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  • A laminar stream is flowing vertically down from a tap of cross-section area . At a

A laminar stream is flowing vertically down from a tap of cross-section area 1 \mathrm{~cm}^2. At a distane 10 \mathrm{~cm} below the tap, the cross-section area of the stream has reduced to 1 / 2 \mathrm{~cm}^2. The volumetric flow rate of water from the tap must be about

Option: 1

2.2 litre/min
 


Option: 2

4.9 litre/min
 


Option: 3

0.5 litre/min
 


Option: 4

7.6 litre/min


Answers (1)

From \mathrm{A_1 V_1=A_2 V_2}
\mathrm{(1) \left(V_1\right)\left(\frac{1}{2}\right) V_2}
\mathrm{ \begin{aligned} & \Rightarrow \frac{V_1}{V_2}=\frac{1}{2} \\\\ & V_2=2 V_1 \end{aligned} }
Now,

\mathrm{ \begin{aligned} & \mathrm{V}_2^2=\mathrm{V}_1^2+2 \mathrm{gh} \\ & 4 \mathrm{~V}_1^2=\mathrm{V}_1^2+2(10)\left(\frac{10}{100}\right) \\ & \mathrm{V}_1=\sqrt{\frac{2}{3}} \end{aligned} }
Now volumetric rate of flow

\mathrm{ \begin{aligned} & =A_1 V_1 \\ & =\frac{1 \times 10^{-4}}{10^{-3}} \times \frac{60 \sqrt{2}}{\sqrt{7}} \\ & =4.9 \text { litre } / \mathrm{min} . \end{aligned} }

Posted by

Sumit Saini

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