Height Of Capillary Rise In Capillary Tube Calculator

Capillary Rise Formula:

\[ h_{Capillary} = \frac{2 \times \sigma_s \times \cos(\Phi)}{\rho \times [g] \times R_c} \]

Surface Tension (σs):

N/m

Contact Angle (Φ):

degrees

Density (ρ):

kg/m³

Radius of Capillary Tube (Rc):

Height of Capillary Rise (hCapillary):

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1. What is the Capillary Rise Equation?

The Capillary Rise Equation calculates the height to which a liquid will rise in a narrow tube due to capillary action. This phenomenon occurs due to the interplay between surface tension, adhesive forces between the liquid and tube, and gravitational forces.

2. How Does the Calculator Work?

The calculator uses the capillary rise formula:

\[ h_{Capillary} = \frac{2 \times \sigma_s \times \cos(\Phi)}{\rho \times [g] \times R_c} \]

Where:

\( h_{Capillary} \) — Height of capillary rise (m)
\( \sigma_s \) — Surface tension (N/m)
\( \Phi \) — Contact angle (degrees)
\( \rho \) — Density of the liquid (kg/m³)
\( [g] \) — Gravitational acceleration (9.80665 m/s²)
\( R_c \) — Radius of capillary tube (m)

Explanation: The equation balances the upward capillary force against the downward gravitational force to determine the equilibrium height.

3. Importance of Capillary Rise Calculation

Details: Understanding capillary rise is crucial in fields such as soil science, plant physiology, inkjet printing, microfluidics, and construction materials where capillary action plays a significant role in fluid transport.

4. Using the Calculator

Tips: Enter surface tension in N/m, contact angle in degrees (0-180), density in kg/m³, and radius in meters. All values must be positive and valid.

5. Frequently Asked Questions (FAQ)

Q1: What is the contact angle and how does it affect capillary rise?
A: Contact angle measures how much a liquid spreads on a solid surface. Smaller contact angles (closer to 0°) indicate better wetting and higher capillary rise.

Q2: Why does capillary rise occur?
A: Capillary rise occurs due to the combination of adhesive forces (liquid attracted to tube walls) and cohesive forces (liquid molecules attracted to each other) overcoming gravity.

Q3: What factors affect the height of capillary rise?
A: The height is directly proportional to surface tension and inversely proportional to tube radius, liquid density, and gravitational acceleration.

Q4: Can capillary rise be negative?
A: Yes, when the contact angle is greater than 90°, the liquid is repelled by the surface, resulting in capillary depression instead of rise.

Q5: What are some practical applications of capillary action?
A: Applications include water movement in plants, ink absorption in paper, wicking in fabrics, and fluid transport in microfluidic devices.