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The figure shows a model of perfume at...

The figure shows a model of perfume atomizer . When the bulb A is compressed , air `("density "rho_(a))` flows through the vertical tube and emerges through the end . If excess pressure applied to the bulb ins progress be ` Delta p `then the minimu speed of air in the tube to lift perfume is :

A

` sqrt((2 [ Delta p +o gh ])/(rho_(a)))`

B

` sqrt((2[ Delta p - rhogh ])/(rho_(a)))`

C

` sqrt((Delta rho + rho gh)/(rho_(a)))`

D

None of these

Text Solution

Verified by Experts

Applying Bernoull.s principle at 1 and 2 , we obtain
`P_(1) +1/2 rho_(a)v_(1)^(2) = P_(2) + 1/2 rho_(a) v_(2)^(2)`
Putting ` v_(1) = 0 ` since of the air is at rest inside the bulb ,
`P_(1) = P_(10) + DeltaP_(r) P_(2) = P_(0) - rho gh ` whre `rho = ` density of liquid ( perfume)
` rho_(a)` density of air
`v_(a)` = minimum velocity of air to lift the liquid through the height h = v (say)
` P_(0)` = atmospheric pressure
Hence ( A) is correct
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