Question

Water is flowing continuously from a tap having an internal diameter 8 x 10${}^{-3}$ m. The water velocity as it leaves the tap is 0.4 m s${}^{-1}$. The diameter of the water stream at a distance 2 x 10${}^{-1}$ m below the tap is close to

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

Answer 1

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

Given data,

$d_1=8\times {10}^{-3}m$

$v_1=0.4m{s}^{-1}$

$h=0.2m$

According to equation of motion,

$v_2=\sqrt{v{}_1^2+2gh}$

$=\sqrt{(0.4{)}^2+2\times 10\times 0.2}$

$\approx 2m{s}^{-1}$

$\therefore$ According to equation of continuity

$a_1{v}_1=a_2{v}_2$

$\pi \times {\left(\frac{8\times {10}^{-3}}{2}\right)}^2\times 0.4=\pi \times {\left(\frac{d_2}{2}\right)}^2\times 2$

$d_2=3.6\times {10}^{-3}m$