A liquid of density `rho` has to spray with help of aspirator pump at height H from liquid level as shown in figure. If gauge pressure inside bulb is P and density of air is `sigma` then velocity of air in tube AB is

Options

A. `{(P +rhogH)/((sigma)/(2))}^((1)/(2))`
B. `{(P -rhogH)/((sigma)/(2))}^((1)/(2))`
C. `{(P +alphagH)/((sigma)/(2))}^((1)/(2))`
D. `{(P +alphagH)/(sigma)}^((1)/(2))`

Answer

A

Explanation

`P_(B)+(1)/(2)sigmaV^(2)=P_(A)+P`

`P_(B)=(P)/(A)+P-(1)/(2)sigma V^(2)`
`=(P)/(A)-rhogH`
`V=sqrt(2(P+rhogH)/(sigma)`