An opentopped tank with diameter D is filled with a liquid w

An open-topped tank with diameter D is filled with a liquid with density rho and viscosity mu to a height h. Under the influence of gravity g, the tank is drained through a hole with diameter d. Using dimensional analysis, find the time t it takes to empty the tank.

Solution

t =time

d = dia o fhole

D dia of tank

h initial ht

rho density

mu viscosity

D dia

g gravitational const

let t = fn( d,v,h,rho,mu,D,g)

get groups ( rho V³)(/mu g)

(t mu)/(rho d²⁾

Vo/d³    , ho/d D/d

t mu/(rho d² ) = fn( length1/length2, --, )