Quiz Corner: Flow error from expected temperature fluctuations

A flowmeter that measures velocity is designed to measure the flow of a gas whose temperature is controlled within 3°C of its setpoint of 27°C. What is the approximate flow error resulting from the expected temperature fluctuation?  

A. ±1 percent

B. ±3 percent

C. ±5 percent

D. ±10 percent

The output of a flowmeter that measures fluid velocity will increase (or decrease) linearly as the size of the fluid increases (or decreases). Therefore, the effect of a 3°C temperature change on the flow measurement depends upon the amount by which the gas volume changes. 

One might be tempted to select Answer D because the temperature change is almost 10 percent (27°C to 30°C). However, the change in size of the gas is related to the change in its absolute temperature, which is relative to the temperature at which all heat is removed — not relative to the freezing and boiling points of water. 

The setpoint of 27°C was, not coincidentally, chosen for this application because it approximates room temperature and corresponds to an absolute temperature of 300 Kelvin. A 3°C temperature change represents a 1 percent change in absolute temperature and a 1 percent volume change (Charles’ Law), so Answer A is correct. 

The answer may seem academic but a deeper understanding reveals that even relatively small temperature variations under nonextreme operating conditions can have a significant effect on flowmeter performance, especially since flowmeter accuracy specifications are often better than 1 percent of rate. The effect under actual conditions can be dramatically larger. 

Additional complicating factors

Flowmeters that do not measure linearly as a function of velocity will exhibit different relationships. For example, a differential pressure flowmeter will exhibit approximately one-half the error as compared to a linear flowmeter. In contrast, thermal flowmeters should not be affected by temperature variations.