well from what i know the lm317 reg. needs a 3V droput minimum, so it wouldnt wotk for 10V, but perfectly for 8 V.
but there is another thing, some fans from teh computers have internal regulators, switching usually, so lowering the voltage will not always help.
and a suggestion for getting 10V. just use 3 rectifiing diodes(1N4001-4007) in series. considering that a diode has a voltage drop around 0.6-0.7V you will get something like 10.2 to 9.9 volts, wich is good