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Publication Number: FHWA-HRT-09-044
Date: October 2009

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APPENDIX

CALCULATIONS

In this appendix, calculations that were used to convert laboratory measurements to units in text, tables, and graphs are provided as examples.

Example 1. Convert Weight/Area (Corrosion in g/inches2) to mils (or mm) Corrosion Penetration

Data for specimen W48: test condition was 30 cycles, 2 soaks, 0.5 percent NaCl, and pH 8.

Typical Data Weight
(Initial)
Weight
(Final)
Area
(L by Wx2)
Corrosion
( wt/inches2 )
Coupon W48 124.90766 g 119.02947 g 34.16 inches2 0.1721 g/inches2

1 inch = 25.4 mm
1 oz = 28.35 g

Convert to centimeters:

Equation 9. Convert corrosion to centimeter units. The quantity 0.1721 g per inch squared times the quantity inch per 2.54 cm closed quantity squared equals 1 g per 2.54 squared cm squared equals 0.02667 g per cm squared.

Convert weight per surface area to penetration (divide by density):

Equation 10. Convert weight per surface area to penetration. The quantity 0.02667 g per cm squared divided by 7.87 g per cm squared equals 0.00339 cm.

Also:

Equation 11. Convert centimeters to millimeters. The quantity 0.00339 cm times 10 mm per cm equals 0.0339 mm.

Convert to mils (1 inch = 1,000 mils):

Equation 12. Convert to mils units. The quantity 0.00339 cm times 1 inch per 2.54 cm times 1,000 mils per inch equals 1.33 mils.

These are the penetration rates in mm, m, cm, or mils for corrosion occurring on one surface. In the case of corrosion occurring on both sides, the overall thickness loss would be doubled.

Example 2. Conversion of ZRA Current to Coulombs

Equation 13. Conversion of ZRA current to coulombs. i times t equals uppercase C, parentheses quantity uppercase A times s equals uppercase C closed parentheses.

Where:

I = Current.
t = Time.
A = Amperes.
s = Seconds.
C = Coulombs.

  • ZRA data logger recorded averaged current (i) each hour.

  • The eight-bit analog-to-digital converter stored the sum of six readings in hexadecimal format, that is, the summed eight-bit readings (0 to 255 hex) were summed to give a value between zero and 05 FA (hex) and stored.

  • Stored data were downloaded from the logger to the computer. Scaling was 255 (hex) = 100 µ A (full-scale).

  • Microsoft Excel® macro converted hexadecimal to decimal, divided by 6, and scaled by 100/255.

  • The result was µ A average current reading per hour.

  • The Microsoft Excel® macro also summed the hourly average current readings (in microamperes) and multiplied them by 3,600 s to yield microcoulombs (i × t = C).

Example: For constant, half-scale readings (50 µA) for 15 days converted to coulombs:

Equation 14. Calculate current of 50 µA for 15 days to coulombs. # uppercase C equals quantity 50 times 10 to the -6 power times uppercase A closed quantity times uppercase C divided by the quantity uppercase A times s closed quantity times 15 days times 24 hours per day times 3,600 seconds per hour equals 64.8 uppercase C.

Note that the data logger recorded a value equal to an average current value each hour. In this example, 0.18 C was measured each hour. Summing (integrating) these hourly values for 15 days yielded 64.8 C.

Example 3. Conversion of Sensor Output (µA) to Corrosion Rate (mpy or mmpy)

Faraday's Law of Electrolysis:

Equation 15. Faraday's law of electrolysis. m equals uppercase I times t times a divided by the quantity n times uppercase F.

Where:

m = Mass (g).
I = Current (A).
t = Time (s).
a = Atomic weight; (g).
n = Number of equivalents, eq, (number of electrons exchanged, for Fe = Fe2+ + 2e- ).
F = Faraday's constant, 96,500 C per equivalent.

For 1 µ A output per year (recall that C=A × s):

Equation 16. Calculation using Faraday's law. m equals uppercase I times t times a divided by the quantity n times uppercase F equals the quantity 10 to the -6 power times uppercase A closed quantity times the quantity 3.15 times 10 to the 7 power times s closed quantity times the quantity 55.8 grams per mole closed quantity all divided by the quantity 2 eq per mole closed quantity times the quantity 96,500 uppercase C per eq closed quantity equals 0.0091 grams.

For 1 µ A output in an area of 1 cm2 and given an iron density of 7.87 g/cm3:

Equation 17. Conversion of current density in µA units to corrosion penetration per year.

Equation 17 demonstrates the conversion of constant or average current density to mils per year or mm per year. The data logger provided the average of six current measurements at 10-minute intervals each hour. These hourly averages are summed and presented in table 15.

Example 4. Comparison of Mass Loss and Sensor Results in Terms of Penetration

Sensor anode area is the two-dimensional ring between the inner washer, r1 , and the outer coated perimeter, r2:

Equation 18. Sensor anode area calculation. Uppercase A subscript sensor equals pi times the quantity r subscript 2 squared minus r subscript 1 squared closed quantity equals pi times the quantity 0.375 inches squared minus 0.250 inches squared closed quantity times the quantity 2.54 cm per inch closed quantity squared equals pi time 0.504 cm squared equals 1.58 cm squared.

To calculate the mass loss from the downloaded converted sensor output (microamperes), substitute C = A × s, (i.e., replace It in equation 15 with the coulomb value). For example, use the first value (7,261 µ A) in table 15 that is an hourly value requiring conversion to seconds (1 h = 3,600 s) as follows:

Equation 19. Calculate mass loss from integrated current using Faraday’s Law. m equals uppercase I times t times a divided by n times uppercase F equals the quantity 7,261 times 10 to the power minus 6 times uppercase A times h times 3,600 s per h times 55.8 g per mole closed quantity divided by the quantity 2 eq per mole times 96,500 uppercase C per eq close quantity equals 0.0076 g.

The calculated mass loss per unit area of the sensor anode is converted to penetration using the density of iron as follows:

Equation 20. Convert corrosion mass loss to penetration. 0.0076 g divided by 1.58 cm squared times cm cubed divided by 7.87 g times 10 mm divided by cm equals 0.0061 mm.

For the cable sensor, no direct comparison with weight loss was possible with the available data. An estimate of corrosion rate (penetration) was made based on sensor area and current output.

Area calculation where:

Anode wire diameter = 0.08 cm.
Active length = 2.5 cm.
Anode area is π dl = 3.14 × 0.08 cm × 2.5 cm = 0.63 cm2.

Sensor output:

From equation 17, 1 µ A/cm2 = 0.46 mpy. For a 0.63-cm2 sensor giving a current reading of 1 µ A, the current density is (1 µ A / 0.63 cm2) = 1.6 µA / cm2, and a sensor reading of 1 µA corresponds to 0.74 mpy as follows:

Equation 21. Convert sensor current to penetration. 1 microampere divided 
by 1.6 microamperes equals 0.46 mpy divided by x. Thus, x equals 0.74 mpy.

 

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