Math Problem Statement

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.

Solution

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

h=2γcos(θ)ρgrh = \frac{2 \gamma \cos(\theta)}{\rho g r}

where:

  • hh = capillary rise (in meters),
  • γ\gamma = surface tension of kerosene (in N/m),
  • θ\theta = contact angle (in degrees),
  • ρ\rho = density of kerosene (in kg/m³),
  • gg = gravitational acceleration (9.81 m/s²),
  • rr = 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, rr = 0.000762 m / 2 = 0.000381 m,
  • Contact angle, θ\theta = 26°,
  • The surface tension of kerosene, γ\gamma = 0.025 N/m (approximate value),
  • Density of kerosene, ρ\rho = 810 kg/m³ (approximate value for kerosene at 68°F).

Now, let's calculate the capillary rise, hh.

h=2×0.025×cos(26)810×9.81×0.000381h = \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 0.01480.0148 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.

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Math Problem Analysis

Mathematical Concepts

Fluid Mechanics
Capillary Action
Trigonometry

Formulas

Capillary rise formula: h = (2γ cos(θ)) / (ρ g r)

Theorems

Capillary Action Law

Suitable Grade Level

Grades 11-12 (Advanced High School Physics or College-Level Fluid Mechanics)