AP in this situation is known to be \frac{\Delta P}{\rho \bar{V}^{2}}=\bar{f}\left(\frac{1}{R e}, \frac{L}{D}\right) If a new prototype pipe is to be designed based on experimental data from a 1:5 model tested in a water tank, then the model and prototype situations will be dynamically similar provided that the Reynolds numbers of the corresponding flow fields over the objects are the same.
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