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Q.

An ideal fluid flows (laminar flow) through a pipe of non-uniform diameter. The maximum and minimum diameters of the pipes are 6.4cm and 4.8cm respectively. The ratio of minimum to maximum velocities of the fluid in the pipe is $\frac{9}{8 n}$ . Find n

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Detailed Solution

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$\begin{array}{l} a_{1} v_{1} = a_{2} v_{2} \Rightarrow \frac{π}{4} d_{min}^{2} v_{max} = \frac{π}{4} d_{max}^{2} v_{min} \\ \Rightarrow \frac{V_{min}}{V_{max}} = {(\frac{d_{min}}{d_{max}})}^{2} = {(\frac{4 .8}{6 .4})}^{2} = {(\frac{3}{4})}^{2} = \frac{9}{16} = \frac{9}{8 (2)} \end{array}$

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