# Turbulent Flow of Power-Law Fluids

*by*Abdul I.Y. Mohammed, Grad. Asst.; Dept. of Civ. Engrg., New Mexico State Univ., Las Cruces, N.M.,

Phillip R. Smith, Prof.; Dept. of Mech. Engrg., New Mexico State Univ., Las Cruces, N.M.,

Narendra N. Gunaji, (M.ASCE), Prof.; Dept. of Civ. Engrg., New Mexico State Univ., Las Cruces, N.M.,

**Serial Information**:

*Journal of the Hydraulics Division*, 1975, Vol. 101, Issue 7, Pg. 885-900

**Document Type:**Journal Paper

**Abstract:**Velocity profiles for the steady incompressible turbulent flow of power-law fluids through circular conduits were calculated by numerical quadrature considering both the viscous stresses and the Reynolds' stresses operative over the entire cross section of the flow. A non-Newtonian stress coeffiecient, K

_{n}, was introduced along with mixing length, l, so that the Reynolds' stresses could be put in a form similar to that of the viscous stresses. The form of the Reynolds' stresses thus obtained reduced to the Newtonian form when the flow behavior index, n, equaled unity. Both l and K

_{n}were assumed dependent upon the Reynolds number. Similarly, friction factors for the turbulent flow of power-law fluids were calculated by numerical quadrature. The calculated friction factors were compared to 146 measured friction factors over a range of Reynolds numbers from 2,670 to 108,800. The mean absolute difference between calculated and measured friction factors for this sample was 3% with a standard deviation of 1.9%.

**Subject Headings:**Turbulent flow | Fluid flow | Reynolds stress | Friction | Fluid velocity | Flow profiles | Viscous flow | Numerical methods

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