These balance equations arise from applying Newton 's second law to fluid motion , together with the assumption that the stress in the fluid is the sum of a diffusing viscous term ( proportional to the gradient of velocity ) and a pressure term -- hence describing `` viscous flow '' .
The equations result from applying Newton 's second law to fluid motion , with the belief that the fluid stress is the sum of a diffusing viscous term ( in relation to the gradient of velocity ) , plus a pressure term .