Agilent Pressure Flow Calculator Model

Agilent Pressure Flow Model:

\[ Flow = \frac{\pi \times r^4 \times (P_1 - P_2)}{8 \times \eta \times L} \]

Tube Radius:

Tube Length:

Inlet Pressure (P₁):

dyn/cm²

Outlet Pressure (P₂):

dyn/cm²

Fluid Viscosity:

poise

Flow Rate:

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1. What is the Agilent Pressure Flow Model?

The Agilent Pressure Flow Model is based on the Hagen-Poiseuille equation, which describes the relationship between pressure difference, flow rate, and tube dimensions for laminar flow of Newtonian fluids in cylindrical tubes.

2. How Does the Calculator Work?

The calculator uses the Hagen-Poiseuille equation:

\[ Flow = \frac{\pi \times r^4 \times (P_1 - P_2)}{8 \times \eta \times L} \]

Where:

\( r \) — Inner radius of the tube (cm)
\( P_1 - P_2 \) — Pressure difference between tube ends (dyn/cm²)
\( \eta \) — Dynamic viscosity of the fluid (poise)
\( L \) — Length of the tube (cm)

Explanation: The equation shows that flow rate is proportional to the fourth power of the radius, making tube diameter the most critical factor in determining flow.

3. Importance of Flow Rate Calculation

Details: Accurate flow rate calculation is essential for designing fluidic systems, chromatography applications, and understanding pressure-flow relationships in analytical instruments.

4. Using the Calculator

Tips: Enter all values in consistent units (cm for dimensions, dyn/cm² for pressure, poise for viscosity). Ensure all values are positive and non-zero.

5. Frequently Asked Questions (FAQ)

Q1: What are the assumptions of this model?
A: The model assumes laminar flow, Newtonian fluid, no-slip boundary conditions, steady-state flow, and a long cylindrical tube with constant circular cross-section.

Q2: When is this model not applicable?
A: Not valid for turbulent flow, non-Newtonian fluids, very short tubes, or tubes with non-circular cross-sections.

Q3: How does temperature affect the calculation?
A: Temperature primarily affects viscosity. Use the correct viscosity value for your operating temperature.

Q4: What is the typical range for HPLC flow rates?
A: Common HPLC flow rates range from 0.1 to 5 mL/min, depending on column dimensions and application requirements.

Q5: How can I convert between different pressure units?
A: 1 bar = 10⁶ dyn/cm², 1 atm = 1.01325 bar, 1 psi ≈ 68947.6 dyn/cm².