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West Bengal University of technology
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1 Fluid Statics
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1.1 Fluid Properties
Fluid
A fluid is a substance, which deforms when subjected to a force. A fluid can offer no permanent resistance to any force
causing change of shape. Fluid flow under their own weight and take the shape of any solid body with which they are
in contact. Fluids may be divided into liquids and gases. Liquids occupy definite volumes. Gases will expand to occupy
any containing vessel.
S.I Units in Fluids
The dimensional unit convention adopted in this course is the System International or S.I system. In this convention,
there are 9 basic dimensions. The three applicable to this unit are: mass, length and time. The corresponding units are
kilogrammes (mass), metres (length), and seconds (time). All other fluid units may be derived from these.
Density
The density of a fluid is its mass per unit volume and the SI unit is kg/m3. Fluid density is temperature dependent and
to a lesser extent it is pressure dependent. For example the density of water at sea-level and 4oC is 1000 kg/m3, whilst at
50oC it is 988 kg/m3.
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The relative density (or specific gravity) is the ratio of a fluid density to the density of a standard reference fluid maintained
at the same temperature and pressure:
ρ gas
For gases:
RDgas =
For liquids:
RDliquid =
ρ air
=
ρ liquid
ρ water
ρ gas
1205
.
kg / m 3
=
ρ liquid
1000 kg / m 3
Viscosity
Viscosity is a measure of a fluid’s resistance to flow. The viscosity of a liquid is related to the ease with which the molecules
can move with respect to one another. Thus the viscosity of a liquid depends on the:
•
Strength of attractive forces between molecules, which depend on their composition, size, and shape.
•
The kinetic energy of the molecules, which depend on the temperature.
Viscosity is not a strong function of pressure; hence the effects of pressure on viscosity can be neglected. However, viscosity
depends greatly on temperature. For liquids, the viscosity decreases with temperature, whereas for gases, the viscosity
increases with temperature. For example, crude oil is often heated to a higher temperature to reduce the viscosity for
transport.
Consider the situation below, where the top plate is moved by a force F moving at a constant rate of V (m/s).
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The shear stress τ is given by:
τ = F/A
The rate of deformation dv (or the magnitude of the velocity component) will increase with distance above the fixed
plate. Hence:
τ = constant x (dv / dy)
2

where the constant of proportionality is known as the Dynamic viscosity (µ) of the particular fluid separating the two plates.
τ = µ x ( V / y)
Where V is the velocity of the moving plate, and y is the distance separating the two plates. The units of dynamic viscosity
are kg/ms or Pa s. A non-SI unit in common usage is the poise where 1 poise = 10-1 kg/ms
Kinematic viscosity (ν) is defined as the ratio of dynamic viscosity to density.
i.e. ν =
µ/ρ
(1.1)
The units of kinematic viscosity are m2/s.
Another non-SI unit commonly encountered is the “stoke” where 1 stoke = 10-4 m2/s.
3

Dynamic Viscosity
Kinematic Viscosity
Centipoise* (cp)
Centistokes (cSt)
Water
1
1
Vegetable oil
34.6
43.2
SAE 10 oil
88
110
SAE 30 oil
352
440
Glycerine
880
1100
SAE 50 oil
1561
1735
SAE 70 oil
17,640
19,600
Typical liquid
Table 1.1 Viscosity of selected fluids at standard temperature and pressure
Note: 1 cp = 10-3kg/ms and 1cSt = 10-6 m2/s
Figure 1.1 Variation of the Viscosity of some common fluids with temperature
Worked Example 1.1
The temperature dependence of liquid viscosity is the phenomenon by which liquid viscosity tends to decrease as its
temperature increases. Viscosity of water can be predicted with accuracy to within 2.5% from 0 °C to 370 °C by the
following expression:
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