Figure shows a crude type of atomizer. is compressed, air flows swiftly through tube `BC` causing a reduced pressure in the particles of the vertical to Liquid rises in the tube, enters `BC` and is sprayed out. if the pressure in the bulb is `P_(a) + P`, where `P` is the gauge pressure and `P_(a)` is the atmospheric pressure, `v` is the speed of air in `BC`, find how large would `v` need to be to cause the liquid to rise to `BC`. Density of air `= 1.3 kg//m^(3)`.

Options

A. `(P+rhogh)/(sqrt(0.65))`
B. `(Phrhog)/(sqrt(0.650))`
C. `(Psqrt(hrhog))/0.65`
D. `P/(hrhogsqrt(0.65))`

Answer

A

Explanation

Absolute pressure in bulb`=`Gauge pressure `+`Atmosphere pressure `=P+P_(a)`
Using Bernoulli's equation
`P_(a)+P=P_(BC)+(rho_(a)v^(2))/2`
Where `rho_(a)` is the density of air
`:. P_(BC)=P_(a)+P=(1.3/2)v^(2)`
`P_(BC)=P_(a)-rhogh`
So equating these two values of `P_(BC)`, we get
`V=(P+rhogh) /sqrt(0.65)`