Process Equipment and Plant Design
In actual operation of distillation column, the vapour is not distributed uniformly among the bubble caps, primarily because of the

Liquid gradient on the tray
Small downcomer liquid seal
Lower skirt clearance
Lower static submergence

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Process Equipment and Plant Design
In the case of a shell and tube heat exchanger, the logarithmic mean temperature difference

May be either more or less than geometric mean and arithmetic mean value depending upon whether the flow of stream is co-current or counter-current
Is always less than arithmetic mean value, but more than geometric mean value
Is always more than arithmetic mean value and the geometric mean value
Is always less than arithmetic average value

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