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

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
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 average value

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Process Equipment and Plant Design
For turbulent flow (NRe > 2100) of low viscosity fluid (μ > 20cp) in steel pipes, the optimum inside pipe diameter is given by(where, Q = fluid flow rate, ft³/sec.ρ = fluid density, lb/ft³ μ = fluid viscosity, centipoise Di = optimum inside pipe diameter, inches)

Di, opt = 4.7 Q0.36 . μ3.2ρ0.13
Di, opt = 3.9 Q0.45 . μ0.95
Di, opt = 3 Q0.36 . μ0.88
Di, opt = 3.9 Q0.45 ρ0.13

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