Mapua Institute of Technology School of Civil Engineering Environmental and Sanitary Engineering

Hydraulics Laboratory

Name: DEL ROSARIO, Johndem F.

Student #: 2007180011

Program & Year: CE-3

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

Group #: 10

Group Members: SANTOS, Emil Carl D. / FELICIA, Timothy Daniel DJ

Date Performed: 10/14/10

Date Submitted: 10/28/10 Rating

Engr. Fibor J. TanInstructor

Experiment No.: 1

Title: FALLING SPHERE VISCOMETER

EXPERIMENT NO. 1FALLING SPHERE VISCOMETER

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 ≤ 1in which d is the diameter of the sphere. The friction or the deformation drag Fd 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 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 π μV td ------------------------------------------------ (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 πμVd+π d3 δL/6−π d3δ s/6 (3)

Solving for 𝓊:

μ=d2(δ s−δL) (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 VS by 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

𝓊 = d2(δS – δL) / 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 ballsHydrometer thermometer

2LABORATORY 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:

From the data obtained in the laboratory, compute for each run1. (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, 𝓊2. Using the computed value of dynamic viscosity “𝓊”, compute for the Kinematic

Viscosity “v”.v = 𝓊 / ρL

3. Plot VS versus d/Dm

FINAL DATA SHEET

NAME: DEL ROSARIO, Johndem F. DATE: 10/14/10SUBJECT & SECTION: CE140-0P / B2 GROUP NO. 10SEAT NO.

EXPERIMENT NO. 1

FALLING SPHERE VISCOMETER

GROUPNO.

TRIALNO.

Y(m)

t(sec)

VS

(m/s)d

(m)Dm

(m)d/Dm k V

(m/s)𝓊

(Pa-s)v

(m2/s)

1

1 1 7.32 0.14 0.00476 0.09285 0.05 1.13 0.16 0.47 3.7x10-4

2 1 26.50 0.04 0.00241 0.09285 0.03 1.06 0.042 0.45 3.5x10-4

3 1 3.39 0.29 0.00792 0.09285 0.09 1.23 0.357 0.58 4.5x10-4

4 1

FINAL SAMPLE COMPUTATION

TRIAL NO. 1

Vs = Yt

= 1 m7.32 s

= 0.14 m/s

dD m

= 0.00476 m0.09285 m

= 0.05

K = 1 + 9d4D m + (9d

4Dm )2

K = 1 + 9(0.00476)4(0.09285) + [9(0.00476)

4(0.09285) ]2

= 1.13

V = (Vs)(K) = (0.14 m/s)(1.13) = 0.16 m/s

γs = (ρs)(g) = (7350 kg/m3)(9.81) = 72103.5 KN/ m3

γL = (ρL)(g) = (1280 kg/m3)(9.81) = 12,556.8 KN/ m3

μ = d2(γ s- γ L)

18(Vs)(K) = (0.00476)2(72103.5 – 12556.8)

18(0.14)(1.13)

μ = 0.47 Pa-s

μ = (V)(ρL)

V = μρ L =

0.471280 = 3.7x10 -4 m 2 /s

RESULTS AND DISCUSSION

When objects are placed within or on the area of the fluid, it experiences a feeling of

deflection, oscillation or resistance and therefore, its velocity may be controlled or reduced.

From the experiment, the absolute viscosity was determined with correction formula due to some

factors like the size of the sphere, the diameter of its opening and the varying velocity of the

sphere. The objective of the experiment was to determine the value of the corrected absolute

viscosity of glycerin. Different steel ball with different diameter is used in the classic

experiment to improve the accuracy of the calculation.

To apply the experimental formula for viscosity of glycerin derived from the principles of

Stoke’s Law. Knowing the terminal velocity, the size and density of the sphere, and the density

of the liquid, Stokes' law can be used to calculate the viscosity of the fluid. Stokes's law is the

basis of the falling-sphere viscometer, in which the fluid is stationary in a vertical glass tube. A

sphere of known size and density is allowed to descend through the liquid. If correctly selected,

it reaches terminal velocity, which can be measured by the time it takes to pass two marks on the

tube.

Errors always occur on an experiment. Sources of errors may have been the values that

have been gathered by measuring, like the diameter of the sphere or the opening, or rounding off

digits that may have made the required value stray. By understanding accurately the procedures

specifying additional data and specific instruction, the source of error would be minimal.

PLOTTED VS versus d/Dm

Vs

d/Dm

0.03 0.05 0.090

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Vs versus d/Dm

Vs versus d/Dm

CONCLUSION

Viscosity is the quantity that describes a fluid's resistance to flow. Fluids resist the

relative motion of immersed objects through them as well as to the motion of layers with

differing velocities within them. If 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. So between parallel, successive layers of a liquid

in motion, opposing force comes into play tending to decrease the relative velocity between

the layers. Viscosity describes a fluid's internal resistance to flow and may be thought of as a

measure of fluid friction.

Furthermore, this resistance acts against the motion of any solid object through the fluid

and also against motion of the fluid itself past stationary obstacles. Viscosity also acts internally

on the fluid between slower and faster moving adjacent layers.

We’ve seen how viscosity acts as a frictional brake on the rate at which water flows through a

pipe; let us now examine its frictional effect on an object falling through a viscous medium. To make it

simple, we take a sphere. If we use a very viscous liquid, such as glycerin, and a small sphere, for

example a ball bearing of radius a millimetre or so, it turns out experimentally that the liquid flows

smoothly around the ball as it falls.

APPENDIX

PRELIMINARY DATA SHEET

REFERENCE

http://en.wikipedia.org/wiki/Viscometer

Munson, B.; Okiishi, T.; Young, D. (2006). “Fundamentals of Fluid Mechanics, 5thEdition”

USA: John Wiley and Sons, Inc.