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System of governing equations in dimensionless form

Lets rewrite the system () into the following form^{21.6}:

(21.23)

(21.24)

(21.25)

(21.26)

(21.27)

(21.28)

(21.29)

where (*) denotes real physical values. Equations () can be transferred to the dimensionless form by following way. Each variable will be divided by its characteristic value of the same dimension.

(21.30)

Typical characteristic values are: velocity of free-stream and some characteristic distance,e.g. diameter of channel . All of the rest variables can be extended with using combination of them:

(21.31)

After having used this relations and (), the system of governing equations can be written in dimensionless form. Following equations describe flow of incompressible fluid: