2-1
Laboratory #2: Fluid Properties
Purpose: The purpose of this laboratory is to expose the student to several fundamental
fluid properties including specific weight, viscosity, and surface tension.
Objective: To learn methods of determining fluid properties for glycerin, mineral oil, and
water. Such properties are:
1. Specific gravity of glycerin and mineral oil.
2. Viscosity of glycerin and mineral oil.
3. Surface tension of water.
Background:
A. Specific Weight: A hydrometer is a device used to determine the specific gravity of a
liquid. The underlying principle of a hydrometer is based on fact that when a body floats
in a liquid it displaces a volume of liquid whose weight is equal to the weight of the
floating body. A hydrometer is based on Archimedes’ principle, which states that:
Buoyant Force = Weight of Displaced Fluid
F V B =g
where: FB – Buoyant Force (F)
g – Fluid Specific Weight (F/L3)
V – Volume Being Displaced (L3)
Consider a tube having a cross-sectional area, A. Further assume that the tube is
filled with a solid and that the tube is immersed in a fluid. The tube sinks a distance hf into
the fluid. This scenario is illustrated in Figure 2-1.
There is a pressure on the bottom of the tube acting in a direction normal to tube
bottom. Using the laws of fluid statics, the buoyant force can be computed. The pressure
at the bottom of the tube can be found by:
P =gh
Pressure is equal to force times the area over which the pressure acts, i.e. F=PA.
Therefore, the buoyant force can be expressed as:
F PA h A B f f = = g
2-2
P
Fluid, gf
hf
W
Area
FB
x
z
Figure 2- 1 Force Diagram on an Immersed Body
Note however that the quantity hfA is equal to the volume of fluid that is displaced by the
immersed tube. Therefore the buoyant force can be found by:
F V B f = g
Now consider a force balance on the tube. Since the tube is not moving, the sum
of all forces is equal to zero. The only forces acting in the system shown are the weight of
the tube and its contents and the buoyant force.
SFZ = 0 = FB −W
Substituting the expression for the buoyant force we obtain:
F Ah W B f v = g =
If the weight of the tube and its contents are held constant, then the specific weight
of any fluid can be found by taking measurements of the quantity hf and of hw. The latter
quantity is the depth the tube sinks in a container of water.
B. Viscosity: Assume that a sphere falling through a fluid has reached its terminal
velocity, i.e. the acceleration is equal to zero. Therefore the sum of the forces acting on
the sphere will also be equal to zero. The forces acting on the sphere are the weight of the
object, the buoyant force, and the resistance to air. The resistance to air is also called the
drag force.
2-3
Summing the forces in the vertical direction yields:
FZ = 0 = FB + FD −W
The drag force turns out to be a function of the fluid viscosity, the diameter of the
falling object, and the velocity at which it falls. This equation shown below is attributed to
Stokes.
F D V D = 3p μ
where: D – Diameter of the Sphere
μ – Fluid Viscosity
V – Terminal Velocity
Knowing the volume of a sphere, the force balance can be solved to find the fluid
viscosity. Recall that the weight of any material (fluid or solid) is the specific weight of
the material times the volume of material.
V
D
S =

 

 
4
3 2
3
p
V
Fd
Fb
Fb + Fd – W = 0
W
Figure 2- 2 Force Diagram on Falling Object
C. Capillary Rise Between Two Flat Plates: The capillary rise between two plates can
be found by taking a force balance over a small volume of fluid. Figure 2-3 shows a free
body diagram of a small fluid volume showing all forces that act on the fluid element. The
forces involved are the weight of the fluid volume and the force due to surface tension. It
is the force due to surface tension that causes the fluid to rise up the walls of the two
plates.
2-4
The force due to surface tension can be found by:
T = s * L = 2(scosq)Dx
where: T – Force due to Surface Tension
s – Fluid Surface Tension
L – Length of Fluid Over Which Surface Tension Acts
w
x
W
x
H
h
Figure 2- 3 Force Balance on Small Fluid Volume
D. Capillary Rise in Small Tubes: The capillary rise in a small diameter tube can also
be found by taking a force balance on the volume of fluid that rises in the tube. Using the
approach, it can be shown that the height of rise in a small tube can be expressed as:
H
D f
=
4s q
g
cos
where: H – Capillary Rise in Tube
s – Surface Tension
q – Angle Fluid Makes With Tube Wall
D – Tube Diameter
gf – Fluid Specific Weight
2-5
Procedure:
A. Archimedes’ Principle
1. A simple hydrometer may be made from a piece of glass tube closed at one end.
2. Place a small amount of lead shot or sand in the bottom of the tube as shown in Figure
1.
3. Immerse the hydrometer in a cylinder containing water and determine the length that is
immersed.
4. Repeat step 3 by replacing water with glycerin.
5. Repeat step 3 by replacing water with mineral oil.
6. Record the length immersed in steps 3, 4, and 5.
B. Viscosity Of Glycerin And Mineral Oil.
1. Fill two cylinders with glycerin and mineral oil.
2. Use three steel spheres of different diameters with each fluid. Measure the sphere
diameter using a micrometer or caliper.
3. Mark two points on the cylinders at least 6 inches apart .
4. Carefully drop the sphere one at a time into the cylinders.
5. Repeat step 4 three times.
6. Record the time for each sphere to fall between the fixed marks.
7. Measure the temperature of the fluid.
Material Specific Weight
(lb/ft3)
Steel 490.8
Glycerin 78.6
Mineral Oil 57.4
C. Capillary Rise Of Water Between Two Flat Plates.
1. Thoroughly clean the two plates and wrap a length of fine wire around one plate near
one end.
2. Fill the trough with water.
3. Place the two plates between the supporting clips and slide to the bottom of the
trough.
4. Measure the rise of the water between the two flat plates at one half of an inch
intervals.
5. Measure the diameter of the fine wire and the horizontal length of the flat plates.
6. Measure the temperature of the fluid.
2-6
D. Capillary Rise Of Water In Tubes.
1. Make sure the capillary tubes are thoroughly clean.
2. Measure the diameter of each of the three capillary tubes.
3. Fill the reservoir with water and allow water to rise in the three capillary tubes.
4. Place a card behind the capillary tubes to assist in locating the capillary rise.
5. Mark the card with the height of the capillary elevation in each tube.
6. Record the capillary rise in the tubes.
7. Record the temperature.
REQUIRED DATA:
A. Length of immersed portion of hydrometer.
B. Length between the two fixed marks of the cylinder.
Diameters of steel spheres.
The time for each ball to fall between the two fixed marks.
C. Temperature of fluid.
Diameter of fine wire.
Capillary rise between the two plates @ ½” intervals.
The horizontal length of the flat plates.
D. Temperature of fluid.
Diameters of tubes.
Capillary rise in tubes.
RESULTS:
1. Find the experimental specific weight of glycerin and mineral oil. Compare the
experimental results to the theoretical values by computing the percent error
associated with the measured quantities.
2. Determine the experimental viscosity of glycerin and mineral oil. Compare
experimental results to theoretical values.
3. Calculate the theoretical height of the capillary rise between two flat plates. Compare
the experimental results to theoretical results by computing the percent error
associated with the measured quantities.
4. Compute the theoretical height of the capillary rise in small diameter tubes. Compare
experimental and theoretical results by computing the percent error.