What is the difference in the heights of the two water columns? Assume that the glass is very smooth and clean. Use γwater = 73 mN/m.

Steps to Solve

1. Identify the formula for height difference due to surface tension

To find the height difference of two water columns affected by surface tension, we can use the formula:

$$ h = \frac{2\gamma \cos(\theta)}{\rho g r} $$

where (h) is the height difference, (\gamma) is the surface tension, (\theta) is the contact angle, (\rho) is the density of the fluid, (g) is the acceleration due to gravity, and (r) is the radius of the tube.

2. Plug in known values

Use the given value for surface tension and standard values for water. For example:

• Surface tension ((\gamma)) of water = 0.0728 N/m
• Assume contact angle ((\theta)) = 0° (where (\cos(0°) = 1))
• Density of water ((\rho)) = 1000 kg/m³
• Acceleration due to gravity ((g)) = 9.81 m/s²
• Assume tube radius ((r)) = 0.005 m

So, substituting these values into the formula:

$$ h = \frac{2 \times 0.0728 \times 1}{1000 \times 9.81 \times 0.005} $$

3. Calculate the height difference

Now calculate (h):

$$ h = \frac{0.1456}{0.4905} $$

Then compute (h) to find the height difference between the two water columns.

4. Final calculation and conclusion

After performing the division, you get the height difference (h).