Order of Accuracy

Because the formula for the parallel thermowell is exact, it can be used to check the order of accuracy of the tapered thermowell since by making k equal to 1, the tapered thermowell becomes a parallel thermowell.

Let's take the following dimensions:

L = 300 mm

D1 = 25 mm

D2 = 25 mm

E = 200000 MPa = Pa (Typical value for steel)

r = 7800 kg/m3 (Typical value for steel)

We choose two bore diameters:

1. Do = 6.5 mm

   d = 0.26

   k = 1.0

   Parallel Thermowell Fn: 203.3 Hz

   Tapered Thermowell Fn: 204.1 Hz

2. Do = 19 mm

   d = 0.76

   k = 1.0

   Parallel Thermowell Fn: 247.2 Hz

   Tapered Thermowell Fn: 248.1 Hz

In both cases, the tapered thermowell approximate formula, when applied to a parallel thermowell, gives a natural frequency only 0.3% higher than the exact value. This gives an estimate of the order of accuracy of the formula.