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. $5.0\times {10}^{-3}m$
• 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

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

From Bernoulli's theorem, $v_2^2=v_1^2+2gh$
From equation of continuity, $A_1{v}_1=A_2{v}_2\Rightarrow \frac{\pi d_1^2}{4}{v}_1=\frac{\pi d_2^2}{4}{v}_2\Rightarrow d_1^2{v}_1=d_2^2{v}_2$
Solving, we get $d_2=\frac{d_1}{{(1+\frac{2gh}{v_1^2})}^{\frac{1}{4}}}=3.6\times {10}^{-3}m$