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  • A liquid flows through a pipe of varying diameter. The velocity of the liquid is <img alt="2 \mathrm{~ms}^{-1}" src="https://entrancecorner.oncodecogs.com/gif.latex?2%20%5Cmathrm%7B%7Ems%7D%5E%7B-1

A liquid flows through a pipe of varying diameter. The velocity of the liquid is 2 \mathrm{~ms}^{-1} at a point where the diameter is 6 \mathrm{~cm}.The velocity of the liquid at a point where the diameter is 3 \mathrm{~cm} will be

Option: 1

\mathrm{1 \mathrm{~ms}^{-1}}


Option: 2

\mathrm{4 \mathrm{~ms}^{-1}}


Option: 3

\mathrm{8 \mathrm{~ms}^{-1}}


Option: 4

\mathrm{16 \mathrm{~ms}^{-1}}


Answers (1)

best_answer

From the equation of continuity of flow, the velocities \mathrm{v_1 \, \, and\, \, v_2} of the liquid at points where the areas of cross-section of the pipe are \mathrm{a_1 \, \, and\, \, a_2} respectively are related as
                    

                                     \mathrm{ \begin{aligned} & a_1 v_1=a_2 v_2 \\ & \therefore \quad v_2=\frac{a_1 v_1}{a_2}=\frac{\pi r_1^2 v_1}{\pi r_2^2} \\ &=v_1\left(\frac{r_1}{r_2}\right)^2 \\ &=2 \times\left(\frac{6}{3}\right)^2=8 \mathrm{~ms}^{-1} \end{aligned} }

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