Fluids Lab Report 1

EXPERIMENT NO. 1 FALLING SPHERE VISCOMETER I. INTRODUCTION Commercial Falling Sphere viscometers are non-available. One type of which is shown on the sketch. The one available is not of the commercial type. This viscometer makes use of the principles in case of flow around a small sphere. For laminar flow vd/2 ≤ 1 in which d is the diameter of the sphere. The friction or the deformation drag F d of the sphere moving at a constant velocity V through a fluid of infinite extend is given by Stoke’s Law with the following assumptions: 1. The particle must be 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 � µ 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. Fd + Fb – W = 0 ------------------------------------------------- (2) Or

3�µVd + �d3�L/6 – �d3�S/6 = 0 ------------------------------ (3)

Solving for µ:

d 2 (δ S−δ L ) µ= 18 V

------------------------------------------------ (4)

Equation (4) has to be corrected in actual practice because the extent of the fluid is not infinite and the influence of boundary proximity on the sphere is large. The correction is usually affected by multiplying the observed velocity of fall Vs by a certain constant “K” which is a function of d/D m the diameter of the sphere and the medium ratio, such that V = Vs K ---------------------------------------------------------- (5) where: K = 1 + 9d/4Dm + (9d/4Dm)2 The equation for viscosity then becomes

d 2 (δ S −δ L ) μ= 18 V S K For which viscosity can be computed.

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

III.

SKETCH OF APPARATUS

fluid. It only measures under one flow condition. Viscometer – it is an instrument used to measure the viscosity of a

Hydrometer – it is an instrument for

Stopwatch – it is a handheld

determining the specific gravity of a

timepiece designed to measure

liquid

the amount of time elapsed from a

commonly

graduated

tube

consisting weighted

of to

a

particular time.

float

upright in the liquid.

Caliper – an instrument for measuring external Thermometer - an instrument used for measuring temperature or temperature gradient.

or

internal

dimensions,

having two hinged legs resembling a pair of compasses and in-turned or out-turned points.

Steel balls– Balls that are made of steel

which

were

used

in

the

experiment.

IV.

LABORATORY PROCEDURE Determine the temperature and specific gravity of the liquid whose viscosity is desired. Drop cautiously one of the spheres noting whether the

Y (m)

1

1

1

1

1

2

3

4

11.17

10.31

7.16

0.089

0.097

0.140

0.370

Vs (m/s)

Dm (m)

0.0931 0.0931 0.0931 0.0931

d (m)

7.93x10-3 3.99x10-3 3.15x10-3 2.99x10-3

k

0.032 1.029

0.034 1.031

0.043 1.106

0.085 1.228

d/ Dm

0.092

0.100

0.155

0.454

V (m/s)

0.348

0.354

0.366

0.493

(Pa-s)

μ

2.70

t (sec)

2.762x10-4

2.810x10-4

2.905x10-4

3.912x10-4

V (m2/s)

V.

TRIAL NO.

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.

RESULTS

VI.

SAMPLE COMPUTATION Given:

y=1 m

d=0.00793 m

t=2.70 s

D=0.0931 m

Solution: Trial 1:

y 1m V s= = t 2.70 s

= 0.370 m/s

d ( 0.00793 ) = D m ( 0.0931 )

= 0.085

k =1+

9 ( 0.00793 ) 9 ( 0.00793 ) 9d 9d 2 + =1+ + 4 Dm 4 D m 4 ( 0.0931 ) 4 ( 0.0931 )

( )

(

2

)

= 1.228

V =V s∗k =0.370 m/s∗1.228 = 0.454 m/s 2

d ( δ s−δ L ) (0.00793)2 ( 76518−12360.6 ) μ= = 18 V s K 18(0.370)(1.228)

μ 0.493 v= = ρ 1260

VII.

= 0.493 Pa-s

= 3.912 x 10-4 m2/s

CONCLUSION

Viscosity is a measure of a fluid’s resistance to flow. It defines the inner

friction of a fluid which is in motion. Furthermore, a fluid with large viscosity resists motion because its molecular makeup gives a lot of internal friction. On the other hand, a fluid with low viscosity flows easily because its molecular makeup results in a smaller friction value when it is in motion. In this experiment, we need to determine the viscosity of a certain fluid including the ratio of the given diameters, correction constant, velocity of fall and the dynamic viscosity. The ratio of the sphere’s diameter to the diameter of medium is obviously dependent on the two diameters. However, as the diameter of the sphere increases in which the diameter of the medium has a constant value will result to an increase in the ratio. Therefore, the relationship between the ratio of the diameters and the sphere’s diameter is directly proportional. In addition, the bigger the value of the diameter of the sphere will have a higher value in its velocity due to the sphere’s weight. For calculating the viscosity of a liquid, we need the dynamic viscosity and the mass density of the liquid. Having a constant value of the mass density of the liquid, as the dynamic viscosity increases the kinematic viscosity will increase also. Thus, kinematic viscosity is directly proportional to the dynamic viscosity. Possible error that can be obtained in this experiment is human error. Human error can include the inaccuracy of measuring the time as it passes through the one-meter distance in the fluid. With the help of the group, it must be observed properly to record and calculate a correct data. In addition, calculations can also be included in human error. Incorrect computations can lead to a higher percentage error.

VIII. APPLICATION TO ENGINEERING Knowing the concepts and principles of viscosity are essential for engineers. Its use is to measure the resistance of a particular fluid to shear stress and to know how fluids work under a certain conditions. Determining the viscosity of a fluid gives the manufacturers an important product dimension. In addition, viscosity helps the engineers to understand the fluids that is being handled to us and we are working with so that we can know how they are acting or behaving in the environment and to force them to change its behaviour according to our requirements and desires. Furthermore, engineers are frequently designing and building devices that is being accompanied by fluids which includes its transportation, for lubrication and other mechanisms that involves fluids. Thus, understanding the viscosity of a fluid will help the engineers to choose the finest fluid that will operate their designs at the same time will not harm the environment

IX.

REFERENCE

A. Uy, F. A., Tan, F., & Monjardin, C. E. (2015). Laboratory Manual in Fluid Mechanics. B. http://dictionary.com/browse C. https://www.princeton.edu/-gasdyn/Research/TC_Research_Folder/Viscosity_def.html D. https://www.teachengineering.org/lessons/view/cub_surg_lesson03 E. www.brookfieldengineering.com/education.asp