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 tube. 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. ` sqrt(2 ((P+ rho gh ))/(rho _a )) `
B. ` (Phrho g ) /(sqrt(rho_a)) `
C. ` (Psqrt(rho gh))/(sqrt(rho _a)) `
D. `(P)/(rho gh sqrt (rho_a)) `

Answer

A

Explanation

Using Bernoulli’s theorem
` P_ 0 + P + 0 + 0 = P_1 + (1)/(2) rho _a v ^ 2 + 0 `
` P_1 = P_0 - rho gh ` (if liquid rises to BC )
`P _0 + P=P _ 0 - rho gh + (1)/(2) rho_a v ^ 2 `
` sqrt(2 ((P + rho gh ))/(rho _a))= v `