Siemens Sitrans, LC 500 Applications Examples, Generic Application Calculations, Appendix E

Applications Examples

Generic Application Calculations

The capacitance expected in a cylindrical tank with a probe centrally mounted is estimated using the following formula:

C = ε	-------------------------24 ⋅ L	pF (L in meters) or C =
	Log(D ⁄d)

Where:

C = capacitance value in pF

εr = relative dielectric constant L = active measurement length D = internal tank diameter

d = electrode diameter

24 = a K constant for dimensions in meters

7.32= a K constant for dimensions in feet or inches

εr = 1 (air)

εr = 2 (oil)

ε	-------------------------7.32 ⋅ L	pF (L in feet)
	Log(D ⁄d)

SITRANS LC 500

d = 16 mm (0.05’)

D = 1.0 m (3.28’)

0.25 m (0.82’)

L = 0.95 m (3.12’)

Examples (using dimensions above):

Capacitance in air:

Dimensions in meters:	Cair	= ε	air	----------------------------------24					⋅	0.95		)-		pF = 12.7pF
				Log		(		1		⁄
										0.016
Dimensions in feet:	Cair	= ε	air		-------------------------------7.32 ⋅					0.82	)-		pF = 12.7pF
					Log		(		1	⁄
										0.06

Capacitance in oil:

If the same vessel is filled with oil, relative dielectric constant for oil (2) replaces the relative dielectric constant for air (1), and the resulting calculation is:

Coil =	ε			----------------------------------24				⋅	0.95		-)		pF = 25.4pF		(dimensions in meters)
		oil		Log		(		1	⁄
									0.016
or
Coil =	ε			7.32 ⋅						3.12				pF = 25.4pF	(dimensions in feet)
			---------------------------------------									)
		oil	Log		(		3.28			⁄
										0.05

The initial capacitance value at 0% (probe in air) is 12.7 pF, and the capacitance value for 100% (tank filled with oil) is 25.4 pF.

7ML19985GE01 SITRANS LC 500 – INSTRUCTION MANUAL Page 91

Appendix E