LINEARIZED THEORY OF A TWO-DIMENSIONAL PLANING FLAT PLATE IN A CHANNEL OF FINITE DEPTH-1

1964 ◽  
Author(s):  
D. K. Ai ◽  
A. J. Acosta ◽  
Z. L. Harrison
Keyword(s):  
Flat Plate ◽  
Finite Depth ◽  
Two Dimensional ◽  
Linearized Theory

Boundary Effects in Wake Flow

1968 ◽  
Vol 35 (3) ◽  
pp. 571-578
Author(s):  
C. Y. Liu
Keyword(s):  
Experimental Data ◽  
Flat Plate ◽  
Analytical Solutions ◽  
Angle Of Attack ◽  
Finite Depth ◽  
Wake Flow ◽  
Boundary Effects ◽  
Arbitrary Angle ◽  
Linearized Theory

Analytical solutions are obtained for the problem of boundary effects on the fully developed wake (or cavity) behind an inclined flat plate at an arbitrary angle of attack. The investigation is based on the Helmholtz free-streamline theory. Results are applied to four cases: (a) Blockage in a fixed-wall tunnel, (b) planing on a stream of finite depth, (c) planing toward a waterfall, and (d) flow over a flat plate in a bounded jet. Comparisons with linearized theory and available experimental data are made.

On the Application of Linearized Theory to Multi-Element Aerofoils Part I: Tandem Flat Plate Aerofoils

1983 ◽  
Vol 34 (1) ◽  
pp. 46-60 ◽  
Author(s):  
G.D. Watt ◽  
G.V. Parkinson
Keyword(s):  
Flat Plate ◽  
Potential Flow ◽  
Flow Theory ◽  
Two Dimensional ◽  
Potential Flow Theory ◽  
Linearized Theory ◽  
Good Agreement ◽  
Hand Calculator

SummaryA linearized two-dimensional incompressible potential flow theory for two-element uncambered tandem aerofoil sections is developed. It leads to formulas for lift and moment which can be calculated rapidly on a programmable hand calculator, and which reduce, when the two aerofoil elements come together, to the familiar thin-aerofoil formulas for an aerofoil with a simple flap. The theory is shown to give lift and moment predictions which are in good agreement with predictions of numerical potential flow theory.

Comparison principles for free-surface flows with gravity

1991 ◽  
Vol 230 ◽  
pp. 231-243 ◽  
Author(s):  
Walter Craig ◽  
Peter Sternberg
Keyword(s):  
Solitary Waves ◽  
Finite Depth ◽  
Free Surface Flows ◽  
Immiscible Fluids ◽  
Steady Flows ◽  
Two Dimensional ◽  
Surface Flows ◽  
Ship Hulls ◽  
Geometrical Information ◽  
Supercritical Flows

This article considers certain two-dimensional, irrotational, steady flows in fluid regions of finite depth and infinite horizontal extent. Geometrical information about these flows and their singularities is obtained, using a variant of a classical comparison principle. The results are applied to three types of problems: (i) supercritical solitary waves carrying planing surfaces or surfboards, (ii) supercritical flows past ship hulls and (iii) supercritical interfacial solitary waves in systems consisting of two immiscible fluids.

The aerodynamic theory of sails. I. Two-dimensional sails

1961 ◽  
Vol 261 (1306) ◽  
pp. 402-422 ◽  
Keyword(s):  
Lift Coefficient ◽  
Linear Equations ◽  
Three Dimensional ◽  
Angle Of Incidence ◽  
Two Dimensional ◽  
Inviscid Incompressible Fluid ◽  
Two Dimensional Flow ◽  
Linearized Theory ◽  
High Degree ◽  
Additional Equation

This paper deals with the preliminaries essential for any theoretical investigation of three-dimensional sails—namely, with the two-dimensional flow of inviscid incompressible fluid past an infinitely-long flexible inelastic membrane. If the distance between the luff and the leach of the two-dimensional sail is c , and if the length of the material of the sail between luff and leach is ( c + l ), then the problem is to determine the flow when the angle of incidence α between the chord of the sail and the wind, and the ratio l / c are both prescribed; especially, we need to know the shape of, the loading on, and the tension in, the sail. The aerodynamic theory follows the lines of the conventional linearized theory of rigid aerofoils; but in the case of a sail, there is an additional equation to be satisfied which ex­presses the static equilibrium of each element of the sail. The resulting fundamental integral equation—the sail equation—is consequently quite different from those of aerofoil theory, and it is not susceptible to established methods of solution. The most striking result is the theoretical possibility of more than one shape of sail for given values of α and l / c ; but there appears to be no difficulty in choosing the shape which occurs in reality. The simplest result for these realistic shapes is that the lift coefficient of a sail exceeds that of a rigid flat plate (for which l / c = 0) by an amount approximately equal to 0.636 ( l / c ) ½ . It seems very doubtful whether analytical solutions of the sail equation will be found, but a method is developed in this paper which comes to the next best thing; namely, an explicit expression, as a matrix quotient, which gives numerical values to a high degree of accuracy at so many chord-wise points. The method should have wide application to other types of linear equations.

The magneto-hydrodynamic boundary layer in the two-dimensional steady flow past a semi-infinite flat plate II. The Falkner-Skan problem

1963 ◽  
Vol 273 (1355) ◽  
pp. 509-517 ◽  
Keyword(s):  
Flat Plate ◽  
Iterative Procedure ◽  
Hypergeometric Functions ◽  
Close Agreement ◽  
Adverse Pressure Gradient ◽  
Iterative Solution ◽  
Two Dimensional ◽  
Confluent Hypergeometric Functions ◽  
First Case ◽  
Hydrodynamic Boundary Layer

The problem investigated is the flow of a viscous liquid past a semi-infinite flat plate against an adverse pressure gradient. The method used is an iterative method suggested in a paper by Weyl. To start the iterative procedure a function is chosen which satisfies some of the boundary conditions and by using this function the first iterative solution has been obtained analytically in terms of confluent hypergeometric functions. Two different starting functions have been considered. In the first case it has been found possible to compare the results obtained with the well-known Hartree numerical solution and even at the first iteration close agreement is achieved. In the second case, the first iterative solution behaves correctly at infinity but the agreement with Hartree ’s solution is not as good as it is in the first case.

Sign in / Sign up

Export Citation Format

Share Document