMICAL AND PETROCHEMICAL PLANTS, Volume 1, 3rd Edition

Fluid Flow 71

Note that the £/D [actor from Figure 2-11 is used uid and cavitation with erosion will occur. Then the cal-
directly in Figure 2-3. As an example that is only applica- culated flow rates or pressure or pressure drops are not
ble in the range of the charts used, a 10% increase in £/D accurate or reliable.
to account for increased roughness, yields from Figure 2-
3, an f of only 1.2% greater than a commercial condition
pipe. Generally the accuracy of reading the charts does Pressure Drop in Fittings, Valves, Connections:
not account for large fluctuations in fvalues. Of course, f, Incompressible Fluid
can be calculated as discussed earlier, and a more precise
number can be achieved, but this may not mean a signifi- The resistance to flow through the various "piping"
cantly greater accuracy of the calculated pressure drop. componenLs that make up the system (except vessels,
Generally, for industrial process design, experience tanks, pumps-items which do not necessarily provide
should be used where available in adjusting the roughness frictional resistance to flow) such as valves, fittings, and
and effects on the friction factor. Some designers increase connections into or out of equipment (not the loss
the friction factor by 10% to 15% over standard commer- through the equipment) are esLablished by test and pre-
cial pipe values. sented in the published literature, but do vary depending
on the investigator,
Pressure Drop in Straight Pipe: Incompressible Fluid
Resistance Lo fluid flow through pipe and p1p1ng
The frictional resistance or pressure drop due to the components is brought about by (1) pipe component
flow of the fluid, hr, is expressed by the Darcy equation: internal surface roughness along with the density and
viscosity of the flowing fluid, (2) directional changes in
the system through the piping components, (3)
fLv 2 •
hr=---,ftofl1md, resistance (2-2) obstructions in the path to flow, and ( 4) changes in sys-
D(2g)
tem component cross-section and shape, whether grad-
fv 2 L ual or sudden.
or, L'.P = p , resistance loss, lbs I sq in. (2-1)
144D (2g)
hr= K (v 2 /2g), ft of the fluid flowing (2-23)
Note: these values for hr and i1P are differentials from
poin L ( l) upstream to point ( 2) downstream, separated by
a length, L. These are not absolute pressures, and cannot be Velocity and Velocity Head
meaningfully converted to such units. Feet of fluid, hr, can
be convened to pounds per square inch by: The average or mean velocity is determined by the flow
rate divided by Lhe cross section area for flow in feet per
L'.P(144) . second, v. The velocity in a pipe is related to the decrease
hr = = fl, for any fluid (2-20) in static head due to the velocity only by:
p

hL =hr= v 2 /2g, termed velocity head, ft (2-24)
Referenced to waler, convert psi to feet of waler:
Note the static reduction (loss) due Lo fluid flowing
[(1 lb/sq in.)] (144)
hf (ft)= = 2.31 fl (2- 21) through a system componenL (valve, fitting, etc.) is
62.3 lb/ cu ft
expressed in terms of velocity head, using the resis-
tance coefficient, K, in the equation above. This K rep-
For conversion, l psi h 2.31 ft of water head resents the number of velocity heads lost due Lo Ilow
This rcp:esents a column of water at 60°F, 2.31 feel through the respective system component. It is always
high. The bottom pressure is one pound per square inch associated with diameter for flow, hence, velocity
(psi) on a gauge. The pressure al the bottom as psi will through the componenl. Actually, for most system com-
vary with the density of the fluid. For fluids other than ponents, the static losses due Lo pipe friction due to
water, the relationship is: internal roughness and the actual length of flow path
are minor when compared to one or more of the other
1 psi = 2.3 l/ (Sp Gr rel. to water), ft fluid (2-22) losses listed in the previous paragraph [3]. The resis-
tance coefficient, K, is considered independent of fric-
With extreme velocities of liquid in a pipe, the down- tion factor or Reynolds number and is treated as a con-
stream pressure may fall Lo the vapor pressure of the liq- siant for any component obstruction (valve or fitting)