Download 966650d0e579650

Viscosity
Determination of a given liquid viscosity
Objectives:to determine of a given liquid viscosity using the falling
ball method
Theory:
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.
Water characterized by a lower viscosity (lower friction force
between its different layers), while honey is characterized by a higher
viscosity (higher friction force between its different layers). Put
simply, the less viscous the fluid is, the greater its ease of movement
(fluidity)
With the exception of superfluids, all real fluids have some internal
resistance to flow and therefore are viscous. A fluid which has no
resistance to flow is known as an ideal fluid or inviscid fluid. In
common usage, a liquid with the viscosity less than water is known as
a mobile liquid, while a substance with a viscosity substantially
greater than water is simply called a viscous liquid. The study of
flowing matter is known as rheology, which includes viscosity and
related concepts.
Let a ball of radius R with density (kg/m3) moves with a constant
terminal velocity v (m/s) in a liquid of density ' (kg/m3) as shown in
the figure 1. The summation of the forces acting on the ball is equal
zero.
Buoyant force + Friction force
Gravitational Force
Figure 1. The forces acting on the ball that is moving with terminal
velocity in a viscous liquid.
Therefore total upright forces and downright forces have to be the
same.
Gravitational force = Buoyant force + Friction force
Where
Gravitational Force = mg =
Buoyant Force =
4
3
3
𝜋 𝑅 3 𝜌𝑔
𝜋 𝑅 3 𝜌′ 𝑔
Friction Force = fv = 6 Rv
Where
4
(Stokes' law)
: viscosity coefficient of the liquid in
R: radius of the ball
(Pa.s.)
f: friction coefficient
So,
4
3
𝜋 𝑅 3 𝜌𝑔 =
4
3
𝜋 𝑅 3 𝜌′ 𝑔 + 6RV
The above equation can be rewrite to get the coefficient of viscosity  :
𝟐𝒈𝑹𝟐
= (
𝟗𝒗
) (𝝆 − 𝝆′ )
Pa.s.
Equipment:
1- Cylinder contains metallic ball and liquid of unknown viscosity
2- Stopwatch
3- Metre ruler
4-
Micrometer screw gauge
Procedure
1- Measure the temperature of the liquid by using of the
thermometer fixed in the outer tube (normally 25 C)
2- Measure the radius of the ball (R) by using of micrometer
(repeat three times)
3- Measure the time the ball need to fall a distance 10 cm.
4- Repeat step 3 three time and take the mean value of the time.
5- then calculate the velocity v (m/s)
(repeat three times)
6- Givens: density of the boron-glass ball  = 2200 kg/m3
the density of a 40 % sugar solution ' = 1180 kg/m3.
Gravity = 9.8 m/s2
7- The tube filled with the liquid is titled by an angle of 10°,
therefore the viscosity coefficient will be calculated from the
relation:
=
𝟐𝒈𝑹𝟐
(
𝟗𝒗
Results:
R = 0.7 cm
t1 =
S
t2 =
S
t3 =
S
Mean time t = (t1 + t2 + t2)/3
Velocity = 10 cm/t =
=
) (𝝆 − 𝝆′ )cos 10
Pa.s.