By Elemer Bobok
ISBN-10: 0444986685
ISBN-13: 9780444986689
Written essentially to supply petroleum engineers with a scientific analytical method of the answer of fluid movement difficulties, this e-book will however be of curiosity to geologists, hydrologists, mining-, mechanical-, or civil engineers. It presents the information precious for petroleum engineers to advance layout equipment for drilling, construction, delivery of oil and gasoline. easy mechanical legislation are utilized for excellent fluid stream, Newtonian fluid, non-Newtonian fluid, and a number of section flows. parts of fuel dynamics, a non-familiar remedy of outrage waves, boundary layer thought, and two-phase stream also are incorporated.
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Example text
It can be expressed as the time derivative of the velocity: * di, a = -. 3 THE ACCELERATION FIELD Acceleration vectors form an acceleration field, which can be determined from the velocity field directly by using Eq. 11). The vector differential of the velocity field is: da = duxF+ duyj+du,ff. J7 aZ doy= - d t + auy Laud x + -dy+ aY ax au, -&, do2= -au, dt+ at av, -dx+ av, -dz. at ax aU, -dy+ aY aZ aZ Substituting into Eq. 11) and taking into account Eq. 2), we obtain the equations: av, aux +uy- a U x +u,- au, ax= -+uxat ax aZ ’ ay auy auy avy av,, ay= - +ox+ v -+ u at ax y a2= au, at - +vx- ay aZ au, av, au, + u - +u,-.
The set of streamlines passing through this curve L form a stream surface (Fig. 6). The velocity vector is perpendicular to the surface normal vector at every point of the stream surface. This can be formulated as 6dA=O. 8) Since the velocity vector has no normal component on the stream surface, there is no flux across it. Thus a solid boundary of a rigid or a deformable body can be Fig. 6. Stream surface Fig. 7. 2 THE VELOCITY FIELD replaced by a stream surface. g. g. a bubble in a water flow.
Entropy is not a quantity which is conserved. There is no axiom to determine the rate of change of entropy during an irreversible process. 6 THE BALANCE OF ENTROPY 53 the balance of entropy equation by starting from the internal energy equation. de e-+divij=T:iroV. 84) where p is the pressure, I is the unit tensor, V is the viscous stress tensor. Since V is symmetric, the product of V and the antisymmetric part of B 0 Vmust vanish. 85) dt where S is the rate of deformation tensor. The first law of thermodynamics can be written as de = Tds-pd ):( .
Fluid Mechanics for Petroleum Engineers by Elemer Bobok
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