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pressure drop with laminar flow (Rev < 100) of liquids across banks of

plain tubes with pitch ratios P/Dt of 1.25 and 1.50:

∆p =  1.6  m

 (6-164)

m = (6-165)

where Rev = DvVmaxρ/µb; Dv = volumetric hydraulic diameter [(4 ×

free-bundle volume)/(exposed surface area of tubes)]; P = pitch (= a

for in-line arrangements, = a or c [whichever is smaller] for staggered



0.57

(Rev)

0.25

ρV2



max

2

µs µb

Dt P 

280Nr

Rev

arrangements), and other quantities are as defined following Eq.

(6-163). Bergelin, et al. (ibid.) show that pressure drop per row is

independent of the number of rows in the bank with laminar flow. The

pressure drop is predicted within about 25 percent.

6-38 FLUID AND PARTICLE DYNAMICS

FIG. 6-43 Friction factors for in-line tube banks. (From Grimison, Trans. ASME, 59, 583 [1937].)

FIG. 6-44 Friction factors vs. transverse spacing for single row of tubes. (From

Boucher and Lapple, Chem. Eng. Prog., 44, 117 [1948].)

FIG. 6-45 Friction factors for transition region flow across tube banks. (Pitch

is the minimum center-to-center tube spacing.) (From Bergelin, Brown, and

Doberstein, Trans. ASME, 74, 953 [1952].)