3
Find the minimum size of glass tube that can be used to measure water level if capillary rise in the tube is to be restricted to
a3mm. Consider surface tension of water in contact with air as 0.073575 N/m.
EXPLANATION
Fluid Statics & Kinematics
- Capillary Rise & Minimum Piezometer Tube Diameter:
- Capillary Rise Equation:
For clean water in a glass tube, contact angle $\theta = 0^\circ \implies \cos\theta = 1$.
- Calculation:
- Surface tension $\sigma = 0.073575\text{ N/m}$
- Density $\rho = 1000\text{ kg/m}^3$, $g = 9.81\text{ m/s}^2$
- Maximum allowable capillary rise $h = 3\text{ mm} = 0.003\text{ m}$
- Conclusion: Minimum diameter of glass tube is 1 cm (Option 4).
Correct option: (4) 1cm
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