Mechanical Properties of Fluids - Result Question 7
7. A small hole of area of cross-section $2 mm^{2}$ is present near the bottom of a fully filled open tank of height $2 m$. Taking $g=10 m / s^{2}$, the rate of flow of water through the open hole would be nearly:
[2019]
(a) $12.610^{-6} m^{3} / s$
(b) $8.910^{-6} m^{3} / s$
(c) $2.2310^{-6} m^{3} / s$
(d) $6.410^{-6} m^{3} / s$
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Answer:
Correct Answer: 7. (a)
Solution:
- (a) Volumetric flow rate of liquid
$Q=au=a \sqrt{2 gh}$
$ \begin{aligned} & =2 \times 10^{-6} m^{2} \times \sqrt{2 \times 10 \times 2} m / s \\ & =2 \times 2 \times 3.14 \times 10^{-6} m^{3} / s \\ & =12.56 \times 10^{-6} m^{3} / s \\ & =12.6 \times 10^{-6} m^{3} / s \end{aligned} $
