The Effect of the Earth’s Rotation on Laminar Flow in Pipes

1956 ◽  
Vol 23 (1) ◽  
pp. 123-127
Author(s):  
G. S. Benton
Keyword(s):  
Laminar Flow ◽  
Secondary Flow ◽  
Cross Section ◽  
Pipe Flow ◽  
Earth’S Rotation ◽  
Laboratory Studies ◽  
Earth's Rotation ◽  
Parabolic Profile ◽  
Set Up ◽  
Laminar Pipe Flow

Abstract The theory of laminar pipe flow has been developed, retaining the effect of the earth’s rotation. A secondary flow is set up in the pipe cross section which results in distortion of the usual parabolic profile. The distortion may be significant in pipes of moderate diameter. Laboratory studies tend to substantiate these conclusions.

Viscous laminar flow in a curved pipe of elliptical cross-section

1987 ◽  
Vol 184 ◽  
pp. 571-580 ◽  
Author(s):  
H. C. Topakoglu ◽  
M. A. Ebadian
Keyword(s):  
Reynolds Number ◽  
Laminar Flow ◽  
Finite Number ◽  
Secondary Flow ◽  
Cross Section ◽  
Expansion Method ◽  
Elliptic Cross Section ◽  
Elliptical Cross ◽  
Curved Pipe ◽  
Elliptic Cross

In this paper, the analysis on secondary flow in curved elliptic pipes of Topakoglu & Ebadian (1985) has been extended up to a point where the rate-of-flow expression is obtained for any value of flatness ratio of the elliptic cross-section. The analysis is based on the double expansion method of Topakoglu (1967). Therefore, no approximation is involved in any step other than the natural limitation of the finite number of calculated terms of the expansions. The obtained results are systematically plotted against the curvature of centreline of the curved pipe for different values of Reynolds number.

Lateral force on a rigid sphere in large-inertia laminar pipe flow

2009 ◽  
Vol 621 ◽  
pp. 59-67 ◽  
Author(s):  
JEAN-PHILIPPE MATAS ◽  
JEFFREY F. MORRIS ◽  
ÉLISABETH GUAZZELLI
Keyword(s):  
Cross Section ◽  
Pipe Flow ◽  
Lift Force ◽  
Suspended Particle ◽  
Plane Channel ◽  
Circular Cross Section ◽  
Lateral Force ◽  
Rigid Sphere ◽  
Neutrally Buoyant ◽  
Laminar Pipe Flow

We present a prediction of the lateral force exerted on a rigid neutrally buoyant sphere in circular cross-section Poiseuille flow. The force is calculated with the method of matched asymptotic expansions. We investigate the influence of the pipe Reynolds number in the range 1–2000 on the equilibrium position and the magnitude of the lateral force. We show that the predicted lift force in a circular geometry is qualitatively similar to, but quantitatively different from, that in a plane channel. The predicted force in the pipe is significantly smaller than the channel result, and the zero of the force which determines the equilibrium radial position of a suspended particle lies closer to the centreline in the pipe.

Unified Approach to the Solution of Problems of Unsteady Laminar Flow in Long Pipes

1983 ◽  
Vol 50 (1) ◽  
pp. 8-12 ◽  
Author(s):  
M. F. Letelier S. ◽  
H. J. Leutheusser
Keyword(s):  
Laminar Flow ◽  
Power Series ◽  
Pipe Flow ◽  
Power Series Expansion ◽  
Solution Procedure ◽  
Time Dependent ◽  
Local Velocity ◽  
Unified Approach ◽  
Forcing Function ◽  
Laminar Pipe Flow

The paper presents a unified approach to the solution of laminar pipe-flow transients in which the forcing function may depend on the motion itself. The key to the solution procedure is a power series expansion of the local velocity in terms of radial position, involving a single time-dependent coefficient. The method of analysis is applied to the solution of two particular cases of transients, namely flow establishment, without and with inflow, respectively. It is found to yield results that are in excellent agreement with other known analytical solutions and experimental observations.

