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Water is flowing through a tube of radius r with a speed v. If this tube is joined to another tube of radius \mathrm{r / 2}, what is the speed of water in the second tube?

Option: 1

\mathrm{\frac{v}{4}}


Option: 2

\mathrm{\frac{v}{2}}


Option: 3

\mathrm{2 v}


Option: 4

\mathrm{4 v}


Answers (1)

best_answer

From the equation of continuity of flow, we have

\mathrm{ \begin{array}{rlrl} a_1 v_1 & =a_2 v_2 \\\\ \text { or } & \pi r_1^2 v_1 =\pi r_2^2 v_2 \\\\ \text { or } \quad \frac{v_2}{v_1} & =\frac{r_1^2}{r_2^2}=\frac{r^2}{(r / 2)^2}=4 \\\\ \text { or } \quad v_2 & =4 v_1=4 v . \end{array} }

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