A horizontal pipe line carries water in a streamline flow. At a point along the pipe where the cross-sectional area is `10cm^(2)` the velocity of water is 1 `ms^(-1)` and pressure is 2000 Pa. What is the pressure at another point. Where the cross-sectional area is `5cm^(2)`?

Explanation

According to the equation of continuity,
`a_(1)v_(1)=a_(2)v_(2)`
`a_(1)=10cm^(2)" "v_(1)=1ms^(-1)`
`a_(2)=5cm^(2)`
`therefore10xx1=5xxv_(2)`
`thereforev_(2)=2ms^(-1)`
According to Bernoulli's theorem,
`P_(2)+(1)/(2)rhov_(2)^(2)=P_(1)+(1)/(2)rhov_(1)^(2)`
`P_(2)+(1)/(2)xx10^(3)xx(2)^(2)=2000+(1)/(2)xx10^(3)xx(1)^(2)`
`P_(2)=2000+500-2000`
Pressure `P_(2)=500` Pa