First slide

Fluid statics

Question

Water from a tap emerges vertically downwards with an initial velocity $V_{0}$ . Assume pressure is constant throughout the stream of water and the flow is steady. Find the distance from the tap at which cross - sectional area of stream is half of the cross-sectional area of stream at the tap.

Moderate

A

$\frac{V_{0}^{2}}{2 g}$
B

$\frac{3 V_{0}^{2}}{2 g}$
C

$\frac{2 V_{0}^{2}}{g}$
D

$\frac{5 V_{0}^{2}}{2 g}$

Solution

$V_{2}^{2} = V_{0}^{2} + 2 gh$ -------------------(i)
and $A_{1} V_{0} = A_{2} V_{2}$
Solving $\frac{A_{2}}{A_{1}} = \frac{V_{0}}{\sqrt{V_{0}^{2} + 2 gh}}$
$\frac{A_{2}}{A_{1}} = \frac{1}{2} = \frac{V_{0}}{\sqrt{V_{0}^{2} + 2 gh}}$
$4 V_{0}^{2} = V_{0}^{2} + 2 gh$
$h = \frac{3 V_{0}^{2}}{2 g}$

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