Discharge In Capillary Tube Method Calculator

Formula Used:

\[ Q = \frac{4 \times \pi \times \rho \times [g] \times h \times r_p^4}{128 \times \mu \times L} \]

Density of Liquid (ρ):

kg/m³

Difference in Pressure Head (h):

Radius of Pipe (r_p):

Viscosity of Fluid (μ):

Pa·s

Length of Pipe (L):

Discharge in Capillary Tube (Q):

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1. What is the Discharge in Capillary Tube Method?

The Discharge in Capillary Tube Method is used to calculate the rate of flow of a liquid through a capillary tube based on the Hagen-Poiseuille equation. This method is particularly useful for analyzing laminar flow in small-diameter tubes and understanding fluid dynamics in capillary systems.

2. How Does the Calculator Work?

The calculator uses the following formula:

\[ Q = \frac{4 \times \pi \times \rho \times [g] \times h \times r_p^4}{128 \times \mu \times L} \]

Where:

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

Explanation: The formula describes the relationship between flow rate and various fluid properties and tube dimensions for laminar flow conditions.

3. Importance of Discharge Calculation

Details: Accurate discharge calculation is crucial for designing fluid transport systems, understanding capillary action, medical applications (such as blood flow in capillaries), and various industrial processes involving fluid flow through narrow passages.

4. Using the Calculator

Tips: Enter all values in appropriate SI units. Ensure density, viscosity, radius, and length are positive values. The calculator assumes laminar flow conditions (Reynolds number < 2000).

5. Frequently Asked Questions (FAQ)

Q1: What is the range of validity for this formula?
A: The Hagen-Poiseuille equation is valid for steady, laminar flow of Newtonian fluids in straight, circular tubes with constant cross-section.

Q2: How does tube radius affect the discharge?
A: Discharge is proportional to the fourth power of the radius (r⁴), meaning small changes in radius significantly affect flow rate.

Q3: What are typical applications of capillary tube flow calculations?
A: Medical devices, microfluidics, inkjet printing, chemical analysis instruments, and various laboratory equipment.

Q4: How does viscosity affect the flow rate?
A: Flow rate is inversely proportional to viscosity - higher viscosity fluids flow more slowly through capillary tubes.

Q5: What are the limitations of this calculation method?
A: The method assumes ideal conditions and may not account for surface roughness, entrance effects, or non-Newtonian fluid behavior.