The Dean equations extended to a helical pipe flow

1989 ◽  
Vol 203 ◽  
pp. 289-305 ◽  
Author(s):  
M. Germano
Keyword(s):  
Secondary Flow ◽  
Cross Section ◽  
Pipe Flow ◽  
Circular Cross Section ◽  
Order Effect ◽  
Displacement Effect ◽  
Elliptical Cross ◽  
First Order ◽  
Helical Pipe ◽  
Axial Pressure Gradient

In this paper the Dean (1928) equations are extended to the case of a helical pipe flow, and it is shown that they depend not only on the Dean number K but also on a new parameter λ/[Rscr ] where λ is the ratio of the torsion τ to the curvature κ of the pipe axis and [Rscr ] the Reynolds number referred in the usual way to the pipe radius a and to the equivalent maximum speed in a straight pipe under the same axial pressure gradient. The fact that the torsion has no first-order effect on the flow is confirmed, but it is shown that this is peculiar to a circular cross-section. In the case of an elliptical cross-section there is a first-order effect of the torsion on the secondary flow, and in the limit λ/[Rscr ] → ∞ (twisted pipes, provided only with torsion), the first-order ‘displacement’ effect of the walls on the secondary flow, analysed in detail by Choi (1988), is recovered.Different systems of coordinates and different orders of approximations have recently been adopted in the study of the flow in a helical pipe. Thus comparisons between the equations and the results presented in different reports are in some cases difficult and uneasy. In this paper the extended Dean equations for a helical pipe flow recently derived by Kao (1987) are converted to a simpler form by introducing an appropriate modified stream function, and their equivalence with the present set of equations is recovered. Finally, the first-order equivalence of this set of equations with the equations obtained by Murata et al. (1981) is discussed.

The Earth's rotation and laminar pipe flow

1998 ◽  
Vol 361 ◽  
pp. 297-308 ◽  
Author(s):  
A. A. DRAAD ◽  
F. T. M. NIEUWSTADT
Keyword(s):  
Coriolis Force ◽  
Pipe Flow ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Viscous Force ◽  
Navier Stokes ◽  
Earth’S Rotation ◽  
Earth's Rotation ◽  
Navier Stokes Equations ◽  
Physical Background

A pipe flow facility with a length of 32 m and a diameter of 40 mm has been designed in which a laminar flow of water can be maintained for Reynolds numbers up to 60 000. Velocity measurements taken in this facility show an asymmetric velocity profile both in the vertical as well as horizontal direction with velocities that deviate strongly from the parabolic Hagen–Poiseuille profile. The cause of this asymmetry is traced back to the influence of the Earth's rotation. This is confirmed by means of a comparison of the experimental data with the results from a perturbation solution and from a numerical computation of the full nonlinear Navier–Stokes equations. The physical background of this unforeseen result lies in the fact that a Hagen–Poiseuille flow is governed by a force equilibrium and inertia forces are everywhere negligible. This implies that the Coriolis force can be balanced only by a viscous force. So even the small Coriolis force due to the Earth's rotation causes a large velocity distortion for a case such as ours where the kinematic viscosity is small.

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.

Secondary flow in a rotating straight pipe

1954 ◽  
Vol 227 (1168) ◽  
pp. 133-139 ◽  
Keyword(s):  
Pressure Gradient ◽  
Secondary Flow ◽  
Cross Section ◽  
Circular Cross Section ◽  
Resistance Coefficient ◽  
Straight Pipe ◽  
Secondary Motion ◽  
Fluid Particles ◽  
Set Up

When a straight pipe of circular cross-section through which liquid is flowing under a pressure gradient is rotated about an axis perpendicular to it, secondary motion is set up and the fluid particles move in spirals relative to the pipe. This secondary motion has been studied in detail and an expression for the consequent rise in the resistance coefficient has been obtained.

scholarly journals Solar Forcing of Changes in Atmospheric Circulation, Earth's Rotation and Climate

2008 ◽  
Vol 2 (1) ◽  
pp. 181-184 ◽  
Author(s):  
Adriano Mazzarella
Keyword(s):  
Surface Temperature ◽  
Sea Surface Temperature ◽  
Atmospheric Circulation ◽  
Sea Surface ◽  
Earth’S Rotation ◽  
Holistic Model ◽  
Earth's Rotation ◽  
Historical Series ◽  
Climatological Model ◽  
Set Up

Cross analysis of available historical series of solar wind turbulence, atmospheric circulation, Earth’s rotation and sea surface temperature, when smoothed from the secular trend and periods shorter than 23 years, allowed a cascade climatological model to be set up that integrates the Sun-atmosphere-Earth system as a simple unit and ties solar corpuscular output to sea surface temperature through atmospheric circulation and the Earth’s rotation. An increase in solar corpuscular activity causes a deceleration of zonal atmospheric circulation which, like a torque, causes a deceleration of the Earth’s rotation that, in turn, causes a decrease in sea surface temperature. Application of this holistic model allows us to predict a gradual decline in global warming starting from the current decade.

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