Equation Of Continuity

For an incompressible fluid in steady flow, mass is conserved so the same volume passes every cross-section each second, expressed by the equation of continuity $A_1{v}_1=A_2{v}_2$. This means the product of area and speed is constant, so a wider pipe forces the fluid to slow down while a narrower pipe speeds it up. Solving for the speed in the wide section, $v_2=v_1\frac{A_1}{A_2}=3\times \frac{6}{18}=3\times \frac{1}{3}=1\text{m/s}$. The value 3 m/s ignores the change in area. The value 6 m/s wrongly increases the speed where the pipe widens. The value 9 m/s multiplies instead of using the inverse area ratio. This conservation-of-mass relation is exactly the equation of continuity presented in NCERT for fluid dynamics. As a plausibility check, since the cross-section triples, the speed must fall to one-third to keep the volume flow rate constant, and the obtained 1 m/s indeed gives the same flow rate of $1800{\text{cm}}^3/\text{s}$ as the original section.