### Abstract

The local time-averaged velocity, the mixed-mean velocity, and the friction factor for fully turbulent flow between parallel plates and in round tubes and concentric circular annuli can be expressed in terms of integrals of the turbulent shear stress. The pressure distribution across a channel can similarly be expressed in terms of an integral of normal stresses. These formulations, which are simple and exact, can be integrated numerically using experimental data, computed values, or correlating equations for turbulent stresses. Their greatest merit, however, may arise from the insight they provide with respect to the contributions of the fluctuating components of the velocity. For example, for concentric circular annuli such a formulation identifies a difference between the locations of the maximum in the velocity and the zero in the total shear stress. This difference, which has been overlooked in most experimental and semitheoretical investigations, introduces an error of unknown but possibly significant magnitude into all of the results. It also precludes the application of the mixing-length, eddy viscosity and k - ε models.

Original language | English (US) |
---|---|

Pages (from-to) | 2513-2521 |

Number of pages | 9 |

Journal | AICHE Journal |

Volume | 41 |

Issue number | 12 |

State | Published - Dec 1995 |

Externally published | Yes |

### Profile

### ASJC Scopus subject areas

- Biotechnology
- Chemical Engineering(all)
- Mechanical Engineering
- Environmental Engineering
- Polymers and Plastics

### Cite this

*AICHE Journal*,

*41*(12), 2513-2521.

**Turbulent flow in channels in terms of local turbulent shear and normal stresses.** / Churchill, Stuart W.; Chan, Christina.

Research output: Contribution to journal › Article

*AICHE Journal*, vol 41, no. 12, pp. 2513-2521.

}

TY - JOUR

T1 - Turbulent flow in channels in terms of local turbulent shear and normal stresses

AU - Churchill,Stuart W.

AU - Chan,Christina

PY - 1995/12

Y1 - 1995/12

N2 - The local time-averaged velocity, the mixed-mean velocity, and the friction factor for fully turbulent flow between parallel plates and in round tubes and concentric circular annuli can be expressed in terms of integrals of the turbulent shear stress. The pressure distribution across a channel can similarly be expressed in terms of an integral of normal stresses. These formulations, which are simple and exact, can be integrated numerically using experimental data, computed values, or correlating equations for turbulent stresses. Their greatest merit, however, may arise from the insight they provide with respect to the contributions of the fluctuating components of the velocity. For example, for concentric circular annuli such a formulation identifies a difference between the locations of the maximum in the velocity and the zero in the total shear stress. This difference, which has been overlooked in most experimental and semitheoretical investigations, introduces an error of unknown but possibly significant magnitude into all of the results. It also precludes the application of the mixing-length, eddy viscosity and k - ε models.

AB - The local time-averaged velocity, the mixed-mean velocity, and the friction factor for fully turbulent flow between parallel plates and in round tubes and concentric circular annuli can be expressed in terms of integrals of the turbulent shear stress. The pressure distribution across a channel can similarly be expressed in terms of an integral of normal stresses. These formulations, which are simple and exact, can be integrated numerically using experimental data, computed values, or correlating equations for turbulent stresses. Their greatest merit, however, may arise from the insight they provide with respect to the contributions of the fluctuating components of the velocity. For example, for concentric circular annuli such a formulation identifies a difference between the locations of the maximum in the velocity and the zero in the total shear stress. This difference, which has been overlooked in most experimental and semitheoretical investigations, introduces an error of unknown but possibly significant magnitude into all of the results. It also precludes the application of the mixing-length, eddy viscosity and k - ε models.

UR - http://www.scopus.com/inward/record.url?scp=0029412557&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0029412557&partnerID=8YFLogxK

M3 - Article

VL - 41

SP - 2513

EP - 2521

JO - AICHE Journal

T2 - AICHE Journal

JF - AICHE Journal

SN - 0001-1541

IS - 12

ER -