Registered User
Join Date: Oct 2006
Posts: 33,142

Thanks Terra, I am familiar with the ideal gas law, I was just trying to figure out what SeanC was values he was using to get his answers. Here's what I get for being mr. streetsmart without calculations.
Volumetric expansions of coolant:
dV = V0 B (t1  t0)
B Water = 0.000214 1/°C
B Ethylene Glycol = 0.00057 1/°C
V0 of E46 Cooling System = ~8.4L
t1 = 100°C
t0 = 0°C
Solving for 50/50 coolant mix
dV = 8.4*.5*(0.000214+0.00057)*(1000)
dV = .329 Liters
Required Change In Volume to get a 2 bar increase in pressure:
Using a modified ideal gas law on the remaining air in the expansion tank(as so clearly explained by TerraPhantm) to find the ratio reduction in expansion tank volume:
V2/V1 = P1T2/P2T1
P1 = 1.013 Bar
P2 = 3.013 Bar
T1 = 273.15 K
T2 = 373.15 K
V1 = Volume of coolant at 0°C and atmospheric pressure
V2 = Volume of coolant at 100°C and atmospheric + 2 bar for expansion tank cap
V2/V1 = (1.013*373.15)/(3.013*273.15)
V2/V1 = 0.459 or 45.9%
So, only factoring the volumetric expansion of coolant with temperature, and the ratio of air before and after coolant expansion to reach the expansion tank venting pressure, the minimum volume of air required to prevent venting through the cap is:
V2 = V1  dV = V1.329
V2/V1 = .459
Solve for V1
V1 = .608 Liters minimum of air in expansion tank to prevent reaching vent pressure.
V2 = .279
checking work, .279+.329=.608, .279/.608=.459; good
There will be some expansion of the block and hoses which will decrease the volumed required a small amount, my guess would be something in the range of .1L or less.
Interpretation of results:
Thinking about this value and looking at the expansion tank, I'd guess the minimum volume is very close to to amount of air that is in the expansion tank when it's properly filled. If you go to a lower pressure radiator cap, you are going to be venting pressure every time the car heats up, and then pulling a little bit of air back in every time the car cools down, and you will lose a small amount of coolant every time through evaporation. With BMW's setup, it seems like the pressure gets very close to the the limit of the expansion tank but doesn't surpass it to prevent very slow coolant losses over time.
Also, with keeping the pressure higher, and having the minimum amount of air volume required, when your engine starts to overheat, the system pressure will increase faster to reduce boiling, and the higher pressure gives a greater safety margin before there is some serious boiling and localized heating, which creates warping. Everything could be modified for a lower pressure, but you just decrease your engine's temperature safety margins, and you will need to increase the expansion tank volume prevent losing however small amount of coolant every warmup and cooldown cycle.
Damn these BMW engineers, I think they are actually pretty darn crafty, even when it comes to something as small as an expansion tank! It's a shame they didn't make the expansion tank just a little bit stronger.
