Fluid Mechanics

In the figure shown a light container is kept in a horizontal rough surface of coefficient of friction μ= 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.

2 Answers

262
Aditya Bhutra ·

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

ρgh = 12ρv2

v2=2gh

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

now dmdt = ρ.dVdt = ρvs

thus Net Force acting on cylinder = ρsv2 -f

now f = μ.N = shV*ρVg = ρsgh

Fnet = 2ρsgh - ρsgh = ρsgh

accn = ρsghρV= sghV= μg

21
Anirban Mukherjee ·

its clear now... thanks.

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