Vacuum Expanded Air Ratio

Overview

Engineering reference data for Vacuum Expanded Air Ratio in miscellaneous.

Key Formulas

Unit Conversion

$y = x \cdot k$

Multiply by conversion factor.

Linear Interpolation

$y = y_1 + \frac{(x - x_1)(y_2 - y_1)}{x_2 - x_1}$

Estimate between two known points.

Percentage

$p = \frac{\text{part}}{\text{whole}} \times 100\%$

Part as fraction of whole.

Variables

Expanded Air Ratio Formula

The core relationship between actual (ACFM) and standard (SCFM) air volume flow under vacuum conditions is defined by the Expanded Air Ratio (EAR). This ratio accounts for changes in air density caused by pressure and temperature variations.

$$\text{EAR} = \frac{\text{ACFM}}{\text{SCFM}} = \left(\frac{30}{P}\right) \left(\frac{T + 460}{520}\right)$$

Where:

• $\text{EAR}$ = Expanded Air Ratio (dimensionless)
• $P$ = Absolute pressure (inches Hg). $P = 29.92$ in. Hg is standard atmospheric pressure.
• $T$ = Temperature (°F)

Calculation Example

To find the actual air volume flow from a known standard flow rate, multiply the SCFM by the Expanded Air Ratio.

Problem: Calculate the actual air flow (ACFM) for a system moving $100 \text{ SCFM}$ of air at $50\%$ vacuum and $70^\circ\text{F}$.

1. Determine Absolute Pressure: $50\%$ vacuum corresponds to approximately $15 \text{ inches Hg}$ absolute pressure ($P = 15$).
2. Apply the EAR Formula: $$\text{EAR} = \left(\frac{30}{15}\right) \left(\frac{70 + 460}{520}\right) = 2 \times \left(\frac{530}{520}\right) \approx 2.038$$
3. Calculate ACFM: $$\text{ACFM} = \text{SCFM} \times \text{EAR} = 100 \times 2.038 = 203.8 \text{ ACFM}$$

SI Unit Consideration

While the primary formula uses imperial units (inches Hg, °F), the principle and diagram referenced in the original source can be adapted for SI units. In this context:

• Actual air flow is denoted as $a_L/s$ (actual liters per second).
• Standard air flow is denoted as $s_L/s$ (standard liters per second).

The Expanded Air Ratio (EAR) remains a dimensionless multiplier to convert between these flow rates under specified pressure and temperature conditions.

References

• Original Source