6.52 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. P6.52. The free surface at the cen- ter of the tank is a depth h below the free surface at r = o. Deter- mine the value of h. Note that h = hforced + hfirce where horced and hfiee are the corresponding depths for the forced vortex and the free vortex, respectively. (See Section 2.12.2 for further discussion regarding the forced vortex.) 10 Ve, ft/s r, ft 2 2 r, ft h IFIGURE P6.52

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Hydronics