Page 351 - APPLIED PROCESS DESIGN FOR CHEMICAL AND PETROCHEMICAL PLANTS, Volume 1, 3rd Edition

Mixing of Liquids 319

Five forces that can usually be used for scale-up are: Heat Transfer, Hydraulic Similarity [29]:
• Input force from mixer, function of [25]
impeller speed h = f (N, D, p, µ, cp, k, d) (5-60)
impeller diameter
• Opposing forces, functions of
viscosity ( result appiied force
density of fluid system conductivity J ( J (5-61)
= f resisting force
surface tension
• Dynamic similarity requires that the ratio of input
force, viscosity, density, and surface tension be equal. (hi)= (N�2pJ [c�µJ (�J
For the same fluid, only two of these four forces need (5-62)
be equal, because the density and viscosity will be the
same [34, 29]. x, y, z are empirical exponents
The geometric and dynamic similarity can use k = thermal conductivity
dimensionless groupings. d = heal transfer tube diameter
• Geometric [29]: p = density of fluid or specific gravity
µ = viscosity of fluid
(5-55)
Blending, Hydraulic Similarity:
Xm, XP = dimension of model. and scale-up unit,
respectively 8 = f (N, D, p, µ, T) (5- 63)
XR = ratio of dimensions
• Dynamic [29]: where 8 = time
T = tank diameter

(Result/system conductivity) = f (applied force/resis-
tancy force)
F = force
Subscripts: l = inertia force 8Np ([ND2p/µ])' (D/T)Z (5- 64)
v = viscosity force
G = gravity x and z are empirical coefficients.
C' = interfacial tension
R = ratio Example 5-1: Scale-up from Small Test Unit [32], See
m = model Figure 5-34
p = :=irototype
Follow the example of Reference [32], using scale-up
Force ratios: rules. A pilot plant test run has been conducted using a
laboratory equipped test vessel. Design equivalent process
results for a 10,000 gallon tank are:
F1
F = N Re = ND 2 p/µ (5- 57)
v Data from Test Unit Proposal Vessel
Vessel dia, T1 = 12 in. T2 = 144 in.
(5- 58) Vessel liquid level, Z 1 = 12 in. Z 2 = 144 in.
Batch volume, V 1 = 6 gal. V 2 = 10,000 gal.
Impeller dia, 0 1 = 4 in. D2 = 48 in.
"Fr = Froude number
Impeller shaft speed,
N 1 = 450 rpm N2 = 90 (calc.)
Impeller width, ,,v = I in. v\/2 = 12 in.
1
(5- 59) Baffle width, (4) B 1 = 1 in. B2 = 12 in.
Distance to impeller, C 1 = 4 in. C 2 = 48 in.
HP input to shaft,
Nwe = ,veber number HP1 = 0.0098 (calc.) HP input HP 2 = 19.5 (calc.)