Explanation
By using Bernoulli’s principle
The velocity of the liquid coming out is given as,
v=√2gh
The mass of the liquid will be
m=ρAV
The change in momentum will be
P=mv
The force will be proportional of v2 which in turn is proportional to h
The difference in pressure is given as,
ΔP=ρgh
0.1×105=ρgh
The velocity of water flow is given as,
v=√2g×0.1×105103×g
v=√20m/s
Given , angle of contact (θ) = 140°
Radius of tube (r) = 1 mm = 10⁻³ m
Surface tension (S) = 0.465 N/m
Density of mercury (ρ) = 13.6 × 10³ kg/m³
Height of liquid rise or fall due to surface tension (h)
= 2S cos θ/rρg = 2 × 0.465 × cos 140°/1 × 10⁻³ × 13.6 × 10³ × 9.8
= 2 × 0.465 × (- 0.7660) / 10⁻³ × 13.6 × 10³ × 9.8
= - 5.34 mm
Hence, the mercury level will depressed by 5.34 mm.
A glass capillary is put in a trough containing one of these for liquids it is observed that the meniscus is convex. the liquid in the trough is Ethyl alcohol.
v_{1}= velocity of surface of liquid
v_{2}= velocity of liquid far om orifice
Acc. to continuity theorem.
A v_{1}=a v_{2} \Rightarrow \dfrac{A v_{1}}{a}=v_{2}
\Rightarrow \dfrac{a v_{2}}{A}=v_{1}
Acc. to Bernoulli's Theorem
P_{0}+\rho g h+\dfrac{1}{2} \rho v_{1}^{2}=P_{0}+\rho g(0)+\dfrac{1}{2} \rho v_{L}^{2}
\rho g h+\dfrac{1}{2} \rho\left[\dfrac{a^{2} v_{1}^{2}}{A^{2}}-v_{1}^{2}\right]=0
\dfrac{v_{1}^{2}}{2}\left[\dfrac{A^{2}-a^{2}}{A^{2}}\right]=g h
v_{1}=\sqrt{2 g h} \sqrt{\dfrac{A^{2}}{A^{2}-a^{2}}}
Answer: \sqrt{2 g h} \sqrt{ \dfrac{A^{2}}{A^{2}-a^{2}}}
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