The History of the Darcy-Weisbach Equation for Pipe Flow Resistance

2002 ◽  
Author(s):  
Glenn O. Brown
Keyword(s):  
Pipe Flow ◽  
Flow Resistance ◽  
History Of

scholarly journals Evaluating the Effects of Sediment Transport on Pipe Flow Resistance

Water ◽  
2021 ◽  
Vol 13 (15) ◽  
pp. 2091
Author(s):  
Vito Ferro ◽  
Alessio Nicosia
Keyword(s):  
Velocity Profile ◽  
Pipe Flow ◽  
Power Distribution ◽  
Flow Resistance ◽  
Unit Length ◽  
Particle Diameter ◽  
Self Similarity ◽  
Sediment Size ◽  
The Mean ◽  
The Relationship

In this paper, the applicability of a theoretical flow resistance law to sediment-laden flow in pipes is tested. At first, the incomplete self-similarity (ISS) theory is applied to deduce the velocity profile and the corresponding flow resistance law. Then the available database of measurements carried out by clear water and sediment-laden flows with sediments having a quasi-uniform sediment size and three different values of the mean particle diameter Dm (0.88 mm, 0.41 mm and 0.30 mm) are used to calibrate the parameter of the power-velocity profile). The fitting of the measured local velocity to the power distribution demonstrates that (i) for clear flow the exponent δ) can be estimated by the equation of Castaing et al. and (ii) for the sediment-laden flows δ is related to the diameter Dm. A relationship for estimating the parameter Гv obtained by the power-velocity profile) and that Гf of the flow resistance law) is theoretically deduced. The relationship between the parameter Гv, the head loss per unit length and the pipe flow Froude number is also obtained by the available sediment-laden pipe flow data. Finally, the procedure to estimate the Darcy–Weisbach friction factor is tested by the available measurements.

1641 Flow Resistance in Unsteady Inlet Pipe Flow

2007 ◽  
Vol 2007.2 (0) ◽  
pp. 269-270
Author(s):  
Masafumi OKUNO ◽  
Toshihiro TAKAMI ◽  
Kazuhiko WAKASA ◽  
Shinichiro YANASE
Keyword(s):  
Pipe Flow ◽  
Flow Resistance ◽  
Inlet Pipe

Applying flow resistance equations to overland flows

2007 ◽  
Vol 31 (4) ◽  
pp. 363-387 ◽  
Author(s):  
Mark W. Smith ◽  
Nicholas J. Cox ◽  
Louise J. Bracken
Keyword(s):  
Laser Scanning ◽  
Flow Resistance ◽  
Overland Flow ◽  
Constant Width ◽  
Surface Flow ◽  
Stream Channels ◽  
Overland Flows ◽  
Erosion Models ◽  
History Of ◽  
Methodological Advance

Resistance to flow determines routing velocities and must be adequately represented both within stream channels and over hillslopes when making predictions of streamflow and soil erosion. The limiting assumptions inherent in flow resistance equations can be relaxed if the spatial and temporal scale over which they are applied is restricted. This requires a substantial methodological advance in the study of overland flows over natural surfaces. It is suggested that terrestrial laser scanning will allow a greater understanding of overland flow hydraulics and present opportunities to investigate resistance to flow over complex morphologies. The Darcy-Weisbach, Chézy and Manning equations are the most widely used empirical equations for the calculation of flow velocity in runoff and erosion models. These equations rest on analyses originally developed for one-dimensional pipe flows and assume conditions which are not met by overland flows. The following assumptions are brought into question: flow can be described as uniform; flow is parallel to the surface; flow is of a constant width and the boundary to the flow is longitudinally uniform; grain roughness is homogeneous over the wetted perimeter and can be considered as random; form roughness and other sources of flow resistance can be ignored; resistance is independent of flow depth; and resistance can be modelled as a function of the Reynolds number. A greater appreciation of the processes contributing to resistance to overland flows must be developed. This paper also presents a brief history of the development of flow resistance equations.

Resistance to Steady Laminar Flow of Pseudoplastic Fluids through Pipes and Valves

1966 ◽  
Vol 8 (2) ◽  
pp. 226-233 ◽  
Author(s):  
J. F. Ury
Keyword(s):  
Laminar Flow ◽  
Friction Factor ◽  
Test Data ◽  
Pipe Flow ◽  
Flow Resistance ◽  
General Procedure ◽  
Consistency Curve ◽  
Pseudoplastic Fluids ◽  
Laminar Pipe Flow ◽  
Steady Laminar

The well-known logarithmic friction factor diagram for laminar pipe flow can be extended in the following two respects: For application to non-Newtonian fluids, by incorporating in the plot a modified form of the consistency curve for a given material. Methods are discussed of obtaining these curves, and of transforming them into the required shape. For prediction of flow resistance through valves and fittings, by use of an auxiliary diagram based on results of appropriate tests. The general procedure is outlined, and it is stressed that results cannot be relied on quantitatively, until test data are obtained for wider ranges of sizes and types than hitherto available.

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