Calculate Viscosity At Different Temperatures

Sutherland's Formula:

\[ \mu_2 = \mu_1 \left( \frac{T_2}{T_1} \right)^{3/2} \frac{T_1 + S}{T_2 + S} \]

Reference Viscosity (μ₁):

Pa s

Reference Temperature (T₁):

Target Temperature (T₂):

Sutherland's Constant (S):

Calculated Viscosity (μ₂):

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1. What is Sutherland's Formula?

Sutherland's formula is an empirical relationship that describes how the viscosity of a gas changes with temperature. It provides a more accurate prediction than simple power-law approximations, especially over wider temperature ranges.

2. How Does the Calculator Work?

The calculator uses Sutherland's formula:

\[ \mu_2 = \mu_1 \left( \frac{T_2}{T_1} \right)^{3/2} \frac{T_1 + S}{T_2 + S} \]

Where:

\( \mu_1 \) — Reference viscosity at temperature T₁ (Pa s)
\( \mu_2 \) — Viscosity at temperature T₂ (Pa s)
\( T_1 \) — Reference temperature (K)
\( T_2 \) — Target temperature (K)
\( S \) — Sutherland's constant (specific to each gas)

Explanation: The formula accounts for the temperature dependence of gas viscosity, with the Sutherland constant S representing an effective temperature characteristic of intermolecular forces.

3. Importance of Viscosity Calculation

Details: Accurate viscosity prediction is crucial for fluid dynamics calculations, aerodynamic design, pipeline flow analysis, and various engineering applications involving gas flow and heat transfer.

4. Using the Calculator

Tips: Enter reference viscosity in Pa s, temperatures in Kelvin, and the appropriate Sutherland constant for the specific gas. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What are typical Sutherland constants for common gases?
A: Air: 110.4 K, Nitrogen: 111 K, Oxygen: 127 K, Carbon dioxide: 240 K (values may vary slightly depending on source).

Q2: What is the temperature range validity for Sutherland's formula?
A: The formula works well for temperatures between approximately 200-1500 K for most gases, though accuracy decreases at very high temperatures.

Q3: Why does gas viscosity increase with temperature?
A: Unlike liquids, gas viscosity increases with temperature because higher thermal velocities enhance momentum transfer between gas layers.

Q4: Can Sutherland's formula be used for liquid viscosity?
A: No, Sutherland's formula is specifically for gases. Liquids exhibit different temperature-viscosity relationships (typically decreasing viscosity with increasing temperature).

Q5: How accurate is Sutherland's formula compared to experimental data?
A: For many engineering applications, Sutherland's formula provides accuracy within 2-5% over moderate temperature ranges when appropriate constants are used.