The surface tension of water is 0.0730 N/m. What is the height of the water in a capillary tube of diameter 1.00 mm?
Question
The surface tension of water is 0.0730 N/m. What is the height of the water in a capillary tube of diameter 1.00 mm?
Solution
To solve this problem, we will use the formula for capillary rise which is given by:
h = 2Tcos(θ)/ρgd
where: h is the height of the water in the capillary tube, T is the surface tension of the water, θ is the contact angle, ρ is the density of the water, g is the acceleration due to gravity, and d is the diameter of the capillary tube.
Given: T = 0.0730 N/m (surface tension of water), θ = 0 degrees (for water), ρ = 1000 kg/m^3 (density of water), g = 9.81 m/s^2 (acceleration due to gravity), and d = 1.00 mm = 0.001 m (diameter of the capillary tube).
Substituting these values into the formula, we get:
h = 20.0730cos(0)/(10009.810.001) h = 0.01486 m or 14.86 mm
Therefore, the height of the water in a capillary tube of diameter 1.00 mm is approximately 14.86 mm.
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