A simple surge tank with fixed valve on the outflow Line is illustrated in figure. If the outflow rate is proportional to the square root of the liquid height, an unsteady-state model for the level in the tank is given by as usual, you can assume that the process initially is at steady state

(a) Find the transfer function H?(s)|Q|(s). Put the transfer function in standard gain/time constant form.

(b) Find the transfer function Q?(s)|Q|(s) and put it in standard form,

(c) If the algebraic relation for the outflow rate is linear instead of square root, the level transfer function can be put into a first-order form,

with K* h(qi, ?* = V/q, and V = Ah is the initial steady-state volume. When written this way, ?* is easily interpreted as the liquid residence tune at the nominal operating conditions. What are equivalent expressions for K and ? in the part (a) level transfer function, that is, for the square root outflow relation?

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