Radius Of Capillary Tube Calculator

Radius of Capillary Tube Formula:

\[ r' = \frac{1}{2} \times \left( \frac{128 \times \mu \times Q \times L}{\pi \times \rho \times [g] \times h} \right)^{\frac{1}{4}} \]

Viscosity of Fluid (μ):

Pa·s

Discharge in Capillary Tube (Q):

m³/s

Length of Pipe (L):

Density of Liquid (ρ):

kg/m³

Difference in Pressure Head (h):

Radius of Capillary Tube (r'):

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1. What is the Radius of Capillary Tube Formula?

The Radius of Capillary Tube formula calculates the internal radius of a capillary tube based on fluid properties and flow characteristics. This formula is derived from the Hagen-Poiseuille equation and considers viscosity, discharge rate, pipe length, fluid density, and pressure difference.

2. How Does the Calculator Work?

The calculator uses the following formula:

\[ r' = \frac{1}{2} \times \left( \frac{128 \times \mu \times Q \times L}{\pi \times \rho \times [g] \times h} \right)^{\frac{1}{4}} \]

Where:

\( r' \) — Radius of Capillary Tube (m)
\( \mu \) — Viscosity of Fluid (Pa·s)
\( Q \) — Discharge in Capillary Tube (m³/s)
\( L \) — Length of Pipe (m)
\( \rho \) — Density of Liquid (kg/m³)
\( [g] \) — Gravitational acceleration (9.80665 m/s²)
\( h \) — Difference in Pressure Head (m)
\( \pi \) — Archimedes' constant (3.141592653589793)

Explanation: The formula calculates the radius by considering the balance between viscous forces and pressure-driven flow in a capillary tube.

3. Importance of Radius Calculation

Details: Accurate radius calculation is crucial for designing capillary systems, understanding fluid behavior in narrow channels, and applications in microfluidics, medical devices, and precision instrumentation.

4. Using the Calculator

Tips: Enter all values in appropriate SI units. Viscosity in Pa·s, discharge in m³/s, length in meters, density in kg/m³, and pressure head in meters. All values must be positive and non-zero.

5. Frequently Asked Questions (FAQ)

Q1: What is the practical application of this calculation?
A: This calculation is used in designing capillary tubes for medical devices, inkjet printers, microfluidic systems, and various precision fluid delivery systems.

Q2: How accurate is this formula?
A: The formula is highly accurate for laminar flow conditions in circular tubes where the flow is fully developed and steady.

Q3: What are the limitations of this formula?
A: The formula assumes Newtonian fluids, constant viscosity, and neglects entrance effects and surface tension influences.

Q4: Can this be used for non-circular tubes?
A: No, this formula is specifically derived for circular cross-sections. Different formulas apply for non-circular geometries.

Q5: What units should be used for input values?
A: All input values should be in SI units: Pa·s for viscosity, m³/s for discharge, meters for length, kg/m³ for density, and meters for pressure head.