How to Calculate Thermowell Length?

There's a couple considerations in determining thermowell immersion lengths, because strength versus fast response is a balancing act.

1) speed of response: the skinnier/thinner the thermowell, the faster the response; the fatter the thermowell, the slower the response.

2) Avoiding conduction error where the thermowell loses heat to the outside due to conduction and radiation (a temperature gradient develops along the thermowell) and the thermowell tip (where the sensor is located) does not get to the same temperature as the fluid.

3) Structural damage, meaning thermowell breakage, due to vibration from the frequency of vortex wakes around the thermowell. A wake frequency calculation for thermowells can be done to determine the mechanical strength of the thermowell with respect to static and dynamic stresses in relation to the operating temperature. ASME has had a standard for since 1974, which was revised as recently as 2010, the ASME PTC 19.3 TW-2010

At least one thermowell vendor has an on-line ASME calculator (requires registration); other vendors will run a calc in-house when you submit a spec sheet with operating conditions.

http://www.jms-se.com/Apps/Tools/ThermowellDesign/Home.aspx

4) Placement error: where the process 'profile' is not uniform, meaning which temperature is the one that's needed.

5) Rules of thumb I have heard over the years

a) 10x diameter of the well (Liptak)

b) Minimum 3" depth, plus the sensor setback from the tip

c) in the center of the pipe

d) get tip into "middle 1/3 of the pipe"

e) insertion depth = 4x tip diameter

You pay your money, you take your choice of rules-of-thumb.