Capillary Back Pressure Calculator

Formula

The formula to calculate the capillary back pressure (ΔP) is:

\[ \Delta P = \frac{8 \eta L Q}{\pi r^4} \]

Where:

ΔP is the Back Pressure (Pa)
η is the Viscosity (Pa·s)
L is the Capillary Length (m)
Q is the Flow Rate (m³/s)
r is the Capillary Radius (m)

What is Capillary Back Pressure?

Capillary back pressure is the pressure required to drive a fluid through a capillary tube. This pressure is influenced by factors such as the fluid’s viscosity, the length and radius of the capillary, and the flow rate of the fluid. Understanding and calculating capillary back pressure is essential in various scientific and industrial applications, including chromatography, microfluidics, and medical diagnostics.

Example Calculation 1

Let's assume the following values:

Viscosity (η) = 0.001 Pa·s
Capillary Length (L) = 0.1 m
Flow Rate (Q) = 0.00001 m³/s
Capillary Radius (r) = 0.001 m

Using the formula:

\[ \Delta P = \frac{8 \times 0.001 \times 0.1 \times 0.00001}{\pi \times (0.001)^4} = 2546.4791 \]

The Capillary Back Pressure is 2,546.4791 Pa.

Example Calculation 2

Let's assume the following values:

Viscosity (η) = 0.002 Pa·s
Capillary Length (L) = 0.2 m
Flow Rate (Q) = 0.00002 m³/s
Capillary Radius (r) = 0.002 m

Using the formula:

\[ \Delta P = \frac{8 \times 0.002 \times 0.2 \times 0.00002}{\pi \times (0.002)^4} = 1273.2395 \]

The Capillary Back Pressure is 1,273.2395 Pa.