Skin friction coefficient turbulent flows

Schlichting [1] has surveyed experimental measurements of friction coefficients for turbulent flow on flat plates. We present the results of that survey so that they may be employed in the calculation of turbulent heat transfer with the fluid-friction-heat-transfer analogy. The local skin-friction coefficient is given by... 

The Chilton-Colburn analogy has been obserx ed to hold quite well in laminar or turbulent flow over plane surfaces. But this is not always the case for internal flow and flow over irregular geometries, and in such cases specific relations developed should be used. When dealing with flow over blunt bodies, it is important to note that/in these relations is the skin friction coefficient, not the total drag coefficient, which also includes tlie pressure drag. 

Note relationships exist for both laminar and turbulent flow defining the skin friction coefficient Cf as a function of Reynolds number (Re). 

The plot below shows how Re and the location of the transition from the laminar flow to the turbulent flow affect the skin friction coefficient. 

The torque due to the end surfaces of the rotating cylinder could not be determined theoretically. However, as the flow In the annular gap is a basically irrotational turbulent flow at a high Reynolds number, the turbulent boundary layers on the end surfaces of the annular gap will be similar to those on the cylinder surfaces. From this it can be assumed that the relationships between skin friction coefficient and Reynolds number will also be similar. 

The above does not apply for flow conditions in a shelf setting, estuarine, or freshwater stream flows where the BBL may become depth limited and subject to turbulent mixing from both upper and lower boundaries. Under such conditions, alternative means for estimating Cd are needed. In Chapter 2, a general equation for the skin friction factor, Cf, for open channel flow was presented (see Equation 2.25). The equivalent formulation for the quadratic drag coefficient is... 

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