The method of calculating the velocity field and shear stresses in incompressible fluid
DOI:
https://doi.org/10.15587/1729-4061.2016.65900Keywords:
incompressible fluid, Poiseuille, flow regimes, velocity gradient, vorticityAbstract
The velocity field calculation method is based on the use of two special cases of the Newtonian fluid motion equations, not including the Navier-Stokes equations. Two shear stress calculation methods are considered. The first method is the differentiation of the velocity field equation, and the second one requires the solution of the first-order differential equation. The second method provides the distribution of shear stresses for any continuous medium, including the Newtonian fluid.
Calculation equations for a laminar flow in a round pipe are found. It is shown that a parabolic velocity distribution along the radius is a special case of a more general equation.
The factors affecting the shear stresses for the three flow models are found. Stresses are determined by the linear velocity gradients in the laminar flow. In the 3D vortex, they can be found by various equations, which include vorticity. Total stresses for the averaged turbulent flow are calculated by summing the previously found stresses.
The equations of the method are incomplete and may be used for the accurate solution of simple problems.References
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