The cylindrical 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 `1.5mmin^(-1)` , what is the speed of ejection of the liquid through the holes ?

Explanation

Cross section area of pipe `A_(1)=8xx10^(-4)m^(2)`
and speed `v_(1)=(1.5)/(60)ms^(-1)=0.025ms^(-1)`
Area of holes at the end of other tube =40
`therefore` Area of cross section at other end ,
`A_(2)=40a`
`=40pixx25xx10^(-8)m^(2)` and the speed of liquid at other end `v_(2)`=? From equation of continuity ,
`A_(1)v_(1)=A_(2)v_(2)`
`8xx10^(-4)xx0.025=40xx3.14xx25xx10^(-8)xxv_(2)`
`thereforev_(2)=(8xx10^(-4)xx0.025)/(40xx3.14xx25xx10^(-8))`
`=0.00006369xx10^(-8)``=0.00006369xx10^(-4)`
`thereforev_(2)=0.64ms^(-1)`