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Determining Viscosity #4341288 02/27/17 03:02 PM
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MolaKule Offline OP
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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.




Last edited by wwillson; 03/10/17 06:15 AM. Reason: insert graphics
Re: Determining Viscosity [Re: MolaKule] #4341488 02/27/17 07:10 PM
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Ohle_Manezzini Offline
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66.83 mm square per second.

Re: Determining Viscosity [Re: MolaKule] #4342055 02/28/17 11:20 AM
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MolaKule Offline OP
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Hints: Use 39.48 for 4*pi^2; Convert all given units to meters and seconds; answer will be in N.s/m^2.


I'm a Student Pilot. Frightening, isn't it?
Re: Determining Viscosity [Re: MolaKule] #4342247 02/28/17 03:41 PM
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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.

Last edited by Garak; 02/28/17 03:42 PM.

Plain, simple Garak.

2008 Infiniti G37 - Shell ROTELLA T6 Multi-Vehicle 5w-30, Wix 57356
1984 F-150 4.9L - Quaker State GB 10w-30, Wix 51515
Re: Determining Viscosity [Re: MolaKule] #4342256 02/28/17 03:51 PM
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Force?

Newton * second / square meters

Re: Determining Viscosity [Re: Ohle_Manezzini] #4342306 02/28/17 04:50 PM
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Newtons are the force, this expression is a dynamic viscosity, where 1 N.s/m^2 = 10 P or 1000 cP.


Plain, simple Garak.

2008 Infiniti G37 - Shell ROTELLA T6 Multi-Vehicle 5w-30, Wix 57356
1984 F-150 4.9L - Quaker State GB 10w-30, Wix 51515
Re: Determining Viscosity [Re: Ohle_Manezzini] #4342399 02/28/17 06:47 PM
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MolaKule Offline OP
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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.


I'm a Student Pilot. Frightening, isn't it?
Re: Determining Viscosity [Re: MolaKule] #4342645 02/28/17 10:34 PM
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So the answer can also be expressed as 200 cP at 40C...
Or:

In cst is 200
In Poise is 2
In stokes is 2
In SSU is 927

RPO

Last edited by Ohle_Manezzini; 02/28/17 10:41 PM.
Re: Determining Viscosity [Re: MolaKule] #4342695 02/28/17 11:14 PM
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Garak Offline
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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


Plain, simple Garak.

2008 Infiniti G37 - Shell ROTELLA T6 Multi-Vehicle 5w-30, Wix 57356
1984 F-150 4.9L - Quaker State GB 10w-30, Wix 51515
Re: Determining Viscosity [Re: MolaKule] #4342742 03/01/17 05:16 AM
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Garak Offline
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There, Mola. I made it look pretty, albeit a bit larger than I intended.



Plain, simple Garak.

2008 Infiniti G37 - Shell ROTELLA T6 Multi-Vehicle 5w-30, Wix 57356
1984 F-150 4.9L - Quaker State GB 10w-30, Wix 51515
Re: Determining Viscosity [Re: MolaKule] #4342794 03/01/17 07:29 AM
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Ohle_Manezzini Offline
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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

Re: Determining Viscosity [Re: Ohle_Manezzini] #4343087 03/01/17 03:36 PM
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MolaKule Offline OP
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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.


I'm a Student Pilot. Frightening, isn't it?
Re: Determining Viscosity [Re: MolaKule] #4343277 03/01/17 08:22 PM
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Ah, 20C, Ok, grin

Re: Determining Viscosity [Re: MolaKule] #4343742 03/02/17 01:57 PM
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MolaKule Offline OP
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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.


Last edited by MolaKule; 03/02/17 02:01 PM.

I'm a Student Pilot. Frightening, isn't it?
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