Process Equipment and Plant Design
In a shell and tube heat exchanger having square pitch, the shell side equivalent diameter is given by (where, P = pitch, d = outside diameter of the tube)

Πd/4P²
4P²/πd
4(P² - πd²/4)/πd
(P² - πd²/4)/πd

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Process Equipment and Plant Design
In a double pipe (concentric) heat exchanger, the hydraulic radius for heat transfer (for a fluid flowing through the annulus) would be

Same as that for fluid flow
Less than that for fluid flow
D₂ - D₁ (D₁ and D₂ are I.D. of inner and outer pipes respectively)
More than that for fluid flow

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