Water is flowing through a horizontal tube of non-uniform cross-section. At a place, the radius of the tube is `1.0cm` and the velocity of water is `2m//s`. What will be the velocity of water where the radius of the pipe is `2.0 cm`?

Explanation

Using equation of continuity,
`A_(1)upsilon_(1)=A_(2)upsilon_(2) " or ", upsilon_(2)=(A_(1)/(A_(2))) upsilon_(1)`
or, `upsilon_(2)=((pir_(1)^(2))/(pi r_(2)^(2))) upislon_(1)=((r_(1))/(r_(2)))^(2)upislon_(1)`
Given, `r_(1)=1 cm =1xx10^(-2)m, r_(2)=2cm = 2xx10^(-2) m`
`upsilon_(1)=2ms^(-1)`
Substituting the above values, we get
`upsilon_(2)=((1.0xx10^(-2))/(2.0xx10^(-2)))^(2) (2) " or " upsilon_(2)=0.5 ms^(-1)`