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

• A. $3.6 \times 10^{-3} m$
• B. $5.0 \times 10^{-3} m$
• C. $7.5 \times 10^{-3} m$
• D. $9.6 \times 10^{-3} m$

Answer 1

Answer: (A)

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

Answer 2

$a_{1} v_{1}=a_{2} v_{2}$ $v_{2}^{2}=v_{1}^{2}+2 g h$ $v_{2}^{2}=(0.4)^{2}+2 \times 10 \times 0.2$ $=(0.4)^{2}+4$ $v_{2}^{2}=4.16$ $v_{2}=\sqrt{4.16}$ $v_{2}=2.04 m / s$ Also, $a_{1} V_{1}=a_{2} V_{2}$ $d_{1}^{2} V_{1}=d_{2}^{2} V_{2}$ $d_{2}=d_{1} \sqrt{\frac{V_{1}}{V_{2}}}$ $=8 \times 10^{-3} \sqrt{\frac{0.4}{2.04}}$ $=3.54 \times 10^{-3} m$