Question

A cylinder tank of base area A has a small hole of areal a at the bottom. At time t=0, a tap starts to supply water into the tank at a constant rate alpha m^(3)//s. (a) What is the maximum level of water h_(max)in the tank? (b) find the time when level of water becomes h(lt h_(max)).

Answer 1

Hence the value of time "t" is t = A / ag [ α / a In { α − a √ 2gh / α} − √ 2gh]

Explanation:

Level will be maximum when

Rate of inflow of water = rate of outflow of water

i.e. α=av

or,α=a √ 2ghmax

⇒h(max) = α^2 / 2ga^2

(b) Let at time t, the level of water be h. then,

A(dh / dt)  = α − a √ 2gh

or ∫h - 0 dh / α − a2√ gh  = ∫t - 0 dt / A

Solving this, we get

t = A / ag [ α / a In { α − a √ 2gh / α} − √ 2gh]

Hence the value of time "t" is t = A / ag [ α / a In { α − a √ 2gh / α} − √ 2gh]