A clean tube of internal diameter 3 mm is immersed in a liquid with a ...
Calculation of the level of liquid in the tube
Determination of the contact angle
The contact angle of the liquid with the glass can be assumed to be 130º.
Determination of the coefficient of capillary rise
The coefficient of capillary rise can be calculated using the formula:
\(\frac{2σcosθ}{ρgr}\)
Where:
- σ = Coefficient of surface tension (0.48 N/m)
- θ = Contact angle (130º)
- ρ = Density of the liquid (13,600 kg/m3)
- g = Acceleration due to gravity (9.81 m/s2)
- r = Internal radius of the tube (1.5 mm or 0.0015 m)
Substituting the given values, we get:
\(\frac{2×0.48×cos(130º)}{13600×9.81×0.0015}\)
On solving the above equation, we get:
h = 0.228 mm
Determination of the level of liquid in the tube
The level of liquid in the tube can be calculated using the formula:
h = \(\frac{ρgh}{σcosθ}\)
Where:
- h = Level of liquid in the tube
- ρ = Density of the liquid (13,600 kg/m3)
- g = Acceleration due to gravity (9.81 m/s2)
- σ = Coefficient of surface tension (0.48 N/m)
- θ = Contact angle (130º)
Substituting the given values, we get:
h = \(\frac{13600×9.81×0.228×10^-3}{0.48×cos(130º)}\)
On solving the above equation, we get:
h = 0.165 mm
Conclusion
The level of the liquid in the tube relative to the free surface of the liquid outside the tube is 0.165 mm.