Mathematical model for the free surface flow under a sluice gate

2002 ◽  
Vol 125 (1) ◽  
pp. 49-58 ◽  
Author(s):  
Titus Petrila
Keyword(s):  
Mathematical Model ◽  
Free Surface ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Sluice Gate

scholarly journals Instability of Liquid-Film Flows With Temperature-Dependent properties Down A Heated Incline

2021 ◽  
Author(s):  
Syeda Rubaida Zafar
Keyword(s):  
Mathematical Model ◽  
Free Surface ◽  
Stability Analysis ◽  
Marangoni Effect ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Temperature Dependent ◽  
The Stability ◽  
Temperature Dependent Properties ◽  
Film Flows

In this thesis we investigate the stability of free-surface flow on a heated incline. We develop a complete mathematical model for the flow which captures the Marangoni effect and also accounts for changes in the properties of the fluid with temperature. We apply a linear stability analysis to determine the stability of the steady and uniform flow. The associated eigenvalue problem is solved numerically by means of a spectral colocation method.

scholarly journals Instability of Liquid-Film Flows With Temperature-Dependent properties Down A Heated Incline

2021 ◽  
Author(s):  
Syeda Rubaida Zafar
Keyword(s):  
Mathematical Model ◽  
Free Surface ◽  
Stability Analysis ◽  
Marangoni Effect ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Temperature Dependent ◽  
The Stability ◽  
Temperature Dependent Properties ◽  
Film Flows

In this thesis we investigate the stability of free-surface flow on a heated incline. We develop a complete mathematical model for the flow which captures the Marangoni effect and also accounts for changes in the properties of the fluid with temperature. We apply a linear stability analysis to determine the stability of the steady and uniform flow. The associated eigenvalue problem is solved numerically by means of a spectral colocation method.

Numerical calculations of the free-surface flow under a sluice gate

1997 ◽  
Vol 330 ◽  
pp. 339-347 ◽  
Author(s):  
J.-M. VANDEN-BROECK
Keyword(s):  
Integral Equation ◽  
Free Surface ◽  
Large Amplitude ◽  
Numerical Solutions ◽  
Free Surface Flow ◽  
Radiation Condition ◽  
Surface Flow ◽  
Boundary Integral ◽  
Sluice Gate ◽  
The Waves

The free-surface flow under a sluice gate is considered. The fluid is assumed to be inviscid and incompressible. The problem is solved numerically by using a boundary integral equation technique. Accurate numerical solutions are obtained when the intersection of the upstream free surface with the gate is a stagnation point. It is shown that the radiation condition is not satisfied far upstream and that there is a train of waves on the upstream free surface. For large values of the downstream Froude number F, the amplitude of the waves is so small that the upstream free surface is essentially flat. However for small values of F, the waves are of large amplitude. They ultimately approach the Stokes' limiting configuration with an angle of 120° at their crest as F is decreased.

The Contraction Coefficient of a Free-Surface Flow Under Gravity Entering a Region Beneath a Semi-Infinite Plane

2012 ◽  
Vol 2 (4) ◽  
pp. 342-352
Author(s):  
L. H. Wiryanto ◽  
H. B. Supriyanto
Keyword(s):  
Free Surface ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Straight Tube ◽  
Infinite Plane ◽  
Constant Depth ◽  
Sluice Gate ◽  
Contraction Coefficient ◽  
Dimensional Approximation ◽  
Infinite Wall

Abstract.Borda's mouthpiece consists of a long straight tube projecting into a large vessel, where fluid enters the tube in a free surface flow that tends to become uniform far downstream in the tube. A two-dimensional approximation to this flow under gravity in the upper part of the tube leads to an evaluation of the contraction coefficient, the ratio of the constant depth of the uniform flow to the width of the tube. The analysis also applies to flow under gravity past a sluice gate, if the semi-infinite wall above the channel is rotated to the vertical. The contraction coefficient depends upon the Froude numberF, and is generally less than the zero gravity value of 1/2 that is approached asF→ ∞.

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