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Question

The diameter of one arm of a U-tube is 5 mm while the other arm is large. If the U-tube contains some water, and both surface are exposed to atmospheric pressure, determine the difference between the water levels in the two arms.

Solution

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The capillary rise of the large diameter arm of the u tube is considered equal to zero, the capillary rise only happens on the small diameters.

For the small diameter tube use this formula from the book 2-42 which is defined by the height of the water rise in the tube, density of the water, acceleration due to gravity, surface tension, and the contact angle at the inner wall of the tube (The surface tension can be found in book Table 2-4),

$h_2 = \frac{2 \sigma_s}{\rho g R} \cdot \cos\phi$

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