Abstract: Using stochastic theory of turbulent flow the turbulent flow of power-law fluids in pipes has been studied.Based on the theoretical analysis,a continuous profile function of velocity over flow field
u_*=A_*ln(1+Xξ)-B_*(1/(1+Xξ))+C_*(1/(1+Xξ)²)+G_*(ξ+1c^-βξ/β-1/β)+F_*
and a formula of pressure gradient
2v_*{A_*[((X+1)²/(2X²))ln(1+X)-1/(2X)-3/4]+B_*[1/X-((1+X)/X²)ln(1+X)] +C_*[1/X-1/X²ln(1+X)]+F_*/2+G_*[1/6-1/(2β)+(c^-β/β²)+1/β²-1/β³]}-u_m=0
are proposed.Further,a calculation graph of turbulent pressure gradient for engineering application is given.