exp1 fallingsphereviscometer madrazo,rolandallen

8/3/2019 Exp1 FallingSphereViscometer MADRAZO,RolandAllen

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Mapua Institute of TechnologySchool of Civil Engineering Environmental and Sanitary Engineering

Hydraulics Laboratory

Name: MADRAZO, Roland Allen T.

Student #: 2008106905

Program & Year: CE-3

Course code & Sec: CE140-OP / B2 (Fluid mechanics)

Group #: 1

Group Members: ANTONIO, Alvin Kim

COLUMNA, Regor Leuric

VIRAY, Jervis Jewel

Date Performed: October 21, 2010

Date Submitted: October 27, 1010 Ratings

Engr. Fibor J. Tan

Instructor

Experiment No.1

Title: FALLING SPHERE VISCOMETER


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EXPERIMENT NO. 1

FALLING SPHERE VISCOMETER

Commercial Falling Sphere viscometers are non-available. One type of which isshown on the sketch. The one available is not of the commercial type this viscometermakes use of the principles in case of flow around a small sphere.

For laminar flow vd/2 1in which d is the diameter of the sphere. The friction orthe deformation drag Fd of the sphere moving at a constant velocity V through a fluid ofinfinite extend is given by Stokes Law with the following assumptions:

1. The particle must be a sphere.2. The surface of the particle must be smooth.

3. The resistance to fall or drag force Fd is due to the viscosity of the fluid.4. The terminal velocity must be constant.

Fd = 3 Vt d ------------------------------------------------ (1)

A free body diagram of the sphere after it has acquired constant velocity or terminal velocity is

shown on the sketch where W is the weight of the sphere. Fb is the buoyant force and Fd is the

deformation drag.

+ = 0 (2)

Or 3 + 3/6 3/6 (3)

Solving for :


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= 2( ) (4)

18V

Equation (4) has to be corrected in actual practice because the extent of the fluid is not infinite

and the influence of the boundary proximity on the sphere is large. The correction is usually affected

by multiplying the observed velocity of fall VSby a certain constant K which is a function of d/Dm the

diameter of the sphere and medium ratio, such that

V = VS K (5)

Where

K = 1 + 9d/ 4 Dm (9d/4 Dm)2

The equation for viscosity then becomes

= d2(SL) / 18VSK

for which the viscosity can be computed.

OBJECTIVE:

The purpose of this experiment is to determine the viscosity of a certain fluid.

APPARATUS:

Viscometer stopwatch caliper steel balls

Hydrometer thermometer

LABORATORY PROCEDURE:

Determine the temperature and specific gravity of the liquid whose viscosity is desired. Drop cautiously

one of the spheres noting whether the sphere is guided correctly or is off center. Determine the time

required for the sphere to travel a certain distance. Repeat the procedure for each sphere.

REPORT:


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From the data obtained in the laboratory, compute for each run

1. (a) Ratio of sphere diameter to diameter of medium, d/Dm

(b) Correction constant, K

(c) The observed velocity of fall, VS

(d) Dynamic Viscosity,

2. Using the computed value of dynamic viscosity , compute for the Kinematic Viscosity v.

v = / L

3. Plot VS versus d/Dm


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FINAL COMPUTATION SHEET

TRIAL NO. 1

VS = Y/t = 1m/ 3.42s = 0.29m/s

d/Dm =0.0063/ 0.09285 = 0.07

K = 1 + 9d/ 4 Dm (9d/4 Dm)2

K = 1 + (9*0.0063/ 4*0.09285) (9*0.0063/ 4*0.09285 )2

K = 1.19

s = 7350*9.81= 72103.5

l = 1280*9.81 = 12556.8

V = VS K = 0.29*(1.19) = 0.35m/s

= d2(SL) / 18VSK

= 0.006632(72103.512556.8) / 18*0.35

= 0.42 Pa-s

= vp ; v ; /p = 0.42/1280 = 3.28 x 10^-4


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0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.03 0.05 0.09

Vs Vs d/Dm

Vs versus d/Dm

ANSWERS TO THE QUESTIONS


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RESULTS AND DISCUSSIONS

The experiment was about testing of the viscosity of a certain fluid which is glycerine. The small steel

balls with differtent sizes was used to be submerged in the fluid. Each ball have their respective time

ith their different corresponding sizes.

The steel balls have different sizes. The smaller the ball, the slower it will sink to the bottom of the

tube. It is directly proportional. The results for both dynamic and kinematic viscosity have a little

discrepancy.

Sources of error must be the incorrect reading of the diameter by using the calibre. Inaccurate start

and stop times may have a small error. I suggest to use an instrument like a photogate to get the exact

time when it passes the mark.

Some practical applications seen is when the speed of the submerging ball is slower due to viscosity of

the glycerine. Viscosity is commonly perceived as the thicknes or resistance to flow. A good application

of this is designing a pipeline of a certain fluid in order to counter the shear force it produces and for

the fluid to flow smoothly.


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CONCLUSION

Viscosity is the measure of the resistance of a fluid to being in a deformed position by either shear

stress or extensional stress. In this experiment, we determined the viscosity of a ball in glycerine. f a

specific layer of a liquid is taken, the layer below it moving with lesser velocity, tries to decrease the

velocity of upper layer due to cohesive forces between the molecules of adjacent layers. In turn the

upper layer which is moving with greater velocity tries to increase the velocity of the lower layer. Thus

between parallel, successive layers of a liquid in motion, opposing force comes into play tending to

decrease the relative velocity between the layers. The force is called viscous drag. It looks like a

tangential shearing force is acting between the layers. To overcome these forces and for maintaining

constant velocity between layers, an external force need to be applied. If there is no external force,

the velocity of flow decreases and becomes zero. From the results that we have attained, we therefore

conclude that the values for dynamic and kinematic viscosity were that the dynamic had a lager value

than the kinetic one. The steel balls have different sizes. The smaller the ball, the slower it will sink to

the bottom of the tube. It is directly proportional. The results for both dynamic and kinematic viscosity

have a little discrepancy.


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REFERENCE:

en.wikipedia.org/wiki/Viscosity

www.britannica.com/.../fluid-mechanics/.../Measurement-of-shear- viscosity -

www.tutorvista.com/physics/fluid-mechanics-viscosity - United States

www.engineeringtoolbox.com/fluid-mechanics-t_21.html

www.efm.leeds.ac.uk/CIVE/CIVE1400/.../Fluid_mechanics.htm -

exp1 fallingsphereviscometer madrazo,rolandallen

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