Question

A water pipe 4 cm in diameter has a constriction if diameter 2 cm. Find the rate of discharge of water through the pipe of the velocity of flow of water in the main pipe is 6 cm/s. Find also the velocity of flow at the constriction. $(75.36\times {10}^{-6}{m}^3/s;24cm/s)$

Answer 1

Rate of discharge $=Q=A_{pipe}\times V_{pipe}$
$=\pi (0.02{)}^2\times 6=0.0075$
from continuity eq
$A_{pipe}\times V_{pipe}=A_{constrictor}\times V_{constrictor}$
$V_{constrictor}=\frac{0.03}{A_{cons}}=\frac{0.0075}{\pi (0.01{)}^2}=24$