Steam flow rate is typically measured using orifice plates, nozzles, venturies, or vortex sheading flow meters. All of these devices respond to volumetric flow, not true mass flow. For any fixed volumetric flow, the mass flow will vary with the line pressure. If the absolute pressure is doubled, the density of the steam will double and the mass flow will double even though the volumetric flow rate displayed by the metering device does not change.

In many applications the nominal line pressure is known and assumed to be relatively constant. In this case the flow metering device is calibrated at the nominal line pressure and any mass flow error due to line pressure change is tolerated.

Most steam systems are operated above nominal pressure at low flow conditions. As steam usage increases the boiler pressure often falls below nominal pressure. At locations far from the boiler it is not uncommon to see the line pressure fall to one half the nominal pressure under maximum flow conditions.

The graph in fig. 1 shows the error in mass flow rate caused by line pressure deviation from nominal conditions for conventional flow rate meters.

In applications requiring high accuracy, the line pressure can be measured and used to correct the volumetric flow measurement to obtain true mass flow. Flow measurement systems that do this automatically are available. They are quite complex and very expensive.

In some cases a pressure regulator is installed immediately upstream of the flow measuring device in order to maintain a constant line pressure regardless of the flow rate or boiler pressure. Again this complicates the system and increases the initial cost as well as the cost of maintaining the system. The MAC true mass flow rate steam meters and transmitters operate on a unique principle which allows accurate mass flow rate indication which is unaffected by changes in the line pressure.

### Principle of Operation

The MAC STM Series Steam Meters use a critical flow nozzle and a single pressure gauge to indicate the true mass flow.

The critical flow nozzle allows the steam to reach sonic velocity at the throat of the nozzle at a very low upstream pressure. Due to the laws of physics the sonic velocity at the throat cannot be exceeded. As the upstream pressure increases the volumetric flow rate does not change, but the density of the steam increases with increasing pressure and thus the mass flow rate is proportional to the upstream pressure. The standard MAC Steam Flow Meters indicate 100% flow when the inlet pressure is 75 PSI. A conical diffuser reduces the sonic velocity at the throat back down to the flow velocity in the pipe while recovering up to 90% of the upstream pressure.

Because of the pressure loss across the nozzle this type of meter can only be used in applications where steam is injected into a lower pressure area. Typical applications include humidification, sparging tanks, atmospheric blanchers, steam eductors, steam injection into process ovens, and any other application where steam is exhausted through a manifold or nozzles to a lower pressure.

There are many applications like those mentioned above where the MAC Steam Meters and Transmitters provide a simple, low cost, and accurate way of measuring steam mass flow rate.

### Application Comparison

Fig. 2 shows a typical arrangement for measuring and throttling the flow of steam into an injection process. Let us assume that pressure P4 is atmospheric pressure and that P3 must be 40 PSI above P4 to get to 100% of the desired flow through the manifold and spray nozzles. Also assume that a delta P of 5 PSI across the orifice is equal to 100% flow. When the throttling valve is closed and there is no steam flowing, P3 is equal to P4, and P1 is equal to P2.

When the flow rate is 100%, P1 will drop to 90 PSI, P2 will be 85 PSI, P3 will be 40 PSI. The pressure drop across the throttling valve is equal to P2-P3 which will be 45 PSI.

When a MAC Steam Flow Meter is used, it must be down stream of the throttling valve. This is because with the valve closed, the Mac Steam Flow Meter would indicate full line pressure and full flow if it was upstream from the valve.

Fig. 3 shows the same application with a MAC Steam Flow Meter. The throttling valve has been placed upstream of the MAC Flow Meter. When the valve is closed and there is no steam flowing, P2, P3, and P4 are all at atmospheric pressure. When the flow rate is 100%, P3 will again be 40 PSI. The MAC Flow Meter will indicate 100% flow rate when P2 is 75 PSI. The pressure drop across the throttling valve is then P1-P2 or 15 PSI.

The flow meter in Fig. 2 will indicate approximately 10% low at 100% flow rate due to the drop in line pressure. The flow rate indicated by the MAC Flow Meter in Fig. 3 will be correct even though the line pressure falls to 90 PSI as the valve is opened and the flow rate increases.

Athough the MAC Flow Meter requires 75 PSI upstream to get to 100% flow, up to 90% of the absolute pressure is recovered and is available to cause flow through down stream restrictions such as pipes, Manifolds, and spray nozzles.

MAC Steam Flow Rate Transmitters operate on the same principle as the MAC Steam Flow Meters. The transmitters include a gauge for local flow indication and a pressure transducer and interface electronics to generate an electrical output of zero to 5v DC or 4-20 mA.