Flow of Fluid of Relatively Low Viscosity Round Obstacles of Regular Shapes

Adeboye, E.A (1971)

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The Chapters one and two give the introduction and a review of the problem of twodimensional flow of non-viscous fluids past a circular cylinder, elliptic cylinder and a flat plate and the boundary layer theory for fluids of ow viscosity Chapter three deals with the two-dimensional viscous flow round a circular cylinder, chapter four with the elliptic cylinder and chapter five with the parabolic cylinder. The viscosity is assumed to be very low, the curvature of the surface of the obstacles small and pressure gradient negative in the direction of flow. The methods used are entirely new and in each case it was found that no matter how small viscosity may be it makes a definite contribution to the pressure distribution about the obstacle. For a circle of radius R, this contribution is found to be 3.46(m.1) VR II q pq2(1-cos20)[2- ---------------------------] R12.11 VR q where q is the free stream speed. For an ellipse of semi-major axis 'a' and semi-minor axis 'b', the contribution is ^pq2(a.b\sin 2n (a b\(sinh 2E.sin 2n (2ab ^) ^ 1.73b2vx1 a 1 k)3[2a2,b2(1 sk1] 3.4 For a parabola of latus a rectum 4p, the contribution is 2a2n2 vkp x 1.73 q Chapter six deals with the case of flow around a flat plate in which the viscosity is not constant. Such a problem can arise in cases where heat is constantly being generated owing to internal friction and carried along with the fluid. A new equation based on the assumption that viscosity is a function of x has been derived for the flat plate problem The equation is 2vf''' ( v xdv H''' dx and has been sholved in a few simple cases.