Can the hydraulic system you designed power a gurney through Guatemala?

Challenge Question:
What is the viscosity of hydraulic fluid with a kinematic viscosity index of 300 and that is exposed to a temperature of 50 degrees Farhenheit?

You and your team are creating an adjustable hospital gurney to be used in a medical clinic in Guatemala. The gurney can be raised or lowered thanks to the hydraulic system you designed. However, the surgical team has decided to go a step further, and will be taking the gurneys to remote villages in the mountains where it can easily drop to 50oF. If you are using a hydraulic fluid with a kinematic viscosity index of 300, what is the viscosity at this temperature (in units of mm2/s)? This is important because if the fluid is too viscous, your gurney won't work!
(Hint: You can calculate this using the Walther equation)


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Kendall Fosse's picture

I will admit I had never even heard of Viscosity Index or the Walther equation before this. A few minuets of googleing reveals that: Viscosity Index (VI) is a measure of the rate of change in a fluids viscosity with changing temperature, with larger values indicating a smaller change in viscosity with temperature. The Walther equation is Log ( Log ( v + 0.7 )) = A + B Log T Where logs are base 10, v is kinematic viscosity, T is temperature and A and B are constants. I presume VI is found by using one or both of the constants from the Walther equation ( I deduced this from an article "Characterizing the viscosity–temperature dependence of lubricants by molecular simulation" McCabe, et al. 2001. Where the method for calculating a viscosity number is described as being similar to calculating a viscosity index). Given the viscosity index one should be able to determine the constants for the Walther equation and solve for kinematic viscosity. As I eluded to earlier there is a problem, I have no idea what the equation for VI is. Google searches for viscosity index often turn up references to ASTM D2270 but do not provide the equation. According to the American Society for Testing and Materials they would be willing to share their standardized method for calculating VI with me for the low low price of $38.00. So here is the question. Do I need to pay 38$ to solve this problem, or is there another way?