Fluid Mechanics

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In the figure shown a light container is kept in a horizontal rough surface of coefficient of friction Î¼= sh/v .A very small hole of area s is made at a depth h.Water of volume v is filled in the container.The friction is not sufficient to keep the container at rest.Find the initial acceleration of the container.

#Physics #Mechanics

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2 Answers

262

Aditya Bhutra ·2012-07-09 02:01:38

let v= efflux vel. ; f=frictional force
using bernoulli's theorem ,
considering area of base of cyliner >> area of hole ,

Ïgh = 12Ïv²

v²=2gh

now force acting on cylinder due to liquid , F = dpdt = dmdt.v

now dmdt = Ï.dVdt = Ïvs

thus Net Force acting on cylinder = Ïsv² -f

now f = Î¼.N = shV*ÏVg = Ïsgh

F_net = 2Ïsgh - Ïsgh = Ïsgh

accn = ÏsghÏV= sghV= Î¼g

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Anirban Mukherjee ·2012-07-15 13:14:00

its clear now... thanks.

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