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New Equations for Flow Drag Force and Its Application

Author(s): Shu-Qing Yang

Linked Author(s): Shuqing Yang

Keywords: Green's theorem, Form Drag, Skin Friction, Boundary Layer theory, wake volume.


Determination of form drag by a blunt object in fluid flows is practically useful and an important topic for fundamental research. Flow resistance has been described by N-S equations, i.e., the boundary shear stress or the skin friction dominates the flow resistance. The skin friction has been well defined and understood, but the definition of form drag is not so successful even in the simplest case, i.e., the pipe flow with roughness like Nikuradse’ experiment. To make attempt to understand those, this paper first defines form drag as d d w = r 2/ = rgkVgUCgAF 2 1 , where ρ = fluid density, g = gravitational acceleration, k = coefficient, A1 = projection area of an object and U = approaching velocity. Yang (2013) noticed that U2 /2g has the length dimension, and the product of area A and a length yields a volume of Vw. He interpreted that the form drag is actually an alternative form of Archimedes’ law, i.e., the drag force is proportional to the volume of wake behind an object. This paper verifies this interpretation by examining the measured volume of wake behind cylinders and spheres using the available data in the literature. It is found that in the existing expression of Cd, the skin friction on the front part is included. If the skin friction is excluded, the Cd should be a constant, not a variable dependent on the Reynolds number. This paper extends the basic idea of boundary layer flow (or the 1st type of boundary layer flow) formed by a flat plate to a blunt object, and “the 2nd type of boundary layer flow” is proposed to express the fluid zone of wake behind the object. The 1st type of boundary layer has been proposed by Prandtl to express the skin friction where the near boundary flow is parallel to the main flow direction, and the viscous effect generates the skin friction that is proportional to the contact area. The 2nd type is caused by the back flow, and its magnitude is proportional to a volume. (2643, 67, 303)


Year: 2017

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