The flow field about a line source considers the symmetric radial flow of an incompressible, inviscid fluid outward from an infinitely long uniform source, coincident with the z-axis of a cylindrical coordinate system. Fluid is being generated at a volumetric rate F per unit length of source. 

(a) Show that the Laplace equation for the velocity potential for this system is 

(b) From this equation find the velocity potential, velocity, and pressure as functions of position: where P_∞ is the value of the modified pressure far away from the source. 

(c) Discuss the applicability of the results in (b) to the flow field about a well drilled into a large body of porous rock. 

(d) Sketch the flow net of streamlines and equipotential lines.   

Transcribed Image Text:

Part (a) dф) r dr dr Part (b) pГ? 8п?r2 Pz – P = In r 2т г Г v, = 2Tr