Product From Upstream Process Storage Tank Feed to Downstream Process F Q Pump Figure 5.11. The storage tank with an outlet pump. 5.7 A storage tank of the type shown in Figure 5.11 in the main text is subject to periodic loading from the upstream process. Because a steady rate of product withdrawal is maintained by the constant speed pump at the tank outlet, this is a true "pure capacity" process. The tank's cross-sectional area is given as 2.5 ft, and that the incoming feedstream fluctuates around its nominal flowrate in essentially sinusoidal fashion with maximum deviation of 10 ft/hr; the frequency of the sinusoidal 172 PROCESS DYNAMICS fluctuation is different from shift to shift, but it may be considered constant on any particular shift. (a) Derive from first principles the expression for the response of the tank level (as a deviation from nominal operating conditions) assuming that the input is a perfect sinusoid with the given amplitude but a yet unspecified frequency . For a given frequency of 0.2 radians/hr, plot on the same graph, both the periodic input loading function and the tank level response. Compare these two functions. (b) In terms of the frequency of the periodic loading, what is the maximum deviation from nominal tank level that will be observed? (c) Given now that the tank is 10 ft high and that the nominal operating level is 5 ft, what condition must the loading frequency satisfy to guarantee that during any particular shift, the tank neither overflows nor runs dry