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Oil Level Checking (Again!)


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OK, I am prepared to be shot down, however having followed this after an oil change it works for me. I used the maths below to work out how much the oil would expand when hot as against cold. Did the oil change ran the engine for a minute to get the filter full and the pressure up, then let it stand until the time reverted to the 6 second checks. Topped up oil cold until the last segment was not illuminated. When the car/oil is run up to temperature and then the oil is checked it gives a full indication.

 

Specific volume of a unit can be expressed as

The change in the units volume when temperature change can be expressed as

 

dV = V0 β (t- t0)          (2)

v = 1 / ρ = V / m         (1)

where

v = specific volume (m3/kg)

ρ = density (kg/m3)

V = volume of unit (m3)

m = mass of unit (kg)

 

The density of a fluid when the temperature is changed can be expressed as

where

 

dV = V1 - V0 = change in volume (m3)

β = volumetric temperature expansion coefficient (m3/m3 oC)

t= final temperature (oC)

t= initial temperature (oC)

 

ρ1 = m / V0 (1 + β (t1 - t0))

 

    = ρ0 / (1 + β (t1 - t0))          (3)

where

ρ1 = final density (kg/m3)

ρ0 = initial density (kg/m3)

 

 

Volumetric Temperature Coefficients - β - of some common Fluids
  • water : 0.000214 (1/oC), 
  • ethyl alcohol : 0.00109 (1/ oC), 0.00061 (1/oF)
  • oil : 0.00070 (1/oC), 0.00039 (1/oF)

 

OK, tin helmet on, awaiting flak  :eek:
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Very simple. All you need is the last line - oil expands 0.00039 per degree.

 

Hot engine ~220F and room temp ~75F and that's 145F temp difference. The oil volume expansion is then 0.00039 * 145 = 5.6%

5.6% of 9L of oil = 0.5L

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