Name: Angle of Contact
Uploaded: 2019-07-19
Duration: 6 min 57 s
Description: What is the contact angle? Which factor does the contact angle depend on? Why does the contact angle for the same liquid on different surfaces differ? Let's...

Question

(a) The radius of a capillary tube is $0.025 mm$ . It is held vertically in a liquid whose density is $0.8 \times 10^{3} kg m^{- 3}$ ,surface tension is $3.0 \times 10^{- 2} N m^{- 1}$ and for which the cosine of the angle of contact is $0.3$ . Determine the height up to which the liquid will rise in the tube. Take $g = 10 m s^{- 2}$
(b) If the capillary is taken down in water slowly until its upper end comes in level of water, will the water come out from this end ?

Accepted Answer

Radius of capillary tube $(r)$ $= 0.025 mm = 25 \times 10^{- 6} m$

Density of liquid $(ρ)$ $= 0.8 \times 10^{3} kg / m^{3}$

Surface Tension of liquid $(T)$ $= 3.0 \times 10^{- 2} N$

Cosine of angle of contact, $\cos θ = 0.3$

Acceleration due to gravity $(g) = 10 m / s^{2}$

To find:

The height up to which the liquid will rise $(h)$ :

$h = \frac{2 T \cos θ}{r ρ g}$

$h = \frac{2 \times 3 \times 10^{- 2} \times 0.3}{0.8 \times 10^{3} \times 0.025 \times 10^{- 3} \times 10}$

$h = 9 cm$

(b) No it won't overflow. That should be obvious since doing so would create a constant flow, constantly using energy, but without any energy input. The same force that pulls the water along the inside of the capillary tube also holds it there when it reaches the end. This force doesn't just pull upward, it pulls the water along the glass. At a certain height, The weight of the water column balance is this pull. In that case the pull is upward since there is water below but not above.

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