The  properties of fluids permit us to distinguish  one fluid from another,  and  they  allow us to make estimates of physical behavior  of any special fluid.

Density
Definition 2 The density of a fluid (or any other form of matter) is the amount  of mass per unit  volume.

or the density at a point  in fluid as

The unit of density is kg/m3.

Pressure
A fluid always  has  pressure.   As a result  of innumerable molecular  collisions,  any  part of the fluid must experience  forces exerted  on it  by adjoining  fluid or by adjoining  solid boundaries.   If,  therefore,  part of the fluid  is arbitrarily  divided  from  the rest  by  an imaginary  plane,  there  will be forces that may  be  considered  as  acting  at that plane. Pressure  cannot be measured  directly; all instruments said to measure  it in fact indicate a difference of pressure.   This  difference is frequently  that between  the pressure  of the fluid under  consideration  and  the pressure  of the surrounding atmosphere.  The  pressure of the atmosphere is therefore commonly  used as the reference or datum pressure  that is the starting point  of the scale of measurement.   The  difference in pressure  recorded  by the measuring  instrument is then termed the gauge pressure.  The absolute pressure, that is the pressure  considered  relative to that of a perfect vacuum,  is then given by

Pabs = Pgauge + Patm .

The pressure is a scalar quantity (not vector!!.  To say that pressure acts in any direction, or even in all directions,  is meaningless.   The  SI unit of pressure  is N · m2 , now termed pascal,  with  the abbreviation  Pa.   Pressures  of large  magnitude  are  often  expressed  in atmospheres (abbreviated  to atm).  For  precise  definition,  one atmosphere  is taken  as 1.01325105 Pa.  A pressure  of 10e5 Pa is called 1 bar.  The  thousandth part of this unit, called a millibar  (abbreviated  to mbar),  is commonly  used by meteorologists.   It should be noted that, although they are widely used, neither the atmosphere nor the bar are accepted for use with SI units.

Viscosity
Viscous fluids tend to be gooey or sticky,  indicating  that fluid parcels  do not slide past one another, or past solid surfaces, very readily.  This can be an indication of some degree of internal
molecular order, or possibly other effects on molecular scales; but in any case it implies a resistance to shear stresses.  These observations lead us to the following definition.

Definition 3 Viscosity  is that  fluid property  by virtue  of which a fluid offers resistance to shear  stresses.
At first glance this may seem to conflict with the earlier definition of a fluid (a substance that cannot resist deformation due to shear stresses), but resistance to shear stress, simply implies that the rate of deformation may be limited.

It is a matter of common  experience  that, under  particular  conditions,  one fluid offers greater  resistance  to flow than another.   Such  liquids  as tar, treacle,honey  and  glycerine  cannot  be  rapidly  poured  or  easily  stirred,  and  are  commonly  spoken  of as  thick; on the other  hand,  so-called  thin liquids  such  as water,  petrol  and  paraffin  flow much more  readily.   (Lubricating  oils with  small  viscosity  are  sometimes  referred  to as light, and those with large viscosity as heavy; but viscosity is not related to density.)  Gases as well as liquids have viscosity, although the viscosity of gases is less evident in everyday life.

Definition 4 Newton’s  Law  of Viscosity  – Newtonian  fluids.  For  a given rate  of angular deformation of a fluid, shear  stress  is directly  proportional to viscosity µ.

In fluid dynamics,  many problems involving viscosity are concerned with the magnitude of the viscous forces compared  with the magnitude of the inertia forces, that is, those forces causing  acceleration  of particles  of the fluid.   Since the viscous  forces are  proportional to the dynamic  viscosity  µ and  the inertia  forces are proportional  to the density  ρ, the ratio µ/ρ is frequently involved.  The ratio of dynamic viscosity to density is known as the kinematic  viscosity

The SI unit for kinematic viscosity is m2/s−1.

Compressibility
All matter is to some extent compressible.  That is to say, a change in the pressure applied to a certain  amount  of a substance  always  produces  some change  in its  volume.   Let  us assume that to the volume V (p1, T ), T = const, is a temperature) was applied the pressure p2 = p1 + ∆p.  Using the Taylor  series we can write

The derivative ∂V/∂p defined by the initial volume V (p1 is used as a measure of compressibility of liquids:

or in the differential form

Since a rise in pressure always causes a decrease in volume, ∂V/∂p is always negative, and the minus sign is included in the equation to give a positive value of ξ . Dimension of  is Pa−1.
As the density  is given by mass/volume = m/V then

so ξ may also be expressed as