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Volume 31 (2024)
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Advances and Applications in Fluid Mechanics
Advances and Applications in Fluid Mechanics
Volume 6, Issue 2, Pages 121 - 140 (October 2009)
BOUNDARY LAYER THEORY IN TWO-DIMENSIONAL LAMINAR MOTION WITH CIRCULAR HYDRAULIC JUMP
A. E. Eyo (Nigeria)
Abstract:
Watson [18] used boundary layer theory and a constant velocity profile to study the radial spread of a liquid jet over a horizontal plane. In this work, we also use boundary layer approach but with the incorporation of Lamb’s velocity profile to study two-dimensional motion of laminar flow of a liquid with circular hydraulic jump. Based on this model, a new relation is obtained for the following parameters: displacement thickness, momentum thickness and the position of the jump. Comparison of the approximate values obtained based on Karman-Pohlhausen [14] method with the exact values due to Blasius [2] shows that the error in the shear rate relation on the plane is only about 1.5% while the error in the thickness ratio is about 2.6%. These percentages, which are smaller than those of Watson [18], show remarkable improvement of our work upon that of Watson. Besides, our values also compare rather favourably with the exact values [2]. Finally, our analysis reveals that the depth of the fluid on the plane is dependent on the velocity profile used.
Keywords and phrases:
boundary layer, two-dimensional, laminar, circular hydraulic jump, velocity profile.
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