# Surface Tension of Water by Capillary Rise Method
> Learn how to determine the surface tension of water using the capillary tube method, including theory, formulas, experimental procedure, and calculations.

Tags: physics-experiment, surface-tension, capillary-rise, fluid-mechanics, laboratory-manual, science-presentation
## Surface Tension of Water by Capillary Tube Method
* **Aim:** To determine the surface tension of water using the capillary rise method.
* **Apparatus:** Capillary tubes, traveling microscope, beaker, distilled water, thermometer, and reading lamp.

## Theory and Derivations
* **Upward Force ($F_{up}$):** $2 \pi r T \cos\theta$
* **Downward Weight ($W$):** $\pi r^2 h \rho g$
* **Final Equilibrium Formula:** $T = \frac{r h \rho g}{2 \cos\theta}$
* For water and glass, $\theta \approx 0^\circ$ is assumed.

## Experimental Procedure
1. Clean the capillary tube with acid and water.
2. Clamp the tube vertically in water and allow for capillary rise.
3. Use a traveling microscope to measure the height of the meniscus ($h$).
4. Measure the internal diameter of the tube in two perpendicular directions to find radius ($r$).

## Observations and Data
* **Height measurement ($h$):** Meniscus reading (12.45 cm) - Pointer reading (9.25 cm) = 3.20 cm.
* **Mean Diameter ($d$):** 0.098 cm, resulting in a radius ($r$) of 0.049 cm.
* **Constants:** Density ($\rho$) = 1000 kg/m³, Gravity ($g$) = 9.8 m/s².

## Calculation and Results
* **Substitution:** $T = \frac{(0.00049)(0.032)(1000)(9.8)}{2}$
* **Experimental Result:** 0.0768 N/m.
* **Error Analysis:** Percentage error of approximately 5.5% compared to the standard value of 0.0728 N/m at 20°C.
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