This document defines and provides the mathematical definitions and units of measurement for viscosity and surface tension. It discusses absolute viscosity, kinematic viscosity, and the effects of viscosity being too high or too low. It also describes four common viscometers used to measure viscosity and the relationship between surface tension, capillary rise, and wetting angle in capillary tubes. Several example problems are provided to calculate viscosity, kinematic viscosity, capillary rise, surface tension, and wetting angle.

1. LECTURE UNIT NO. 2
8. Absolute Viscosity or Coefficient of Viscosity or Dynamic Viscosity or simply “Viscosity”
- Measures of the sluggishness with which a fluid flows. When the viscosity is low,
indicative of a “thin” fluid like water, the fluid flows easily. Conversely, the “thickest”
fluids, such as certain types of oil, are the most viscous and do not flow easily.
Mathematical Definition of Viscosity
ν
F ν
ν Moving Plate
P dν
H
dy
Velocity Profile
Stationary Plate
Slope = _dν_ = _ν_ = velocity gradient
dy H
By experiment, force F is proportional to the plate area A and to the slope of the velocity profile.
F α A ν_
H
The constant of proportionality is called the absolute viscosity, μ
F = μν A
H
F/A is the shear stress developed in the fluid and acting on the bottom surface of the moving plate.
μ = _ τ__ For two closely parallel plates, velocity gradient
ν/H is constant
μ = _ τ __ For non constant velocity gradient
dν/dy
Units of Absolute viscosity
Eng’g Units: lbf_-sec
ft2
SI Units: N – s or Pa-s or Poise, P
m2
Note: 1 poise = 100 cP
1 poise = 1 dyne-s/cm2 = 0.1 Pa - s where: 105 dynes = 1 N
Kinematic Viscosity
- Ratio of absolute viscosity to mass density of fluid
ν = _μ_
ρ
Eng’g Units: ft2/sec
SI Units: m2/s
Note: 1 stroke (S) = 1 cm2/s = 1 x 10-4 m2/s

2. Effects of Viscosity:
Too high viscosity
- High resistance to flow, which causes sluggish operation.
- Increased power consumption due to increased frictional losses.
Too low viscosity
- Increased leakage losses past seals.
- Excessive wear due to the breakdown of the oil film between mating components.
Measurement of Viscosity
- The devices designed to measure viscosity are called viscometers or viscosimeters.
Four commonly used viscometers
1. Rotating drum viscometer
2. Falling-ball viscometer
3. Capillary tube viscometer
4. Saybolt viscometer
Surface Tension
- Property that results from the attractive forces between molecules
Capillary
- due to adhesion and cohesion
d
θ
F F
h
h θ
d F F
Has greater adhesion Has greater cohesion
θ < 90° θ > 90°
Where: σ = surface tension, N/m
γ = specific weight of liquid, N/m3
See table A.1 Physical Properties of water and table A.4 Physical Properties of
Common Liquids at Standard atmospheric Pressure (Fluid Mechanics with
Engineering Applications by Daugherty, Franzini and Finnemore)
θ = wetting angle, degrees
d = diameter of tube, m
h = capillary rise, m

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PROBLEMS:
1. Convert a pressure of -5 psi into absolute pressure.
Convert a pressure of 150 kPa (abs) into a gage pressure
2. A viscometer is constructed with two 30-cm long concentric cylinders, one 20.0 cm in diameter and
the other 22 cm in diameter. A torque of 0.13 N m is required to rotate the inner cylinder at 400
rpm (revolutions per minute). Calculate the viscosity.
3. A liquid has an absolute viscosity of 23.0 cP. It weighs 8.4 kN/m 3. What is its kinematic viscosity?
4. Determine the height that 20 ºC water would climb in a vertical 0.2 cm diameter tube if it attaches
to the wall with an angle of 20 º to the vertical.
5. A 2 mm diameter clean glass tube is inserted in water at 15 ºC. Determine the height that the
water will climb up the tube. The water makes a contact angle of 0 º with the clean glass.
6. (a) Find the depression h of the mercury in the glass capillary tube having a diameter of 2 mm if
the surface tension is 0.514 N/m for θ = 40° (b) Compute the force caused by surface tension (c)
Determine the density of mercury
7. (a) Determine the surface tension in a tube with 0.2 m radius and wetting angle 0° and capillary
rise of 5mm. (b) Determine the surface tension in lb/ft (c) If wetting angle θ = 80°, determine the
surface tension
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