Uniform vertical velocity along the fracture

Example 2-5. Uniform vertical velocity along the fracture. 

Example 2-4 solved the velocity flux problem for a general liquid inflow distribution 5p(x,0- )/. In the form given, the integral on the first line of Equation 2-91 describes the spatial variation of pressure, whereas the remainder of Equation 2-91 supplies an overall pressure level that accounts for near- and farfield interaetions. How does fracture pressure behave with x for a simple flow rate distribution  

Evaluation of singular integrals. In Examples 2-1 and 2-2, we introduced singular or improper integrals whose integrands contain infinities. Most calculus books offer satisfactory discussions, e.g., refer to Thomas (1960). 

In this example, we evaluate typical integrals by assuming uniform veloeity flux at the fracture, taking 5p(x,0-l-)/ constant with x, setting 

From Equation 2-91, the solution to this simplified problem is 

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