A glass capillary tube is of the shape of a truncated cone with an apex angle α so that its two ends have cross-sections of different radii. When dipped in water vertically, the water rises in it to a

Question

A glass capillary tube is of the shape of a truncated cone with an apex angle $α$ so that its two ends have cross-sections of different radii. When dipped in water vertically, the water rises in it to a height $h$ , where the radius of its cross-section is $b$ . If the surface tension of water is $S$ , its density is $ρ$ , and its contact angle with glass is $θ$ , then the value of $h$ will be ( $g$ is the acceleration due to gravity)

TestHub · Accepted Answer

If R be the meniscus radius, ⇒ R cos ⁡ θ + α 2 = b Excess pressure on concave side of meniscus = 2 S R h ρ g = 2 S R = 2 S b cos ⁡ θ + α 2 ⇒ h = 2 S b ρ g cos ⁡ θ + α 2

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