What you have is a circular slide rule. In this case, I suspect that the bezel is fixed, so basically you have a slide rule to do do conversion from US Gallons to Liters. On your watch you have both the inner and outer scale reading from 10 to 90. This is a C and D log scale.
When using the slide rule, remember to ignore the decimal place, but use the the two digits closest to your input value. For example if you want to input 5, you look at 50, if you want to input 2.5, you look at 25. If you want to input 100, you look at 10, 230 you look at 23. You adjust the decimal place after the calculations.
Since your bezel is fixed (sorry if I am wrong), the calculations is rather simple. 1 US Gallons is 3.79 liters. So if you want to calculate say how many liters is 20 US Gallons, look at 20 on the inner scale and it will align to about 76 liters. If you want to know how many liters is 3.5 US Gallons, you look at 35 on the inner scale and it will align with 13.3 liters.
Hope that helps.
