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Federal Highway Administration Research and Technology
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Publication Number: FHWAHRT09044 

APPENDIXCALCULATIONSIn 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 PenetrationData for specimen W48: test condition was 30 cycles, 2 soaks, 0.5 percent NaCl, and pH 8.
1 inch = 25.4 mm Convert to centimeters: Convert weight per surface area to penetration (divide by density): Also: Convert to mils (1 inch = 1,000 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 CoulombsWhere: I = Current.
Example: For constant, halfscale readings (50 µA) for 15 days converted to coulombs: 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: Where: m = Mass (g). For 1 µ A output per year (recall that C=A × s): For 1 µ A output in an area of 1 cm^{2} and given an iron density of 7.87 g/cm^{3}: 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 10minute 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 PenetrationSensor anode area is the twodimensional ring between the inner washer, r_{1} , and the outer coated perimeter, r_{2}: 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: The calculated mass loss per unit area of the sensor anode is converted to penetration using the density of iron as follows: 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:
Sensor output: From equation 17, 1 µ A/cm^{2} = 0.46 mpy. For a 0.63cm^{2} sensor giving a current reading of 1 µ A, the current density is (1 µ A / 0.63 cm^{2}) = 1.6 µA / cm^{2}, and a sensor reading of 1 µA corresponds to 0.74 mpy as follows:
