A horizontal pipeline carries water in a streamline flow. At a point along the pipe, where the cross- sectional area is `10cm^2`, the water velocity is `1ms^-1` and the pressure is 2000 Pa. The pressure of water at another point where the cross-sectional area is `5cm^2`, is........Pa. (Density of water `=10^3kg.m^-3`)

Explanation

Applying the equatiion of continuity at section `1` and section `2`, we get
`A_(1)V_(1)=A_(2)V_(2)`
`implies10xx1=5xxV_(2)`
`impliesV_(2)=2m//s`
`P_(1)=2000P_(a)`

Applying Bernoulli's theorem, we get
`P_(1)+1/2rhoV_(1)^(2)=P_(2)+1/2rhoV_(2)^(2)`
`implies2000+1/2xx1000xx1^(2)=P_(2)+1/2xx1000xx2^(2)`
`impliesP_(2)=500Pa`