Example No 2 -  (7 Height of liquid at any time 2...

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Example No 2: Liquid Level in a leaking tank Figure 1. Leaking tank A tank as shown in Figure 1 is leaking. The instantaneous velocity for liquid leaking out of the tank is given by the following equation L o gh P 2 C u (1) Develop a model that will predict the variation in the liquid level and mass flow rate with time. Solution: for a tank with a constant cross section, A T , the total mass of liquid above the leak and the instantaneous mass flow rate are given by L T h A m (2) L o h h m gh P 2 C A A u Q (3)
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The rate of mass changes in the tank m Q dt dm (4) Substitution of (2) and (3) into (4) L T H o L gh P 2 A A C dt dh (5) Intergrating from an initial height 0 L h to L h t 0 T h o h h L L dt A A C gh P 2 dh L 0 L (6) t A A C gh P 2 g 1 gh P 2 g 1 T h o 0 L L
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Unformatted text preview:    (7) Height of liquid at any time 2 T h o L T h o L L t A A C 2 g t gh P 2 A A C h h                                     (8) the mass flow rate at a given time after the leak is obtained by substituting equation (8) into equation (3) t A A gC gh P 2 C A Q T 2 h 2 L o h m                        (8) the time to empty the vessel is obtained by solving equation (8) and setting h L equal to zeor                                P 2 gh P 2 A A g C 1 t L h T o e (9)...
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Example No 2 -  (7 Height of liquid at any time 2...

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