Fluid Mechanics: Chapter6_Laminar and Turbulent flow

In this book we look at an alternative way of deriving the governing equations of fluid flow using conservation of energy techniques on a differential element undergoing shear stress or viscous forces as it moves along a pipe and we use the expression for friction coefficient for laminar flow to derive the equations. We also derive a friction coefficient to work for Torricelli flow. We look at laminar, and turbulent flow. We look at cases where there is a pipe on a tank or an orifice and we develop the governing equations. We then develop a universal formula or equation that works for all types of flow i.e., laminar, transition and turbulen t flow in one equation. We go ahead and demonstrate Pouiselle flow and the conditions under which it will be observed. We explain other phenomena too.

In order to complete this tutorial you should already have completed level 1 or have a good basic knowledge of fluid mechanics equivalent to the Engineering Council part 1 examination 103.

The ANZIAM Journal, 2014

Fluid turbulence is often modelled using equations derived from the Navier–Stokes equations, perhaps with some semi-heuristic closure model for the turbulent viscosity. This paper considers a possible alternative hypothesis. It is argued that regarding turbulence as a manifestation of non-Newtonian behaviour may be a viewpoint of at least comparable validity. For a general description of nonlinear viscosity in a Stokes fluid, it is shown that the flow patterns are indistinguishable from those predicted by the Navier–Stokes equation in one- or two-dimensional geometry, but that fully three-dimensional flows differ markedly. The stability of linearized plane Poiseuille flow to three-dimensional disturbances is then considered, in a Tollmien–Schlichting formulation. It is demonstrated that the flow may become unstable at significantly lower Reynolds numbers than those expected from Navier–Stokes theory. Although similar results are known in sections of the rheological literature, the p...

arXiv: General Physics, 2017

The onset of turbulence in laminar flow of viscous fluids is shown to be a consequence of the limited capacity of the fluid to withstand shear stress. This fact is exploited to predict the flow velocity at which laminar flow becomes turbulent and to calculate, on a theoretical basis, the corresponding critical value of the Reynolds number. A constitutive property essential to the present analysis is the ultimate shear stress of the fluid. The paper shows how this stress can be determined experimentally from a test in plane Couette flow. For water at 20 °C, the value of the ultimate shear stress is calculated from the experiments reported in the literature. This value is then is employed to predict the Reynolds number corresponding to the onset of turbulence in Taylor-Couette flow and in pipe flow of circular cross section. The results are realistic and their significance is assessed critically. The procedure can be applied to predict the onset of turbulence in any non-turbulent flow...

1961

The so-called laminar sublayer is shown to be the region where the turbulent velocity fluctuations are directly dissipated by viscosity. A simplified linearized form of the equations of motion for the turbulent fluctuations is used to describe the turbulent field between the wall and the fully turbulent part of the flow. The mean flow in the sublayer and the turbulence field outside the sublayer are assumed to be known from the experiments. The thickness of the sublayer arises naturally in the theory and is directly analogous to the inner viscous region for the fluctuations in a laminar flow. It is shown that the large scale fluctuations containing most of the turbulent energy are convected downstream with a velocity characteristic of the middle of the boundary layer._ Thus Taylor's hypothesis does not apply to these large scale fluctuations near the wall. The convective velocity found in the measurements of pressure fluctuations at the boundaries of turbulent flows is in accord with the theory. Calculations are given for the energy spectra and u' fluctuation level in the sublayer and other aspects of the fluctuation field are discussed. It is shown that the production of turbulent energy is a *A preliminary account of this work was presented to the ftJrnnual Meeting of the Fluid Dynamics Division, American Physical Society, in November 1959 at Ann Arbor, Michigan. 3 maximum where the laminar shearing stress is equal to the turbulent shearing stress. The linear pressure fluctuation field at the edge of the sublayer is calculated and found to be much larger than the non-linear field. Examining the effect of strong free stream turbulence on laminar boundary layer transition, it appears that the physical model underlying Taylor's parameter is incorrect.

Citeseer

2010

Whether a flow is laminar or turbulent depends of the relative importance of fluid friction (viscosity) and flow inertia. The ratio of inertial to viscous forces is the Reynolds number. Given the characteristic velocity scale, U, and length scale, L, for a system, the Reynolds number is Re = UL/ν, where ν is the kinematic viscosity of the fluid. For most surface water systems the characteristic length scale is the basin-scale. Because this scale is typically large (1 m to 100's km), most surface water systems are turbulent. In contrast, the characteristic length scale for groundwater systems is the pore scale, which is typically quite small (< 1 mm), and groundwater flow is nearly always laminar. The characteristic length-scale for a channel of width w and depth h is the hydraulic radius, R h = wh/P, where P is the wetted perimeter. For an open channel P = (2h + w) and for a closed conduit P = 2(h+w). As a general rule, open channel flow is laminar if the Reynolds number defined by the hydraulic radius, Re = UR h /ν is less than 500. As the Reynolds number increases above this limit burst of turbulent appear intermittently in the flow. As Re increases the frequency and duration of the turbulent bursts also increases until Re > O(1000), at which point the turbulence is fully persistent. If the conduit boundary is rough, the transition to fully turbulent flow can occur at lower Reynolds numbers. Alternatively, laminar conditions can persist to higher Reynolds numbers if the conduit is smooth and inlet conditions are carefully designed.

Fundamentals of Fluid Mechanics (7th ed, Munson et al, 2012)

An elementary analytical fluid flow is composed by a geometric domain, a list of analytical constraints and by the function which depends on the physical properties, as Reynolds number, of the considered fluid. For this object, notions of laminar or weakly turbulent behavior are described using a simple mathematical model.

This textbook is designed for undergraduate students in mechanical or civil engineering and applied sciences. Assuming a background in calculus and physics, it focuses on using mathematics to model fluid mechanics principles. The book is organized into 13 chapters and uses both SI and British gravitational units. It includes a brief description of the engineering system and a discussion of gc for illustrative purposes.