Question

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 $0.4m{s}^{-1}$. The diameter of the water stream at a distance $2\times {10}^{-1}m$ below the tap is close to

• A. $5\times {10}^{-3}m$
• B. $7.5\times {10}^{-3}m$
• C. $9.6\times {10}^{-3}m$
• D. $3.6\times {10}^{-3}m$

Answer 1

The correct option is D $3.6\times {10}^{-3}m$

$Diameter=8\times {10}^{-3}m{v}_1=0.4m/s{v}_2=\sqrt{v_1^2+2gh}=\sqrt{(0.4{)}^2+2\times 10\times 0.2}=2m/s{A}_1{v}_1=A_2{v}_2\pi {\left(\frac{8\times {10}^{-3}}{2}\right)}^2\times 0.4=\pi \times \frac{d^2}{4}\times 2\Rightarrow d\approx 3.6\times {10}^{-3}m$.