Properties of Matter 4 Question 13
15. Statement I The stream of water flowing at high speed from a garden hose pipe tends to spread like a fountain when held vertically up, but tends to narrow down when held vertically down.
Statement II In any steady flow of an incompressible fluid, the volume flow rate of the fluid remains constant.
$(2008,3 M)$
Passage Based Questions
Passage 1
A spray gun is shown in the figure where a piston pushes air out of nozzle. A thin tube of uniform cross-section is connected to the nozzle. The other end of the tube is in a small liquid container. As the piston pushes air through the nozzle, the liquid
and is sprayed out.
For the spray gun shown, the radii of the piston and the nozzle are $20 mm$ and $1 mm$ respectively. The upper end of the container is open to the atmosphere.
(2014 Adv.)
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Answer:
Correct Answer: 15. 6
Solution:
- Although not given in the question, but we will have to assume that temperatures of $A$ and $B$ are same.
$$ \begin{aligned} \frac{n _B}{n _A} & =\frac{p _B V _B / R T}{p _A V _A / R T}=\frac{p _B V _B}{p _A V _A} \\ & =\frac{p+4 S / r _A \times 4 / 3 \pi\left(r _A\right)^{3}}{\left(p+4 S / r _B\right) \times 4 / 3 \pi\left(r _B\right)^{3}} \end{aligned} $$
Substituting the values, we get
$(S$ = surface tension $)$
$$ \frac{n _B}{n _A}=6 $$
