Determining Viscosity

MolaKule

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This exercise is a bit more involved and requires a Scientific Calculator and is open to all. One way of measuring viscosity is to use a "Rotating Concentric Cylinder" viscosimeter, sometimes called a, "Couette" viscosimeter. A rotating cylinder (the Inner Cylinder), is placed inside another (outer) cylinder and the fluid whose viscosity is to be measured in poured into the gap, g. The Inner Cylinder is rotated at a specific RPM and the amount of Torque to rotate the Inner Cylinder is measured. Note: * is multiplication and X^n is a number raised to the "nth" power since we don't have an equation editor in BITOG. The viscosity is given by: u = T*g/(4*pi^2*R^3*n*L) = Absolute Viscosity in SI units of N.s/m^2 T is torque, measured at 1.8 N.m, g is gap between Inner and Outer Cylinder, or 0.15 cm, Outer Diameter of Inner Cylinder is 12 cm, L is length of each each cylinder which is 40 cm long, n is RPM, 300 RPM R is Radius of Inner Cylinder. Hints: Use 39.48 for 4*pi^2; Convert all given units to meters and seconds; answer will be in N.s/m^2. We will disregard any "end" effects. The result will be a 30 Grade motor oil at ~ 40C.
 
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Showing units: 1.8 N.m × 0.0015 m / [4 × pi^2 × (0.06m)^3 × 5 rev/s × 0.4m] = 0.158314349 N.s/m^2 = 0.2 N.S/m^2, given one significant figure. wink Calculating through the units does indeed show the units you asked for are obtained.
 
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MolaKule

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Originally Posted By: Ohle_Manezzini
Force? Newton * second / square meters
Excellent Garak. happy RPO, had I given you the density you could have determined the Kinematic Viscosity in the SI units of m^2/s or cgs units of centistokes or cSt, with proper conversion coefficients.
 
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Originally Posted By: MolaKule
Excellent Garak.
Thanks. Technically, I shouldn't have put rev/s as a unit in my equation, since revs really aren't a unit. To be rigorous, I should have just used the unit of s^-1. wink
 

MolaKule

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Originally Posted By: Ohle_Manezzini
And the range for a 30 weight oil @ 40C is: 55cP to 82cP! So, this oil isn't a 30 grade at all Sorry Mola, could't resist, just grabbed a coffee wink Cqd,, RPO
RPO, you need more than coffee. grin2 Look at F.M. White's, Fluid Mechanics, McGraw-Hill, 2003. He has a chart of various fluids (Viscosity vs. Temperature) expressed in Absolute Viscosity or N.s/m^2, and the SAE 30 oil [email protected] does indeed pass through the answer given by Garak.
 

MolaKule

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A viscosity curve will pass through various values of Absolute Viscosity verses temperature. For Garak's round-up value of 0.2, the curve is right on at 20C. At 0.1583 N.s/m^2, the curve passes through 26C because of it's slope. I accepted any numerical value between 0.158 N.s/m^2 and 0.2 N.s/m^2.
 
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