An R mm radius glass tube is inserted into the water at 20°C in a cup. At 200 C the surface tension is 0.0728 N/m. The angle of contact is Theta degree.Here,R=0.6 mmTheta=(180/3)degreeDetermine the capillary rise of water in the tube in millimeters unit.
Question
An R mm radius glass tube is inserted into the water at 20°C in a cup. At 200 C the surface tension is 0.0728 N/m. The angle of contact is Theta degree.Here,R=0.6 mmTheta=(180/3)degreeDetermine the capillary rise of water in the tube in millimeters unit.
Solution
The capillary rise of water in a tube can be calculated using the formula:
h = (2Tcosθ)/(ρgr)
where: h = height of the capillary rise T = surface tension θ = angle of contact ρ = density of the fluid g = acceleration due to gravity r = radius of the tube
Given: T = 0.0728 N/m θ = 180/3 = 60 degrees ρ (for water at 20°C) = 1000 kg/m³ g = 9.81 m/s² r = 0.6 mm = 0.6 x 10^-3 m
First, convert the angle θ from degrees to radians because the trigonometric function in the formula uses radians.
θ = 60 * (π/180) = π/3 radians
Then, substitute the given values into the formula:
h = (2 * 0.0728 * cos(π/3)) / (1000 * 9.81 * 0.6 x 10^-3) h = 0.00744 m
Convert the height from meters to millimeters:
h = 0.00744 * 10^3 = 7.44 mm
So, the capillary rise of water in the tube is approximately 7.44 millimeters.
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