'Water enters a cylindrical tank nf crnsssectinnal area A at a cnnstant rate [ynlnme per unit time). The tank has a small hnle nf area a in the hnttnm, and sn water nws nnt thrnngh the hnle. Let Mt] he the depth cf the water in the tank at time t. A yersinn nf Eernnnlli's Principle in hydrnlngy says that the square cf the rate nf nw nnt cf the tank is prnpnrtinnal tn h. [a] Develnp a differential equatinn far It. GlVE aphysical interpretatinn nf all mndel parameters ynn intrnclnce. Hint: Develnp a differential eqnatinn fnr V rst, where V = Vft) is the ynlnme nf water in the tank at time t, in terms nf h, then think ahnnt the rel atinnship between V and h {yen can assume that the tank is standing upright}. {In} Find the steady state If\". lGiye a physical interpretatinn cf the steady state, and discuss the dependence nf h.\" an the mndel parameters dn the relatinnships make sense? {c} Determine the stability cf the steady state