6.39 The motion of a liquid in an open tank is that of a combined vortex consisting of a forced vortex for 0 2 ft. The velocity profile and the corresponding shape of the free surface are shown in Fig. P6.39. The free surface at the center of the tank is a depth h below the free surface at r = ∞. Determine the value of h. Note that h = and hfree are the corresponding depths for the forced vortex and the free vortex, respectively. (See Section 2.12.2 for further discussion of the forced vortex.) hforced + hfree, where hforced 10 Vg, ft/s r, ft r, ft Figure P6.39

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Hydronics