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Print( ' Centered difference took %f seconds' % (time.time() - tc1)) Print( ' Backward difference took %f seconds' % (time.time() - tb1)) # set first element by forward difference dyb = (y - y)/(x - x) '''and now a backwards difference''' tb1 = time.time() Print( ' Forward difference took %f seconds' % (time.time() - tf1)) # set last element by backwards difference dyf = (y - y)/(x - x) ''' lets use a forward difference method: that works up until the last point, where there is not a forward difference to use. they are surprisingly fast even up to 10000 points in the vector. Synthetic oils have higher viscosity indices making them superior to the mineral oils in this regard as well.''' These are the brainless way to calculate numerical derivatives. For lubrication purposes there is an optimal viscosity for every engine and the less the oil deviates from this optimum, the better. (Remember the discussion about the monograde and multigrade oils before? Monograde oils’ viscosities change more as temperature changes multigrade oils’ change less so multigrade oils have higher viscosity indices.) We like oils with higher viscosity indices more because it means that the oil is more stable viscosity-wise. Those that change less have a higher viscosity index, those that change more have a lower one. Some oils change their viscosity more when temperature changes some change less. However, the degree of this temperature related change of viscosity is not the same in case of every oil. The hotter the temperature gets the lower is the viscosity, the colder it gets the higher the viscosity. Viscosity (actual viscosity, not the viscosity grade) changes with temperature. API SN or GM Dexos 2) required by the car manufacturer then the oil should meet those specifications and should also have the correct viscosity in order to be used for that particular vehicle. It’s important to keep in mind that viscosity is not the only important property of the oil: if there are some further specifications (e.g. Older cars are usually ok with a 10W-30 oil, while newer cars usually like a lower viscosity oil, like 5W-30, 0W-30 or sometimes even 0W-20.
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As a rule of thumb always follow the car manufacturer’s recommendations. There is no single best motor oil viscosity. Monograde oils are still used for special purposes but usually not as engine lubricants. These oils can be used regardless of season. Thanks to the synthetic base oils and the viscosity modifier additives, nowadays most motor oils are so-called multigrade oils that don’t change their viscosity with temperature that much, so they meet the limits of a winter and that of a summer viscosity grade at the same time. These products were monograde oils and car owners had to change oil at least twice a year: once for the winter and once for the summer. Several decades ago motor oils either fell in one of the winter viscosity grades or in one of the summer viscosity grades. The numbers that have a W after them are the so-called winter viscosity grades while the numbers that don’t have a W are the so-called summer- or operating temperature viscosity grades. SAE J 300 - Table of engine oil viscosity grades Low-Shear-Rate Kinematic Viscosity (cSt) at 100 ☌ max. Low-Shear-Rate Kinematic Viscosity (cSt) at 100 ☌ min. Low-Temperature (☌) Pumping Viscosity, cP max with no yield stress Low-Temperature (☌) Cranking Viscosity cP max. These limits are listed in the SAE J 300 table: SAE Viscosity Grade In case of engine oils, these grades, also known as “weights” were set by the SAE (Society of Automotive Engineers) and in order for a fluid to fall in a given category it has to meet certain limits. The viscosity is measured in mPa*s (millipascal-seconds) or its equivalent cP (centiPoise) but in everyday life we don’t use the actual measured viscosity, we use viscosity grades instead. In case of lubricants the viscosity is very important because it affects the oil’s ability to reduce friction and transfer heat.
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Viscosity is a fluid’s resistance to flow.