Worksheet: The Young–Laplace Equation

In this worksheet, we will practice using the Young–Laplace equation to calculate the pressure differential across a curved surface.

Q1:

At 25.0C, water rises in a glass capillary tube to a height of 8.4 mm, perfectly wetting the glass surface. What is the inner diameter of the capillary tube to two significant figures? Use values of 1.00 g/cm3 for the density of water, 0.07199 kg/s2 for the surface tension of water, and 9.81 m/s2 for the acceleration due to gravity.

Q2:

At 25.0C, how high will water rise in a glass capillary tube with an inner diameter of 0.280 mm if there is perfect wetting of the glass surface? Use values of 1.00 g/cm3 for the density of water, 71.99 mN/m for the surface tension of water, and 9.81 m/s2 for the acceleration due to gravity.

Q3:

At 25.0C, water rises in a glass capillary tube to a height of 17.0 cm, perfectly wetting the glass surface. What is the inner diameter of the capillary tube to two significant figures? Use values of 1.00 g/cm3 for the density of water, 71.99 mN/m for the surface tension of water, and 9.81 m/s2 for the acceleration due to gravity.

  • A 4 . 3 × 1 0 m
  • B 1 . 7 × 1 0 m
  • C 1 . 7 × 1 0 m
  • D 8 . 6 × 1 0 m
  • E 8 . 6 × 1 0 m

Q4:

A liquid rises to a height of 3.27 cm in a glass capillary tube with an inner diameter of 0.400 mm. The density of the liquid is 1.02 g/cm3, the acceleration due to gravity is 9.81 m/s2, and the contact angle is 41.0. Calculate the surface tension of the liquid to three significant figures.

Q5:

A liquid rises to a height of 2.055 cm in a glass capillary tube with an inner diameter of 0.6400 mm. The density of the liquid is 0.8760 g/cm3, the acceleration due to gravity is 9.807 m/s2, and the surface tension of the liquid is 28.88 mN/m. Calculate the contact angle between the liquid and glass.

Q6:

At 25C, mercury sinks to a depth of 2.026 cm in a glass capillary tube with an inner diameter of 0.5010 mm. The density of mercury is 13.69 g/cm3, the surface tension of mercury is 458.48 mN/m, and the acceleration due to gravity is 9.807 m/s2. Calculate, to 3 significant figures, the contact angle between mercury and glass.

Q7:

A liquid sinks to a depth of 0.772 cm in a capillary tube with an inner diameter of 0.620 mm. The density of the liquid is 0.896 g/cm3, the acceleration due to gravity is 9.81 m/s2, and the contact angle is 109.5. Calculate the surface tension of the liquid to three significant figures.

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