A liquid of density \(600kg/{m}^{3}\) flowing steadily in a tube of varying cross-section. The cross-section at a point …

Given:

\({A}_{1}=1.0c{m}^{2},{A}_{2}=20m{m}^{2}=0.2c{m}^{2}\)

Using continuity equation:

\({A}_{1}{v}_{1}={A}_{2}{v}_{2}\)

\(1\times 10=0.2\times {v}_{2}\Rightarrow {v}_{2}=50cm/s\)

Using Bernoulli’s theorem at the same horizontal level:

\({P}_{1}+\frac{1}{2}\rho {v}_{1}^{2}={P}_{2}+\frac{1}{2}\rho {v}_{2}^{2}\)

\({P}_{1}-{P}_{2}=\frac{1}{2}\rho \left({v}_{2}^{2}-{v}_{1}^{2}\right)\)

Convert to SI:

\({v}_{1}=0.1m/s,{v}_{2}=0.5m/s\)

\({P}_{1}-{P}_{2}=\frac{1}{2}(600)\left(0.{5}^{2}-0.{1}^{2}\right)=72Pa\)