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### Static Temperature vs Total Temperature Formula and Calculator

Static Temperature Versus Total Temperature Formula and Calculator

When a fluid stream impinges on a temperature-sensing element such as a thermometer or thermocouple, the element is at a temperature greater than the true stream temperature. The difference is a fraction of the temperature equivalent of the stream velocity te.

te = ( 3600 · V2 ) / ( 2 · gc · J · cp )

Where:

te = temperature equivalent of stream velocity, °F
V = stream velocity, fpm
gc = gravitational constant = 32.174 lbm·ft/lbf ·s2
J = mechanical equivalent of heat = 778.3 ft·lbf /Btu
cp = specific heat of stream at constant pressure, Btu / ( lbm·°F )

1 kj / (kg × °C) =.23885 Btu / ( lbm °F )

This fraction of the temperature equivalent of the velocity is the recovery factor, which varies from 0.6 to 0.8°F for bare thermometers to 1.0°F for aerodynamically shielded thermocouples. For precise temperature measurement, each temperature sensor must be calibrated to determine its recovery factor. However, for most applications with air velocities below 2000 fpm (or Mach number M below approximately 0.1), the recovery factor can be omitted.

Various sensors are available for temperature measurement in fluid streams. The principal ones are the static temperature thermometer, which indicates true stream temperature but is cumbersome, and the thermistor, used for accurate temperature measurement within a limited range.

Related:

References:

Dow Chemical (2001b)