NOMOGRAPH FOR
Apparent viscosity of Sulfite Stock D. S. DAVIS Wyandotte Chemicals Corporation, Wyandotte, Mich-
N#
I
C, V L ~ o s i t y ,Per cent /bs./ft. see. consktanc y
Nominal diumeter of pipe, k. 12-
10-
/ 0/
\
Apparent
/
/
/ \
fikcosity
of
J d f i t e Stow 6-
Key:
0.2
/ V O dla-d-C ~
4
Cl-p-U
T
HE standard friction factor plot (1, 4, 6, 6) in general use for the correlation of data on the flow of Newtonian liquids also serves for the flow of suspensions in the turbulent range when the Reynolds numbers are above 20,000,if the viscosity of the suspension is taken to be that of the suspending medium (8). Under prevailing circumstances in the paper mill, sulfite stocks exhibit viscous flow and require some other value to be used for the viscosity. From determinations of the pressure drops in the pumping of sulfite stock a t various consistencies and velocities in 6-12 inch pipes under conditions of viscous flow, Cooper (9) calculated the apparent viscosities of the suspensions. He correlated extensive data by an expression which enabled head losses to be computed within the usual tolerance of * 15 per cent: log I(
the key, connect 10 on the scale representing the nomina1 diameter of the pipe with 3.1 on the C scale and note the intersection with the ct axis. Connect this point with 4.5 on the U scale and read the apparent viscosity on the p scale R S approximately 1.4 pounds per foot-second. For stock flowing in &inch pipes a t low velocities and a t consistencies above 3.75 per cent, the coefficient of U in the equation becomes 0.025. Under such conditions half the value of U should be used in applying the nomograph. Apparent viscosity p , determined from the nomograph, is used in computing an apparent Reynolds number from which head losses are calculated from the standard friction factor plot. LITERATURE CITED
= log 0.095DCs- 0.05U
(1) Badger and McCsbe, “Elements of Chemical Engineering”, 2nd ed., p. 37, New York, McGraw-Hill Book Co., 1936. (2) Caldwell, D. H., and Babbitt, H. E., IND.ENQ.CEHIM., 33, 249 (1941). (3) Cooper, J., Paper Trade J., 115, TAPPI Sect. 270 (1942). (4) Keyes and Deem, Chemical Engineers’ Manual, 1st ed., p. 3. New York, John Wiley & Sons, 1942. (6) Perry, Chemical Engineers’ Handbook, 2nd ed., p. 811. New York, McGraw-Hill Book Co., 1941. (6) Walker, Lewis, McAdams, and Gilliland, “Principles of Chemical Engineering”, 3rd ed., p. 78, New York, McGraw-Hill Rook Co., 1937.
= apparent viscosity, Ib./ft.-sec. D = internal diameter of pipe, ft. C = moisture-free consistency, per cent U = average linear velocity, ft./sec. The use of the nomograph, which enables convenient solution of the equation, is illustrated as follows: What is the apparent viscosity of sulfite stock under conditions such that IL linear velocity of 4.5feet per second is attained in a standard 10-inch pipe when the consistency is 3.1 per cent? Following
where p
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