HYDRAULICS DEPARTMENT

Name:_______________________________
Subject & Section:_____________________ Date Performed:________________
Instructor:____________________________ Date Submitted:________________

EXPERIMENT NO. 1

FALLING SPHERE VISCOMETER

Commercial Falling Sphere viscometers are non-available. One type of which

For laminar flow vd/2  1 in 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   Vt d ------------------------------------------------ (1)

Dm

Viscometer

W
Y

FB

Fd

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Vd +  d3L/6 - d3s/6 = 0 --------------------------------(3)

Solving for :

 = d 2 (s - L) ----------------------------------------------------(4)

18V

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/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(s - L) / 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

2
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:

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 “”.
 =  / L

3. Plot VS versus d/Dm.

3
EQUIPMENT DIAGRAM:

Hole

Cap

1st mark
Glycerin oil

Viscometer

d Steel ball

Dm, dia. of medium

2nd mark

4
 FINAL DATA SHEET
NAME:___________________________________________________ DATE: _______________________
SUBJECT & SECTION:_______________________________________ GROUP NO.___________________
SEAT NO. __________

EXPERIMENT NO. 1

FALLING SPHERE VISCOMETER

GROUP TRIAL Y t VS d Dm V  
d/Dm k
NO. NO. (m) (sec) (m/s) (m) (m) (m/s) (Pa-s) (m2/s)
1 1
2 1
1
3 1
4 1
1 1
2 1
2
3 1
4 1
1 1
2 1
3
3 1
4 1

5
GROUP TRIAL Y t VS d Dm V  
d/Dm k
NO. NO. (m) (sec) (m/s) (m) (m) (m/s) (Pa-s) (m2/s)
1 1
2 1
4
3 1
4 1
1 1
2 1
5
3 1
4 1
1 1
2 1
6
3 1
4 1