For a large part the study of the mechanics of liquids and gasses are identical. One major difference is that only liquids have a free surface level. Another difference is that gasses are generally more compressible than liquids.

### Fluid characteristics

When dealing with fluid mechanics, one uses a continuum model to model the characteristics of the fluid, thereby bypassing the intricacies of the material on a lower level.### Density

Mass per unit of volume gives the density of the material under study, generally denoted with the symbol ρ (ρ, or rho, for those that don't get these HTML symbols to work). The dimension for density follows from the definition, as given by the SI:-
[ρ] = M L

^{-3}; the SI unit is 1 [kg/m

^{3}]

Values normally used are:

- fresh water: ρ = 1000 [kg/m
^{3}] - salt water: ρ = 1025 [kg/m
^{3}]

### Constitutive equations

The constitutive equations give the relationship between the stress in a material and the resulting distortion of volume and shape. The three areas for which we need equations are:- Stress
- Compressibility
- Fluidity

#### Stress

In liquids and gasses tensile stress is a very rare occurrence, and therefore the definition pressure (*p*) is introduced, which is equivalent to the isotropic part of the compressive stress in a liquid or gas:

*p*= - σ

_{0}= - 1/3 (σ

_{xx}+ σ

_{yy}+ σ

_{zz})

#### Compressibility

If the pressure increases, fluids become compressed. The relation between volume (*V*) and pressure (

*p*) for fluids under the idealization of elasticity is expressed using the

**compressibility modulus**.

*K*The value of

*K*increases with increasing pressure. However, for a large range of pressures the value of

*K*for water (without gas bubbles!) is practically constant, namely equal to roughly 2.2 x 10

^{9}[Pa].

#### Fluidity

The**dynamic viscosity**determines the fluidity of a liquid or gas, and has the dimension (according to the SI) of M L

*η*^{-1}T

^{-1}(which is 1 [Pa s] = 1 [kg m

^{-1}s

^{-1}]).

Usually the

**kinematic viscosity**is used in calculations, which is defined as follows:

*ν**ν = η / ρ*

### The rest

The above information is the main background needed to understand fluid mechanics, at least in the context of situations in the size range usually encountered in civil engineering. One of the things still left out here is**capillary attraction**, which is a phenomenon that is only of importance in very slow and tiny distortions.

Another omission in the above is the importance of dimensionless parameters in fluid mechanics. For example, the discussion of the

**compressibility modulus**can be followed further to the definition of the

*K***Mach number**, which is the ratio of the velocity of the flow of a medium to the velocity of sound in that medium (which is linked to the compressibility of the medium → sound == compression waves).

The

**Reynolds number**is another such dimensionless parameter, which can be arrived at by following the discussion of the fluidity further. The Reynolds number gives an indication whether a certain flow situation is turbulent or laminar. It is also used to do simulations on differing scales, the idea being that if the Reynolds number is kept constant the simulation is dynamically similar to the original.

**Sources:**

An adaptation of one of my college textbooks - node your homework

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My first nodeshell rescue
August 16, 2001
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