Streamfunction for general fluids in heterogeneous and anisotropic formations

Discussion 4-2. Streamfunction for general fluids in heterogeneous and anisotropic formations. 

In a manner similar to Discussion 4-1, Equation 4-14 suggests that we can define a function T(X, Y) such that 

Substitution of Equations 4-17 and 4-18 into Equation 4-14 yields a 0 = 0 identity, showing that no additional assumptions have been invoked. First, let us determine how T varies, if at all, along a streamline. Equation 4-7, which provides the kinematic description for a streamline, still holds. Thus, 

From calculus, the total differential for any two-variable function is 

Are sueh streamlines perpendicular to lines of constant pressure The answer is, No. To see this, note that the unit normals to lines having constant P s and P s are proportional to 5 P/5X i + ffV/dY j and cP/9X i + dP/dY j, respectively. The inner or scalar dot product formed by these normals is 

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