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  3. l a tank shown in figure 2 is being supplied...

Question: l a tank shown in figure 2 is being supplied...

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l. A tank shown in Figure 2 is being supplied liquid water F in m/s of from a tap at a initial steady state temperature T of 40°C. The water is leaving the tank at a volumetric flow rate of Fo through an exit valve at a steady state temperature. The cylindrical tank has a diameter D of 5 m and steady state tank height H of 4 m. The coefficient K is 2. Assume the change in the properties of water is negligible due to temperature. Assume the fl rates are at steady state for the system with no accumulation of mass in tank. Assume also the tank is insulated. The dynamics of the temperature of the liquid T in the well mixed tank change with respect to the inlet flow temperature. ow (a) State all assumptions then derive and simplify mass balance. (b) State all assumptions then derive and simplify thermal energy balance. (c) Find the transfer function Gfs) where the temperature of the tank can be the output and the inlet flow temperature can be the input. (d) If Tit) step changed from 40°C to 50°C, how to represent Tlt) in time domain? Hint: equation includes step function term (e) If T/e) step changed from 40°C to 50°C, what is the time domain equation for T(t)? (f) What is the initial value of T(t)? (8) What is the final value or steady state temperature of Tt? Figure 2. Simplified diagram of a tank system being cooled by a cooling jacket (not shown).
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