The cylinderical tube of a spray pump has a cross-section of `8.0cm^(2)` one end of which has 40 fine holes each of diameter 1.0mm. If the liquid flow inside the tube is 1.5 m per minute, what is the speed of ejection of the liquid through the holes?

Explanation

Here, `a_(1)=8cm^(2)=8 xx 10^(-4) m^(2)`
`v_(1)=1.5" m min"^(-1) =(1.5)/(60) ms^(-1)`
r=radius of hole `=1/ mm =0.5 mm =0.5 xx 10^(-3)m`
Area of cross section of 40 holes `=40 xx pir^(2)`
`=40 xx 3.14 xx (0.5 xx 10^(-3))^(2)`
`a_(2)=31.4 xx 10^(-6) m^(2)`
`a_(2)=31.4 xx 10^(-6) m^(2)`
`v_(2)=?`
As `a_(1)v_(1)=a_(2)v_(2) ("equation of continuity")`
`8 xx 10^(-4) xx (1.5)/(60) =31.4 xx 10^(-6) xx v_(2)`
`v_(2)=0.637 ms^(-1)`