A wide tank of cross-sectional area A containing a liquid to a heightH , has a small orifice at its base of area a (a<1) :
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a
t=(Aa)[1g(H−Hη)]
b
t=(aA)[2g(H−Hη)]
c
t=(aA)[1g(H−Hη)]
d
t=(Aa)2g(H−Hη)
answer is D.
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Detailed Solution
Let h be the instantaneous height of the liquid in a tank. Then, the instantaneous velocity of flow through the hole is,v=2ghUsing equation of continuity,A(−dhdt)=av=a2ghor, −∫+HH/ηdhh=aA2g∫0tdt∴ t=(Aa)2g(H−Hη)