Question

Water from a tap emerges vertically down with an initial speed of $1.0m{s}^{-1}$. The cross sectional area of tap is $10c{m}^2$. Assume that the pressure is constant through out the stream of water,and that the flow is steady, the cross sectional area of the steam $0.15m$ below the tap is

• A. $5\times {10}^{-4}{m}^2$
• B. $5\times {10}^{-5}{m}^2$
• C. $5.0\times {10}^{-5}{m}^2$
• D. $50\times {10}^{-4}{m}^2$

Answer 1

Answer: (A), (C)

The correct options are
A $5\times {10}^{-4}{m}^2$
C $5.0\times {10}^{-5}{m}^2$

Given initial velocity $u=1m{s}^{-1}$
Area $A=10c{m}^2=10\times {10}^{-4}{m}^2$
Velocity at height 0.15 m below the tap is: $v^2=u^2+2gh$
$=(1{)}^2+2\times 10\times 0.1s$
$=4$
$\Rightarrow v=2m{s}^{-1}$

We know that by continuity Theoram $A_1{v}_1=A_2{v}_2$
$1\times 10\times {10}^{-4}=A^2\times 2$
$5\times {10}^{-4}=A^2$