Height Of Liquid In Tube Calculator

Capillary Rise Formula:

\[ h_{liquid} = \frac{4 \times \sigma \times \cos(\theta)}{\rho_l \times g \times d} \]

Surface Tension (σ):

N/m

Contact Angle (θ):

radians

Density of Liquid (ρₗ):

kg/m³

Acceleration Due to Gravity (g):

m/s²

Diameter of Tube (d):

Height of Liquid in Tube (h):

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1. What is the Height of Liquid in Tube Formula?

The height of liquid in tube formula calculates the capillary rise or depression of a liquid in a narrow tube due to surface tension effects. This phenomenon is governed by the balance between surface tension forces and gravitational forces.

2. How Does the Calculator Work?

The calculator uses the capillary rise formula:

\[ h_{liquid} = \frac{4 \times \sigma \times \cos(\theta)}{\rho_l \times g \times d} \]

Where:

\( h_{liquid} \) — Height of liquid in tube (m)
\( \sigma \) — Surface tension (N/m)
\( \theta \) — Contact angle between liquid and tube (radians)
\( \rho_l \) — Density of liquid (kg/m³)
\( g \) — Acceleration due to gravity (m/s²)
\( d \) — Diameter of tube (m)

Explanation: The formula demonstrates how liquids rise in capillary tubes due to surface tension, with the height being inversely proportional to the tube diameter and liquid density.

3. Importance of Capillary Rise Calculation

Details: Understanding capillary action is crucial in various fields including soil science, biomedical applications, inkjet printing, and microfluidics. It helps explain how plants draw water from roots to leaves and how blood moves through small vessels.

4. Using the Calculator

Tips: Enter surface tension in N/m, contact angle in radians, density in kg/m³, gravity in m/s², and tube diameter in meters. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the physical significance of the contact angle?
A: The contact angle indicates the wettability of the surface. A contact angle less than 90° indicates wetting (liquid rises), while greater than 90° indicates non-wetting (liquid depresses).

Q2: Why is there a factor of 4 in the numerator?
A: The factor of 4 comes from the geometry of the capillary tube and the relationship between surface tension force and the weight of the liquid column.

Q3: How does tube diameter affect the height?
A: The height is inversely proportional to the tube diameter - smaller tubes produce greater capillary rise due to increased surface tension effects relative to gravitational forces.

Q4: What are typical values for surface tension?
A: Water at 20°C has surface tension of about 0.0728 N/m, mercury about 0.465 N/m, and ethanol about 0.0223 N/m.

Q5: When is this formula not applicable?
A: The formula assumes ideal conditions and may not be accurate for very small diameters where other forces dominate, or for non-Newtonian fluids and complex surface interactions.