Question: Also unsure -im assuming that got gi'm using the general gravitational constant of9.81m per second. I know my first step isto separate the variables and
Also unsure -im assuming that got gi'm using the general gravitational constant of9.81m per second. I know my first step isto separate the variables and then integrate but i'm a bit stuck.The initial water level in the tank ish0, and the water level drops continuously afteropened. Accounting for discharge losses via a coefficient dhh2+Cd2g2(d2D2)dt=0h(t)t,DdgCdh(t)h(0)=h0h(t)0, thedraining process is modeled by the separable differential equation:dhh2+Cd2g2(d2D2)dt=0where h(t)is the water height at time t,Dis the diameter of the tank, dis the diameterof the outflow orifice, gis the gravitational constant, and Cdis the discharge coefficient.(a)Solve the differential equation (8) and express the general solution in terms ofh(t).(b)Determine the constant of integration from part (a) using the initial condition h(0)=h0,and hence express h(t) explicitly.
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