Derive an expression for capillary height then calculate the capillary rise in a glasstube of 2.5mm diameter when immersed in (a)water angle of contact 00 and surfacetension =0.0725 N /m and (b) mercury angle of contact 1300 and surfacetension =0.52 N /m.(sp.gravity of mercury is 13.6)
Question
Derive an expression for capillary height then calculate the capillary rise in a glasstube of 2.5mm diameter when immersed in (a)water angle of contact 00 and surfacetension =0.0725 N /m and (b) mercury angle of contact 1300 and surfacetension =0.52 N /m.(sp.gravity of mercury is 13.6)
Solution
The capillary rise or fall in a small diameter tube is given by the Jurin's Law, which is expressed as:
h = 2σcosθ / (ρgr)
where: h = height of the liquid column σ = surface tension of the liquid θ = contact angle ρ = density of the liquid g = acceleration due to gravity r = radius of the tube
(a) For water: θ = 0 degrees (for water, cos 0 = 1) σ = 0.0725 N/m ρ = 1000 kg/m^3 (density of water) g = 9.81 m/s^2 r = 2.5mm/2 = 0.00125 m (radius is half the diameter)
Substituting these values into the equation, we get:
h = 20.07251 / (10009.810.00125) h = 0.145 / 0.0122625 h = 11.83 m
(b) For mercury: θ = 130 degrees (for mercury, cos 130 = -0.6428) σ = 0.52 N/m ρ = 13.6*1000 kg/m^3 (density of mercury is 13.6 times the density of water) g = 9.81 m/s^2 r = 0.00125 m
Substituting these values into the equation, we get:
h = 20.52(-0.6428) / (136009.810.00125) h = -0.66736 / 0.16722 h = -3.99 m
The negative sign indicates that the mercury level in the capillary is lower than the surrounding mercury level, which is a capillary depression.
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