An ideal fluid flows (laminar flow) through a pipe of nonuniform diameter.
Question:

An ideal fluid flows (laminar flow) through a pipe of nonuniform diameter. The maximum and minimum diameters of the pipes are $6.4 \mathrm{~cm}$ and $4.8 \mathrm{~cm}$, respectively. The ratio of the minimum and the maximum velocities of fluid in this pipe is:

  1. (1) $\frac{9}{16}$

  2. (2) $\frac{\sqrt{3}}{2}$

  3. (3) $\frac{3}{4}$

  4. (4) $\frac{81}{256}$


Correct Option: 1

Solution:

(1) From the equation of continuity

$A_{1} v_{1}=A_{2} v_{2}$

Here, $v_{1}$ and $v_{2}$ are the velocities at two ends of pipe. $\mathrm{A}_{1}$ and $\mathrm{A}_{2}$ are the area of pipe at two ends

$\Rightarrow \quad \frac{v_{1}}{v_{2}}=\frac{A_{2}}{A_{1}}=\frac{\pi(4.8)^{2}}{\pi(6.4)^{2}}=\frac{9}{16}$

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