Two Dimensional Laminar Flow of a Liquid with Circular Hydraulic Jump

Asuquo Essien Eyo,Paul J Udoh,Enobong E Joshua

doi:10.5539/mas.v5n3p56

Abstract

We examine two-dimensional laminar flow of a liquid with circular hydraulic jump using boundary layer approach, but with the inclusion of a velocity profile approximated by a quadratic function. Our motivation is due to an earlier work of * on radial spread of a liquid over a horizontal plate. We obtain a new relation for the displacement thickness, momentum thickness and position of the jump. Our approximate values based on ** are compared with the exact values due to ***. The comparison shows the error of about 9% in the shear rate relation on the plate and the error of about 3.5% in the thickness ratio. Our values agree to a large extent with the exact values and also show improvement of our work upon that of * with respect to the thickness ratio.

Highlights

It is commonly observed, for example, in a kitchen sink, that a stream of liquid falling vertically on to a horizontal plate spreads out radially in a particular manner
In this paper our objective is to discuss circular hydraulic jump by means of boundary layer theory, but with the inclusion of a velocity profile approximated by a quadratic function
Is indeterminate, whereas incorporation of viscous effects (2) in (11) coupled with the use of the principles of momentum and continuity at the jump leads to the modified result (91) for the position x x1 of the jump is given by (91) for x1 x0 or (96) for xx11

Summary

Introduction

For example, in a kitchen sink, that a stream of liquid falling vertically on to a horizontal plate spreads out radially in a particular manner. Bush et al (2006) presented the results of an experimental investigation of the striking flow structures that may arise when a vertical jet of liquid impinges on a thin fluid layer overlying a horizontal boundary. Their experiments revealed a new class of steady asymmetric jump forms that included structures resembling cat’s eyes, three – and four – leaf clovers, bowties and butterflies. Kate et al (2008) used oblique impingement of a circular liquid jet with a horizontal target to obtain hydraulic jumps of unique non-circular shapes They investigated experimentally the hydrodynamics of this phenomenon and they observed hydraulic jumps of two broad categories. Note that x0 is given by the condition h , so that the whole flow passes through the boundary layer

Ideal Theory

Blasius Solution of Two Dimensional Laminar Boundary Layer Equations

Jump Conditions

Discussion and Conclusion