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## Homework Statement

An open-topped vertical tube of diameter D is filled with water up to a height h.The narrow bottom-end of the tube ,of diameter d, is closed by stop .

when the stop is removed ,the water starts flowing out through the bottom orifice with approximate speed v=√(2gh). However ,this speed is reached by the liquid only after a certain time t.obtain an estimate of the order of magnitude of t.Ignore viscous effects.

## Homework Equations

equation of continuity(mass conservation), A.v=constant

bernoulli's equation, P+0.5ρv

^{2}+ρgh =constant

the total energy,potential +kinetic ,of water is conserved.

## The Attempt at a Solution

i assumed that i) water level falls with "constant" acceleration a.

then in a small time dt, i found the mass of water that came out of the hole,and decrease in water level.this gives me the loss of potential energy.i know velocity at the end of that small interval,i used it to find kinetic energy.using energy conservation ,i got a=g.

i don't know how to proceed now. also i am not sure about my first assumption.and once the liquid starts falling out at v=√(2gh),will this acceleration magically disappear? does the fact that a=g,implies normal force from the bottom surface is 0 during the acceleration period?