Flow between two tanks (Fig. 7B.4). Case I: A fluid flows between two tanks A and B because PA > PB. The tanks are at the same elevation and there is no pump in the line. The connecting line has a cross-sectional area Si and the mass rate of flow is w for a pressure drop of (p_A – p_B)_t. Case II: It is desired to replace the connecting line by two lines, each with cross section Sn = ½ S₁. What pressure difference (p_A – p_B)_II is needed to give the same total mass flow rate as in Case I? Assume turbulent flow and use the Blasius formula (Eq. 6.2-12) for the friction factor. Neglect entrance and exit losses.

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Circular tube of cross section S, Circular tubes of cross section S B B Mass flow rate w Sum of mass flow rates is w