Rotary Meters

Introduction

The Rotary Meter Values calculator determines the volumetric flow rate through a rotary positive displacement meter, or calculates the required inlet pressure for a target flow rate, under specified operating conditions. The calculator applies a pressure-based capacity adjustment that corrects the meter’s published rated capacity to actual field conditions, accounting for operating pressure, temperature, gas specific gravity, compressibility factor, and base conditions. There is no consensus standard for sizing rotary meters — the calculator implements a single derived method based on empirical industry references. Results should ALWAYS be evaluated alongside the specific meter manufacturer’s documentation, particularly regarding rotor speed limits.

Background

Pressure and Capacity

Rotary meters are a type of positive displacement (PD) meter, a category that also includes diaphragm meters. Positive displacement devices measure gas flow by repeatedly filling and emptying a chamber of known, fixed volume. Each fill-and-empty cycle represents a discrete, measurable quantity of gas at the prevailing pressure and temperature. By counting these cycles, the meter accumulates a running total of the volume passed through it.

Manufacturers rate rotary meters at a specific inlet pressure. For example, a meter might carry a nameplate rating of 11,000 cfh at an inlet pressure of 0.25 inches W.C. It has long been industry practice to operate rotary meters at pressures other than their rated conditions — particularly at higher pressures — to handle larger flow applications with a smaller, less expensive meter body.

Because gas is compressible, the mass of gas contained in the meter’s reference chamber varies with pressure. Increasing the chamber pressure increases the number of standard volumes of gas the chamber holds at each cycle, which in turn increases the number of standard volumes the meter can measure per unit time. The fundamental relationship between pressure and volumetric flow rate is therefore the primary lever for adjusting a rotary meter’s effective capacity beyond its nameplate rating.

Meter sizing equations use this pressure-volume relationship to convert between the meter’s rated conditions and the actual operating conditions. The rated capacity is first corrected to the specified base pressure and temperature, then further corrected for the actual flowing pressure, temperature, specific gravity, and compressibility factor.

Meter Speed and Physical Limits

Increasing the differential pressure across the meter increases the rotational speed of the impellers. While higher speed increases the volumetric throughput, each rotary meter has a manufacturer-specified maximum speed. Exceeding this limit is likely to cause immediate or premature mechanical failure. Technical Toolboxes does not predict rotor speed and does not enforce speed-limit constraints — operators must consult the manufacturer’s documentation to confirm that the calculated operating point does not exceed the meter’s physical limits.

When sizing a rotary meter for a service, consideration should also be given to diversity of the downstream load. Where many gas-using appliances or pieces of equipment are present, the total connected load is typically derated by a coincidence or diversity factor to arrive at the design flow rate used for meter sizing.

Equations

Generic Rotary Meter Flow

The flow rate at flowing (metered) conditions is calculated in two steps. First, the meter’s rated capacity is converted to the specified base conditions:

Q_R = Q_{RATED} \times \left[\frac{P_{BR}}{P_B}\right] \times \left[\frac{T_B}{T_{BR}}\right] \times \left[\frac{Z_B}{Z_{BR}}\right]

Q_R = Q_{RATED} \times \left[\frac{P_{BR}}{P_B}\right] \times \left[\frac{T_B}{T_{BR}}\right] \times \left[\frac{Z_B}{Z_{BR}}\right]

This base-corrected capacity is then adjusted to the actual flowing conditions:

Q_F = Q_R \times \left[\frac{P_F}{P_R}\right] \times \left[\frac{SG_R}{SG}\right]^{0.5} \times \left[\frac{T_R}{T_F}\right]^{0.5} \times \left[\frac{Z_R}{Z_F}\right]^{0.5}

Q_F = Q_R \times \left[\frac{P_F}{P_R}\right] \times \left[\frac{SG_R}{SG}\right]^{0.5} \times \left[\frac{T_R}{T_F}\right]^{0.5} \times \left[\frac{Z_R}{Z_F}\right]^{0.5}

Where:
Q_F − Meter capacity at flowing (metered) conditions, ft³
Q_R − Meter capacity at rated conditions converted to specified base pressure and temperature, ft³
Q_RATED − Meter capacity at rated base pressure and temperature, ft³
P_B − Base pressure, psia
P_BR − Base pressure at rated conditions, psia
P_F − Pressure at flowing (metered) conditions, psia
P_R − Pressure at rated conditions, psia
SG − Specific gravity of flowing (metered) gas
SG_R − Specific gravity at rated conditions
T_B − Base temperature, °R
T_BR − Base temperature at rated conditions, °R
T_F − Temperature at flowing (metered) conditions, °R
T_R − Temperature at rated conditions, °R [Assumed to be 60 °F/ 519.67 °R]
Z_B − Compressibility factor at specified base conditions
Z_BR − Compressibility factor at rated base conditions [Assumed to be 1.0]
Z_F − Compressibility factor at flowing (metered) conditions
Z_R − Compressibility factor at rated conditions

Absolute pressures are derived from gauge readings as follows:
P_F = P_FG + P_ATM
P_R = P_RG + P_{R_ATM}

Where P_FG and P_RG are gauge pressures (psig) and P_ATM, P_{R_ATM} are the respective atmospheric pressures (psia). Atmospheric pressure may be entered directly or calculated from elevation using the AGA method, as configured in Base Conditions.

Rated Capacity Adjustment Factor

The Rated Capacity Adjustment Factor expresses the ratio of the actual flowing capacity to the meter’s nameplate rated capacity:

FACTOR = \frac{Q_F}{Q_{RATED}}

FACTOR = \frac{Q_F}{Q_{RATED}}

Where:
FACTOR − Rated Capacity Adjustment Factor, dimensionless
Q_F − Meter capacity at flowing (metered) conditions, ft³
Q_RATED − Meter capacity at rated base pressure and temperature, ft³

A factor greater than 1.0 indicates the meter can pass more standard volume flow than its nameplate capacity under the given operating conditions. The factor incorporates adjustments for operating pressure, temperature, differential, specific gravity, compressibility factor, atmospheric pressure, and base conditions.

Case Guide

Part 1: Create Case

Input Parameters

Part 2: Outputs/Reports

Results

References

• American Gas Association — Measurement, GEOP Series Book M-1, 1993.
• DMD Dresser — The Application of Temperature and/or Pressure Correction Factors in Gas Measurement, RM 135, 1999.

FAQ