Question

Water flows through a horizontal pipe of varying cross-section at the rate of 1/2 litre/second. Determine the velocity of flow of water at a point where diameter is 4 cm.

Answer 1

Dear student
$$\begin{gathered} Rateofflow=velocity\times areaofcrosssection \\ 1litre={10}^{-3}{m}^3 \\ diameter=4cm \\ radius=2cm=.02m \\ AreaofcrosssectionA=\pi \times 4\times {10}^{-4}{m}^2 \\ rateofflow=\frac{1}{2}litre/sec=\frac{{10}^{-3}}{2}{m}^3/sec \\ \frac{{10}^{-3}}{2}{m}^3/sec=velocity\times \pi \times 4\times {10}^{-4}{m}^2 \\ velocity=\frac{.5\times {10}^{-3}}{\pi \times 4\times {10}^{-4}}=\frac{10\times .5}{4\times \pi }=\frac{5}{4\times \pi }=\frac{1.25}{\pi }=.398m/sec \\ Regards \end{gathered}$$