Question

An ideal fluid flows through a pipe of circular cross-section made of two sections with diameters $2.5\, cm$ and $3.75\, cm$. The ratio of the velocities in the two pipes is

• A. $9 : 4$
• B. $3 : 2$
• C. $\sqrt{3} : \sqrt{2}$
• D. $\sqrt{2} : \sqrt{3}$

Answer 1

Answer: (A)

As,
$A_{1}v_{1}=A_{2}v_{2}$
$\Rightarrow \frac{v_{1}}{v_{2}}=\frac{A_{2}}{A_{1}}=\frac{\left(\pi D^{2}_{2}/4\right)}{\left(\pi D^{2}_{1}/4\right)}$
$=\left(\frac{D_{2}}{D_{1}}\right)^{2}$
or $\frac{v_{1}}{v_{2}}=\left(\frac{3.75\,cm}{2.5\,cm}\right)^{2}$
$=2.25=9:4$