A 0.03-in-diameter glass tube is inserted into kerosene at 68°F. The contact angle of kerosene with a glass surface is 26°. Determine the capillary rise of kerosene in the tube.

To determine the capillary rise of kerosene in the tube, we can use the following formula for capillary action:

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

where:
- \( h \) = capillary rise (in meters),
- \( \gamma \) = surface tension of kerosene (in N/m),
- \( \theta \) = contact angle (in degrees),
- \( \rho \) = density of kerosene (in kg/m³),
- \( g \) = gravitational acceleration (9.81 m/s²),
- \( r \) = radius of the tube (in meters).

### Given:
- Diameter of the tube = 0.03 in = 0.000762 m (converted from inches to meters),
- Radius of the tube, \( r \) = 0.000762 m / 2 = 0.000381 m,
- Contact angle, \( \theta \) = 26°,
- The surface tension of kerosene, \( \gamma \) = 0.025 N/m (approximate value),
- Density of kerosene, \( \rho \) = 810 kg/m³ (approximate value for kerosene at 68°F).

Now, let's calculate the capillary rise, \( h \).

\[
h = \frac{2 \times 0.025 \times \cos(26^\circ)}{810 \times 9.81 \times 0.000381}
\]

I'll calculate the result.The capillary rise of kerosene in the glass tube is approximately \( 0.0148 \) meters, or 14.8 mm.

Would you like more details, or do you have any questions?

Here are five related questions:
1. How does the surface tension of kerosene affect the capillary rise?
2. What is the impact of tube diameter on the capillary rise?
3. How does the contact angle influence the capillary action?
4. What would happen to the capillary rise if the tube material changes?
5. How does temperature affect the surface tension and thus the capillary rise?

**Tip:** The smaller the tube's diameter, the greater the capillary rise for the same liquid.

Explore how to calculate the capillary rise of kerosene in a 0.03-in-diameter glass tube at 68°F with a contact angle of 26°. This problem delves into fluid mechanics concepts such as capillary action and includes key formulas for surface tension, contact angle, and more. Suitable for advanced high school and college-level students.

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