Water is flowing continuously from a tap having an internal diameter 8 × 10^{-3}, m . water velocit

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9-1.Fluid Mechanics

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Water is flowing continuously from a tap having an internal diameter $8 \times 10^{-3}\, m$. The water velocity as it leaves the tap is $0.04\, ms^{-1}$. The diameter of the water stream at a distance $8 \times 10^{-1}\, m$ below the tap is close to

A

$9.6 \times {10^{ - 3}}\,m$

B

$3.6 \times {10^{ - 3}}\,m$

C

$0.8 \times {10^{ - 3}}\,m$

D

$6.4 \times {10^{ - 3}}\,m$

Solution

$\mathrm{V}_{2}^{2}=\mathrm{V}_{1}^{2}+2 \mathrm{gh}$

$\mathrm{V}_{2}^{2}=(0.04)^{2}+2 \times 10 \times 8 \times 10^{-1}$

${{\rm{V}}_2} \simeq 4{\mkern 1mu} {\rm{m}}/{\rm{s}}\quad {\rm{D}}_1^2{{\rm{V}}_1} = {\rm{D}}_2^2{{\rm{V}}_2}$

$\left(8 \times 10^{-3}\right)^{2} \times 0.04=\mathrm{D}_{2}^{2} \times 4 $

$\Rightarrow \mathrm{D}_{2}=0.8 \times 10^{-3} \mathrm{\,m}$

Standard 11

Physics

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