Page 131 - Chemical Process Equipment - Selection and Design

6.6. NON-NEWTONIAN LIQUIDS 103
LE 6.8+(continued) Steam
2. Purchase costs of pumps, motors and drives are taken from = 10.14 kg/HP (from the “manual”)
Manual of Economic Analysis of Chemical Processes, Institut
Fi-ancais du Penole (McGraw-Hill, New York, 1976). = 10.14(0.2883)(2.204)hp/1000 = 0.006443hp, 1000 Ib/hr.
3. All prices are as of mid-1975. Escalation to the end of 1984
requires a facton of 11.8. However, the location of the optimum Power cost:
will be approximately independent of the escalation if it is
assumed that equipment and utility prices escalate approximately 0.065(8000)( kw) , $/yr,
uniformly; so the analysis is made in terms of the 1975 prices.
Annual capital cost is 50% of the installed price/year. Steam cost:

The summary shows that a 6-in. line is optimum with motor 4.5(8000)(1000 lblhr), $/yr.
drive, and an 8-in. line with turbine drive. Both optima are
insensitive to line sizes in the range of 6-10 in. Installed pump cost factors for alloy, temperature, etc (data in the
“manual”)
Q = 1000/(7.48)(60) = 2.2282 cfs, 227.2 m3/hr,
4epl 4(2.22,82)(0.81)(62.4) - 71,128 = 2[2.5(1.8)(1.3)(0.71)] = 8.2.
= --
NRe __ E
nDp n(0.000672)(3)0 D ’ Summary:
0.135(0.00015)+ 6.50
f = 1.636411n D 71,128 IPS 4 6 8 10
Pump head: D (ft) 0.3355 0.5054 0.6651 0.8350
lOOf 1.89 1.87 1.89 1.93
hp (ft) 898 41 3 360 348
Pump efficiency 0.71 0.71 0.71 0.71
motor (kW) 214.6 98.7 86.0 83.2
= 341.88 + 124.98f /D5 ft. Steam, 1000 Ib/hr 5.97 2.66 2.32 2.25
Motor power: Pump cost, 2 installed 50,000 28,000 28,000 28,000
Motor cost, 2 installed 36,000 16,000 44,000 14,000
Qp 2.2282(50.54) Turbine cost, 2 installed 56,000 32,000 28,000 28,000
P,=- Pipe cost 18,000 27,000 36,000 45,000
qpq, hp =550(0.71(0.90)) hp Valve cost 23,750 31,546 38,584 45,107
= 0.3204hp, NP Equip cost, motor drive 127,750 93,546 107.584 123,107
Equip cost, turbine drive 147.750 109,546 1 21,584 137,107
Turbine power: Power cost ($/yr) 111,592 51,324 44,720 43,264
Steam cost ($/yr) 208,440 95,760 83,520 80,834
Annual cost, motor drive 175,467 98,097 98,512 104,817
Annual cost, turbine drive 282,315 150,533 144.31 2 149.387

gradient, y = ,a’u/dx. The concept is represented on Figure 6.2(a): polymers and in suspensions of solids in liquids. Some a-y plots are
one of the planes is subjected to a shear stress and is translated shown in Figure 6.2, and the main classes are described following.
parallel to a fixed plane at a constant velocity but a velocity gradient 1. Pseudoplastic liquids have a a-y plot that is concave
is developed between the planes. The relation between the variables downward. The simplest mathematical representation of such
may be writtell relations is a power law
a = F/A = pL(du/dx) = py, (6.34) a=Ky”, n<l (6.36)

where, by definition, p is the Viscosity. In the simplest case, the with n < 1. This equation has two constants; others with many more
viscosity is constant, and the fluid is called Newtonian. In the other than two constants also have been proposed. The apparent viscosity
cases, more complex relations between t and i, involving more than is
one constant are needed, and dependence on time also may be
present. Classifications of non-Newtonian fluids are made according pa = t/y = K/yl-”. (6.37)
to the relation between t and by formula or shape of plot, or
according to the mechanism of the resistance of the fluid to Since n is less than unity, the apparent viscosity decreases with the
deformation. deformation rate. Examples of such materials are some polymeric
The concept of an apparent viscosity solutions or melts such as rubbers, cellulose acetate and napalm;
suspensions such as paints, mayonnaise, paper pulp, or detergent
Pa = a/? (6.35) slurries; and dilute suspensions of inert solids. Pseudoplastic
properties of wallpaper paste account for good spreading and
is useful. In the Newtonian case it is constant, but in general it can adhesion, and those of printing inks prevent their running at low
be a function of z, y9 and time 8. speeds yet allow them to spread easily in high speed machines.
Non-Newtonian behavior occurs in solutions or melts of 2. Dilatant liquids have rheological behavior essentially