10.29 | Water rises in a glass capillary tube to a height of 17 cm. What is the diameter of the
Автор: ThetaBuddy
Загружено: 2024-12-13
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Water rises in a glass capillary tube to a height of 17 cm. What is the diameter of the capillary tube?**Finding the Diameter of the Capillary Tube:**
1. *Capillary Rise Equation:*
The capillary rise equation is:
h = (2 * γ * cos(θ)) / (ρ * g * r)
Where:
h = height of the liquid rise (0.17 m)
γ = surface tension of water (0.072 N/m at 20°C)
θ = contact angle (0° for clean glass, so cos(θ) = 1)
ρ = density of water (1000 kg/m³)
g = acceleration due to gravity (9.81 m/s²)
r = radius of the capillary tube
2. *Rearranging to Solve for Radius (r):*
r = (2 * γ * cos(θ)) / (ρ * g * h)
3. *Substituting Known Values:*
r = (2 * (0.072 N/m) * (1)) / (1000 kg/m³ * 9.81 m/s² * 0.17 m)
4. *Calculating the Radius:*
r ≈ 8.64 × 10^-5 m = 0.0864 cm
5. *Finding the Diameter (d):*
d = 2r = 2 * 0.0864 cm = 0.173 cm
Thus, the diameter of the capillary tube is approximately **0.173 cm**.
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