The stresses and contain velocity derivatives with respect to Cartesian coordinates, see Eq. (37.7); these have to be expressed in terms of general coordinates .The quantities and become

	(38.1)

Where J is the Jacobian of the coordinate transformation defined by:

(38.2)

The Jacobian and the derivatives of Eq. (38.1) need to be evaluated at the cell face locations “e” and “n” (Fig 37.1). The relations for the “e”-face will be derived in the following text. The remaining equations follow by analogy.

For the “e” face, the coordinate refer Fig 37.1 is taken to connect the points P and E (from P to E), and runs along the “e” cell face (form “se” to “ne”). The derivatives etc., can be approximated as (refer Fig. 37.1):

(38.3)

The origin of the and coordinates can be defined as desired. We can calculate i.e the distance between points P and E; similarly, is set equal to i.e. the length of the cell face between vertices and . The Jacobian can then be approximated by:

(38.4)

Thus for an orthogonal grid The derivatives in Eqs. (38.1) can now be expressed by involving expressions (38.3) and (38.4) to yield:

	(38.5)

The denominator in the above expressions represents the volume defined by the scalar product of and . This will be denoted as hereafter.