First slide

Fluid dynamics

Question

Water from a tap emerges vertically downwards with an initial speed of 1.0 m/s. The cross-sectional area of the tap is 10^-4m². Assume that the pressure is constant throughout the stream of water and that the flow is steady, the cross-sectional area of the stream 0.15 m below the tap is

Moderate

A

$5 \cdot 0 \times 10^{- 4} m^{2}$
B

$1 \cdot 0 \times 10^{- 5} m^{2}$
C

$5 \cdot 0 \times 10^{- 5} m^{2}$
D

$2 \cdot 0 \times 10^{- 5} m^{2}$

Solution

Hero $A_{1} v_{1} = A_{1} v_{2}$
Further, $v_{2}^{2} = v_{1}^{2} + 2 gh = 1 + 2 \times 10 \times 0 \cdot 15$
or $v_{2} = 2 m / s$
Now $10^{- 4} \times 1 = A_{2} \times 2$
$∴ A_{2} = \frac{1}{2} \times 10^{- 4} = 5 \times 10^{- 5} m^{2}$

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