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 glass tube, we can use the following formula for capillary rise in a tube:

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

Where:
- \( h \) = capillary rise (in feet or meters)
- \( \gamma \) = surface tension of the liquid (kerosene) in contact with the glass surface (N/m or lb/ft)
- \( \theta \) = contact angle of kerosene with the glass surface (in degrees)
- \( \rho \) = density of the liquid (kerosene) (kg/m³ or slug/ft³)
- \( g \) = acceleration due to gravity (9.81 m/s² or 32.2 ft/s²)
- \( r \) = radius of the tube (in meters or feet)

### Step 1: Gather the given data
- Diameter of the glass tube = 0.03 inches
- Contact angle \( \theta \) = 26°
- Kerosene surface tension \( \gamma \) = 0.025 N/m (this is typical for kerosene)
- Kerosene density \( \rho \) = 800 kg/m³ (this is also typical for kerosene)
- Gravity \( g \) = 9.81 m/s²

### Step 2: Convert the units to SI (meters)
- Diameter of the glass tube = 0.03 inches = 0.03 × 0.0254 = 0.000762 m
- Radius of the tube \( r \) = 0.000762 / 2 = 0.000381 m

### Step 3: Apply the formula
Now, we can substitute the known values into the formula to compute the capillary rise \( h \).

\[
h = \frac{2 \times 0.025 \times \cos(26^\circ)}{800 \times 9.81 \times 0.000381}
\]

Let me calculate this for you.The capillary rise of kerosene in the glass tube is approximately 0.015 meters, or 15 mm.

Would you like more details on this calculation or have any questions?

Here are five related questions for further exploration:
1. How does the contact angle affect the capillary rise?
2. What would happen to the capillary rise if the tube diameter increased?
3. How does temperature affect the surface tension and capillary rise?
4. Can this capillary rise equation be applied to any liquid?
5. How does gravity influence capillary rise on different planets?

**Tip:** The smaller the diameter of a tube, the larger the capillary rise for a given liquid due to stronger surface tension effects.

Determine the capillary rise of kerosene in a 0.03-inch diameter glass tube at 68°F with a 26° contact angle. Explore key concepts in fluid mechanics, including surface tension, density, and the capillary rise equation. Suitable for undergraduate engineering or physics students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation