Question

Water is flowing continuously from a tap having an interal 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 $2\times {10}^{-3}m$ 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

Answer: (C)

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

Interal diameter $\left(2r_1\right)=8\times {10}^{-3}m$

$r_1=4\times {10}^{-3}m$

$V_1=0.4{ms}^{-1}$

velocity below $2\times {10}^{-3}m$

$V^2=u^2+2as$

$V_2^2=v_1^2+2gs$

$V_2^2=(0.4{)}^2+(2\times 10\times 2\times {10}^{-3})$

$V_2=0.45{ms}^{-1}$

Now

$A_1{V}_1=A_2{V}_2$

$0.4\times (\pi \times 4\times {10}^{-3}\times 4\times {10}^{-3})=0.45\times (\pi \times r^2)$

$r_2=4.8\times {10}^{-3}m$

Thus diameter $=9.6\times {10}^{-3}m$