The Padnos School of Engineering by ywp5Yn

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									 Grand Valley State University
The Padnos School of Engineering




     VISCOSITY LAB
    EGR 365 – FLUID MECHANICS




         Brad Vander Veen

           May 13, 2003

           Lab Partners
            Julie Watjer
           Thomas Freundl
PURPOSE:
The purpose of this lab is to experimentally determine the absolute viscosity, , of a fluid
using a Stormer Viscometer and to determine whether the fluid being tested is newtonian
or non-newtonian.

THEORY:
The viscosity of a fluid is a transport property associated with the transport of momentum
through that fluid via intermolecular collisions and intermolecular forces. Fluid
immediately adjacent to a solid surface will move at the surface velocity. This is known
as the no-slip boundary condition and is a direct result of momentum transfer between the
fluid molecules and the solid surface. Moving away from the solid surface the fluid
velocities can change indicating fluid shear stresses. Fluid shear stresses acting over the
surface of a solid body result in fluid forces on that body.


Consider Newton’s Second Law for rotating bodies:


                                     applied   resist  I                           (1)


               -where  is the torque, I is the mass moment of inertia, and  is the
               angular acceleration


Now consider the experimental setup in Figure 1 below:
Applying Equation (1) to the setup:

                                                                                     dw
                           (W  rs )   viscous _ side   viscous _ bottom  I               (2)
                                                                                     dt

Since the angular velocity is constant:


                                 (W  rs )   viscous _ side   viscous _ bottom              (3)


FIRST FIND viscous_side:



It is known that:


                                       viscous _ side  Fviscous _ side  R                    (4)


By definition:


                                                             velocity
                                    Fviscous _ side                A                        (5)
                                                            clearance


                 -where  is the viscosity of the fluid, and A is the lateral surface area of
                 the rotating cylinder


Substituting:


                                                        R 
                                Fviscous _ side            2  R  L                       (6)
                                                         hs

Simplifying:


                                                            R2 
                                   Fviscous _ side              2  L                      (7)
                                                             hs
Substituting (7) into (4):


                                                           R2 
                                   viscous _ side             2  L  R             (8)
                                                            hs
Simplifying:


                                                R3 
                          viscous _ side           2  L                            (9)
                                                 hs

NOW FIND viscous_bottom:




It is known that:


                                    viscous _ bottom   R  dFviscous _ bottom         (10)


By definition:


                                                                velocity
                                    dFviscous _ bottom                 dA            (11)
                                                               clearance


                 -where A is a differential area (ring) on the bottom of the cylinder, and 
                 is the viscosity of the fluid


Substituting (11) into (10):


                                                               velocity
                              viscous _ bottom   R                 dA             (12)
                                                              clearance
Simplifying:


                                                                R 
                             viscous _ bottom   R               2  R  dR      (13)
                                                                 hb

Simplifying:


                                                          2
                                viscous _ bottom                     R        dR
                                                                            3
                                                                                        (14)
                                                           hb
Integrating:


                                                                2 R 4
                                     viscous _ bottom                                (15)
                                                                  hb                4
Simplifying:


                                                                2  R 4
                                      viscous _ bottom                                (16)
                                                                    2hb



The governing equations are now set up for the Viscometer:

For Steady State:

                                              R3                 2  R 4
                            (W  rs )             2  L                           (17)
                                               hs                   2hb


For Full, Unsteady State:


                                       R3                 2  R 4     dw
                    (W  rs )              2  L                   I            (18)
                                        hs                   2hb             dt



NOTE: In this lab the viscous torque from the bottom will be neglected because it is small
compared to the torque created by the viscous torque on the side.
APPARATUS:

ITEM

Stormer Viscometer

Meter stick

Stopwatch

Calipers


Various Masses




PROCEDURE:

1). Measure all pertinent dimensions of the Stormer Viscometer.



2). Set the Viscometer on the edge of a table or something similar at a height of at least 2

meters off the ground.



3). Mark a distance of 1.5 meters off the ground.



4). Hang various masses on the string of the Viscometer, allowing the mass to reach

terminal velocity before the 1.5-meter mark. Time how long it takes for the mass to go

from a height of 1.5 meters to 0 meters (ground).
RESULTS:

Below is a list of the measured properties of the Stormer Viscometer:


                                          rs =30.10 mm
                                          hs =2.52 mm
                                          hb = 12.0 mm
                                          R = 57.65 mm
                                          L = 74.2 mm
                                           m = .95 kg


NOTE: Each measurement above has the last significant digit after the decimal place
estimated


In Table 2 below, the results of the time trials can be seen.


                          TRIAL       MASS(kg)      TIME(seconds)
                             1             0.05           66.3
                             2             0.10           32.6
                             3             0.20           16.1
                             4             0.30           12.7

                                 Table 2 – Time Trial Results


The distance traveled by the mass was 1.5 meters. In Table 3 below, the calculated
velocity of the mass can be seen as well as the angular velocity of the spool.


             TRIAL        VELOCITY (m/s)          ANGLULAR VELOCITY (rad/s)
               1                 0.0226                         0.7516
               2                 0.0460                         1.5286
               3                 0.0932                         3.0953
               4                 0.1181                         3.9239

                                  Table 3 – Velocity Values
ANALYSIS:
Using results from Table 2, the experimental viscosity can be found. Consider the
following equation:


                                                     R3 
                               viscous _ side           2  L                     (9)
                                                      hs


By substituting W  rs in for  , and solving for :


                                                  (rs  W h s )
                                                                                     (19)
                                                  R 3  2L  


The result of inserting velocity values into this equation is seen below in Table 4.


                              TRIAL          VISCOSITY (Ns/m)

                                 1                   0.5536
                                 2                   0.5444
                                 3                   0.5377
                                 4                   0.6362

                                Table 4 – Viscosity Values
CONCLUSION:

The experimental viscosity of the glycerin used in this lab experiment was found by
averaging the results from trails one, two, and three. The fourth trial was excluded
because of the difficulty in measuring the velocity of the falling mass. It was hard to
measure the velocity because of the errors in starting and stopping the stopwatch on time.
Since in the fourth trail, the mass was falling the fastest, the error in starting and stopping
was amplified. Therefore, the experimental viscosity is as follows:
                                                   1   2   3
                                              
                                                         3
                                                 .55 Ns/m2


Since the experimental viscosity of the fluid did not change as we doubled, and even
quadrupled the falling mass, it can be assumed that glycerin is Newtonian Fluid.

ERROR CALCULATION:
The propagated error in this lab is as follows:


                           U rs            U t 2 U hs 2        U         U          U
           error  4  (          )2  (       ) (    )  9  ( R ) 2  ( L ) 2  ( L ) 2
                            rs             t       hs           R        L          L

                        .01 2       1       .01 2        .01 2        .1 2        .1 2
       error  4  (          )  ( )2  (      )  9(        ) (         ) (       )
                       60 .20      32      2.52         57 .65      1500 .0      74 .2


                                           propagated error = .03


Therefore, the viscosity of the glycerin with error calculation is .55  .03 Ns/m.


The recognized value of the viscosity of glycerin at room temperature is 0.8 Ns/m
The experimental value found in this lab was .55 Ns/m. Therefore the discrepancy
between the two is 0.25 Ns/m. This turns out to be a % error of 31.25%.

								
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