Page 120 - Chemical Process Equipment - Selection and Design

92 FLOW OF FLUIDS
TABLE 6.1. Flow Quantities, Reynolds Number, and Friction 6.2. ENERGY BALANCE OF A FLOWING FLUID
Factor
The energy terms associated with the flow of a fluid are
Typical Units
Flow Symbol and
Quantity Equivalent Common SI 1. Elevation potential (g/g,)z,
2. Kinetic energy, u2/2gc,
Linear U ft/sec m/sec 3. Internal energy, U,
Volumetric 0 = UA = xD2u/4 cuft/sec rn3/sec 4. Work done in crossing the boundary, PV,
Mass m =pQ =pAu Ib/sec kg/sec 5. Work transfer across the boundary, W,,
Weight w = yQ = yAu Ibf/sec N/sec 6. Heat transfer across the boundary, Q.
Mass/area G = pu Ib/(sqft)(sec) kg/rn2 sec
Weightiarea G,, = yo Ibf/(sqft)(sec) N/m2 sec Figure 6.1 represents the two limiting kinds of regions over which
energy balances are of interest: one with uniform conditions
throughout (completely mixed), or one in plug flow in which
Reynolds Number (with A = xD2/4)
gradients are present. With single inlet and outlet streams of a
uniform region, the change in internal energy within the boundary
is

Friction Factor

f=g/(Lg) =2gcDAP/Lpu2= 1.6364
P 029, One kind of application of this equation is to the filling and
(Round's equation) emptying of vessels, of which Example 6.2 is an instance.
AP L u2 8LQ2 8Lm2 LG2
-=-_ f= fz- (3) Under steady state conditions, d(mU) = 0 and dm, = dm, =
2 2
P 029, gcx P D 5f=- 2g,DpZf dm, so that Eq. (6.6) becomes
AH + Au2/2gc + (g/g,)Az = (Q - KYm, (6.7)
In the units
or
D = in., m = Ib/hr
Q = cuftlsec, p = CP AU+ A(PV) + Au2/2g, + (g/g,)Az = (Q - y)/m, (6.8)
p =specific gravity
6 314m 1.418(106)p0 or
Re=-= (4)
DU DU
AP 3.663(10-9)ri.12 AU + A(P/p) + Au2/2gc + (g/g,)Az = (Q - K)/m. (6.9)
-= f, atrn/ft (5)
L 0D5
5.385(1 0-*)m2 For the plug fiow condition of Figure 6.l(b), the balance is
- f, psifft made in terms of the differential changes across a differential length
-
PD5 dL of the vessel, which is
-- 0.6979~0' f, psi/ft
-
D5
dH + (l/g,)U du + (g/g,) dz = dQ - dW,, (6.10)
Laminar Flow where all terms are per unit mass.
Rei 2300
f = 64/Re
AP/L=32pu/D2

Gravitation Constant I I
gc = 1 kg m/N sec2 Unit Cross Section
= 1 g crnldyn sec2 (b) dQ d Ws
= 9.806 kg m/kgf sec2 Figure 6.1. Energy balances on fluids in completely mixed and plug
= 32.174 Ibm ft/lbf sec' flow vessels. (a) Energy balance on a bounded space with uniform
= 1 slug ft/lbf sec2 conditions throughout, with differential flow quantities dm, and
= 1 Ibm ft/poundal sec2 dm,. (b) Differential energy balance on a fluid in plug flow in a tube
of unit cross section.