In the calculation of Reynold’s Number for the Friction factor of the annulus tube, which is the correct formula for equivalent diameter De?

In the calculation of Reynold’s Number for the Friction factor of the annulus tube, which is the correct formula for equivalent diameter De? Correct Answer \(\frac{4×(D_{oi}^2 – D_{io}^2)×\frac{π}{4}}{π(D_{io}+D_{oi})}\)

While friction factor is calculated for the annulus pipe, the wall friction is provided by both the sides of the tube. Hence when we are calculating the Hydraulic diameter for the annulus, we consider the complete wetted perimeter, that is, P = π(Dio + Doi).
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