Solutions to Two Problems of Pipe Flow

Author(s):  
Shouhong Wu ◽  
Femi Ade

This paper assesses two aspects of liquid flow in pipes. The first aspect is the relation between pipe critical flow depth and flow discharge. The critical flow depth in a pipe is generally expressed as an implicit function. The paper proposes two simple expressions that can be used to explicitly express pipe critical flow depth as a function of pipe diameter and discharge. The approximation errors associated with these proposed expressions were found to be within 1.0%. The second aspect is the flow transition from open pipe flow to full pipe flow in a long pipe. Theoretically, when a pipe is close to flowing full, a given discharge may correspond to multiple head differences. This paper presents a practical solution approach that yields a unique solution for the pipe flow depth for a given discharge in the transition zone.

2006 ◽  
Vol 18 (7) ◽  
pp. 074104 ◽  
Author(s):  
Fernando Mellibovsky ◽  
Alvaro Meseguer
Keyword(s):  

2018 ◽  
Vol 30 (1) ◽  
pp. 015111 ◽  
Author(s):  
Melissa C. Brindise ◽  
Pavlos P. Vlachos

2018 ◽  
Vol 848 ◽  
pp. 467-507 ◽  
Author(s):  
Henry C.-H. Ng ◽  
Hope L. F. Cregan ◽  
Jonathan M. Dodds ◽  
Robert J. Poole ◽  
David J. C. Dennis

Pressure-driven laminar and turbulent flow in a horizontal partially filled pipe was investigated using stereoscopic particle imaging velocimetry (S-PIV) in the cross-stream plane. Laminar flow velocity measurements are in excellent agreement with a recent theoretical solution in the literature. For turbulent flow, the flow depth was varied independently of a nominally constant Reynolds number (based on hydraulic diameter, $D_{H}$; bulk velocity, $U_{b}$ and kinematic viscosity $\unicode[STIX]{x1D708}$) of $Re_{H}=U_{b}D_{H}/\unicode[STIX]{x1D708}\approx 30\,000\pm 5\,\%$. When running partially full, the inferred friction factor is no longer a simple function of Reynolds number, but also depends on the Froude number $Fr=U_{b}/\sqrt{gD_{m}}$ where $g$ is gravitational acceleration and $D_{m}$ is hydraulic mean depth. S-PIV measurements in turbulent flow reveal the presence of secondary currents which causes the maximum streamwise velocity to occur below the free surface consistent with results reported in the literature for rectangular cross-section open channel flows. Unlike square duct and rectangular open channel flow the mean secondary motion observed here manifests only as a single pair of vortices mirrored about the vertical bisector and these rollers, which fill the half-width of the pipe, remain at a constant distance from the free surface even with decreasing flow depth for the range of depths tested. Spatial distributions of streamwise Reynolds normal stress and turbulent kinetic energy exhibit preferential arrangement rather than having the same profile around the azimuth of the pipe as in a full pipe flow. Instantaneous fields reveal the signatures of elements of canonical wall-bounded turbulent flows near the pipe wall such as large-scale and very-large-scale motions and associated hairpin packets whilst near the free surface, the signatures of free surface turbulence in the absence of imposed mean shear such as ‘upwellings’, ‘downdrafts’ and ‘whirlpools’ are present. Two-point spatio-temporal correlations of streamwise velocity fluctuation suggest that the large-scale coherent motions present in full pipe flow persist in partially filled pipes but are compressed and distorted by the presence of the free surface and mean secondary motion.


AIChE Journal ◽  
1996 ◽  
Vol 42 (4) ◽  
pp. 901-909 ◽  
Author(s):  
Eric Grolman ◽  
Niels C. J. Commandeur ◽  
Eduard C. de Baat ◽  
Jan M. H. Fortuin
Keyword(s):  

Author(s):  
R. J. Wilkens ◽  
S. R. Glassmeyer ◽  
G. J. Rosebrock ◽  
K. M. Storage ◽  
T. M. Storage

A set of experiments was performed to study flow pattern suppression in gas-liquid pipe flow by means of surfactant additive. Results suggest that addition of the surfactant to gas-liquid flow significantly reduces the occurrence of slug flow. In addition, previously unreported flow patterns were observed to exist between slug and dispersed bubble flows. It is concluded that new mechanisms for slug flow transition need to be considered.


1996 ◽  
Vol 118 (4) ◽  
pp. 729-735 ◽  
Author(s):  
Eric Grolman ◽  
Jan M. H. Fortuin

A model is presented for transient, cocurrent gas-liquid pipe flow in the stratified-smooth and stratified-wavy flow regimes. It is based on the equations of continuity and motion in the direction of flow and results in two hyperbolic partial differential equations, which are solved numerically using the combined methods of lines (Schiesser, 1991) and characteristics (Stoker, 1957). In wavy gas-liquid pipe flow, three different interfacial areas and corresponding shear stresses are identified. Three friction-factor correlations were derived on the basis of an extensive set of 2500 steady-state measurements. The transient behavior of inclined gas-liquid pipe flow is successfully simulated and compares well with the results obtained from on-line measurements, right up to the onset of slug flow.


2021 ◽  
Vol 55 (2) ◽  
pp. 317-325
Author(s):  
Hailong Jiang ◽  
Kui Zhang ◽  
Boyu Jiang ◽  
Xuejin Dai

In order to study the electrochemical corrosion law for the 13Cr stainless-steel tubing material in a high-speed Cl-containing liquid, a high-speed-flow experiment and a small three-electrode system, embedded in a small pipe, were used. The open circuit potential (OCP), polarization curve (PC) and electrochemical impedance spectroscopy (EIS) of the stainless-steel surface were tested in a medium with a flow velocity ranging from 10 to 22 m/s containing 1 w/% and 2 w/% of NaCl. By comparing it with the changes in the electrochemical-reaction parameters of the material in distilled water, the results of the experiment including the critical flow velocity, the change of corrosion rate and the electrochemical-reaction control steps were obtained. By theoretically solving the frictional force of the liquid against the wall surface and the adsorption capacity of the oxide film, and assuming that the oxide film is a macromolecular combination, the relationship between the adsorption capacity of different surface films and the critical flow velocity in the high-speed pipe flow was established. The results of this experiment and calculation can provide a preliminary prediction of the critical flow velocity corresponding to the inflection point of the wall-surface corrosion rate in an industrial pipe flow, thereby improving the process parameters and reducing the wall damage.


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