Water from a tap emerges vertically downwards with an initial speed of 1.0 m s - 1 . The cross - sectional area of the tap is 10 - 4 m 2 . Assume that the pressure is constant throughout the stream of

Question

Water from a tap emerges vertically downwards with an initial speed of $1.0 m s^{- 1}$ . The cross $-$ sectional area of the tap is $10^{- 4} m^{2}$ . Assume that the pressure is constant throughout the stream of water and that the flow is streamlined. The cross $-$ sectional area of the stream, $0.15 m$ below the tap would be:
(Take $g = 10 m s^{- 2}$ )

TestHub · Accepted Answer

Velocity of water after falling through distance $0.15 m$ is
$v^{2} = u^{2} + 2 a s$
$= 1 + 2 \times 10 \times 0.15$
$v^{2} = 4$
$v = 2 m / s$
From equation of continuity
$A_{1} v_{1} = A_{2} v_{2}$
$A_{2} = \frac{10^{- 4} \times 1}{2} = 5 \times 10^{- 5} m^{2}$

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