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**Hint:**Calculate the maximum and minimum area of the pipe using given diameters. The velocity of the flow is maximum when the area of cross-section is minimum. Use the continuity equation for the flow of fluid through a pipe.

**Complete step by step answer:**

Equation of continuity.

\[{A_{\max }}{v_{\min }} = {A_{\min }}{v_{\max }}\]

Here, \[{v_{\min }}\] is the minimum velocity and \[{v_{\max }}\] is the maximum velocity.

Complete step by step answer:

We know that the circular cross-section of pipe of radius r has area, \[A = \pi {r^2}\]. Therefore, the maximum area of the pipe is,

\[{A_{\max }} = \pi r_{\max }^2\]

\[ \Rightarrow {A_{\max }} = \pi {\left( {\dfrac{{{d_{\max }}}}{2}} \right)^2}\]

\[ \Rightarrow {A_{\max }} = \dfrac{{\pi d_{\max }^2}}{4}\] …… (1)

Also, the minimum area of the pipe is,

\[{A_{\min }} = \dfrac{{\pi d_{\min }^2}}{4}\] …… (2)

According to equation of continuity in the laminar flow, we have,

\[{A_{\max }}{v_{\min }} = {A_{\min }}{v_{\max }}\]

Here, \[{v_{\min }}\] is the minimum velocity and \[{v_{\max }}\] is the maximum velocity.

The above equation implies that the velocity of the flow is maximum through the minimum area of cross-section of the pipe.

We rearrange the above equation as follows,

\[\dfrac{{{v_{\min }}}}{{{v_{\max }}}} = \dfrac{{{A_{\min }}}}{{{A_{\max }}}}\]

Use equation (1) and (2) to rewrite the above equation as follows,

\[\dfrac{{{v_{\min }}}}{{{v_{\max }}}} = \dfrac{{\dfrac{{\pi d_{\min }^2}}{4}}}{{\dfrac{{\pi d_{\max }^2}}{4}}}\]

\[ \Rightarrow \dfrac{{{v_{\min }}}}{{{v_{\max }}}} = {\left( {\dfrac{{{d_{\min }}}}{{{d_{\max }}}}} \right)^2}\]

Substitute 4.8 cm for \[{d_{\min }}\] and 6.4cm for \[{d_{\max }}\] in the above equation.

\[\dfrac{{{v_{\min }}}}{{{v_{\max }}}} = {\left( {\dfrac{{4.8\,cm}}{{6.4\,cm}}} \right)^2}\]

\[ \Rightarrow \dfrac{{{v_{\min }}}}{{{v_{\max }}}} = {\left( {0.75} \right)^2}\]

\[ \Rightarrow \dfrac{{{v_{\min }}}}{{{v_{\max }}}} = \dfrac{9}{{16}}\]

**Note:**The equation of continuity can be applied to any flow on the condition the flow should cover the whole area of cross-section through which the liquid is flowing. The equation of continuity can be used to calculate the velocity of the water flowing through the lower opening of the water tank.

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