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Ans. Thermometric Well Fig. 3.6 shows an arrangement which is used to measure the temperature of gas flowing through a pipeline. A small tube called thermometric well is welded radially into the pipeline.

The well is partially filled with some liquid and the thermometer is immersed into this liquid. When the temperature of the gas flowing through the pipeline is higher than the ambient temperature, the heat flows from the hot gases towards the tube walls along the well.

This may cause temperature at the bottom of well to become colder than the gas flowing around. Obviously the temperature indicated by the thermometer will not be the true temperature of the gas. The error in the temperature measurement is estimated with the help of the theory of fins.

The protective tube (well) can be considered as a hollow fin (internal diameter d,

thickness ö and length 1), and the temperature distribution obtained by using the relation applicable to a fin with tip insulated:

where is the temperature of the pipe wall, ta is the temperature of hot gas or air flowing through the pipeline, and is the temperature at any distance x measured from pipe wall along the thermometric well.

If x = 1 then,

where t1 is the temperature recorded by the thermometer at the bottom of well and represents error in temperature measurement.

The perimeter of the protective well P = and its cross-sectional area Therefore,

then,

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