Capillary Rise Or Depression When Tube Is Inserted In Two Liquids Calculator

Capillary Rise Formula:

\[ h_c = \frac{2 \cdot \sigma \cdot \cos(\theta)}{r_t \cdot W \cdot (S_1 - S_2) \cdot 1000} \]

Surface Tension (σ):

N/m

Contact Angle (θ):

radians

Radius of Tube (r_t):

Specific Weight of Water (W):

kN/m³

Specific Gravity of Liquid 1 (S₁):

Specific Gravity of Liquid 2 (S₂):

Capillary Rise (or Depression):

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1. What is Capillary Rise or Depression?

Capillary rise or depression is the phenomenon where a liquid rises or falls in a narrow tube due to the interplay between surface tension and adhesive forces between the liquid and tube material. This occurs when a tube is inserted into two different liquids.

2. How Does the Calculator Work?

The calculator uses the capillary rise formula:

\[ h_c = \frac{2 \cdot \sigma \cdot \cos(\theta)}{r_t \cdot W \cdot (S_1 - S_2) \cdot 1000} \]

Where:

\( h_c \) — Capillary rise or depression (m)
\( \sigma \) — Surface tension (N/m)
\( \theta \) — Contact angle (radians)
\( r_t \) — Radius of tube (m)
\( W \) — Specific weight of water (kN/m³)
\( S_1 \) — Specific gravity of liquid 1
\( S_2 \) — Specific gravity of liquid 2

Explanation: The formula calculates the height difference caused by capillary action when a tube is placed between two liquids with different specific gravities.

3. Importance of Capillary Rise Calculation

Details: Understanding capillary rise is crucial in various fields including soil mechanics, petroleum engineering, and microfluidics. It helps predict liquid behavior in porous materials and small channels.

4. Using the Calculator

Tips: Enter all values in the specified units. Surface tension and radius must be positive values. The specific gravity difference (S₁ - S₂) should not be zero to avoid division by zero.

5. Frequently Asked Questions (FAQ)

Q1: What causes capillary rise or depression?
A: It's caused by the imbalance between cohesive forces within the liquid and adhesive forces between the liquid and tube surface.

Q2: When does capillary depression occur?
A: Capillary depression occurs when the contact angle is greater than 90°, indicating the liquid does not wet the surface well.

Q3: How does tube radius affect capillary rise?
A: Capillary rise is inversely proportional to tube radius - smaller tubes produce greater capillary rise.

Q4: What are typical surface tension values?
A: Water at 20°C has surface tension of about 0.0728 N/m, while mercury has about 0.465 N/m.

Q5: Why is the specific weight of water used?
A: The specific weight provides the gravitational force component needed to balance the capillary forces in the calculation.