Hence to find the shear stress, the time average on both sides of the equation Where u’, v’ = fluctuating component of velocity in the direction of x and y due to turbulence.Īs u’ and v’ are varying and hence τ will also vary. Reynolds developed an expression for turbulent shear stress between two layers of a fluid at a small distance apart, which is given as: Reynolds Expression for Turbulent Shear Stress. If the shear stress due to viscous flow is also considered, then …. The ratio of η (eddy viscosity) and (mass density) is known as kinematic eddy viscosity and is denoted by ϵ (epsilon). U bar = average velocity at a distance y from the boundary. Where τ t = shear stress due to turbulence Boussinesq expressed the turbulent shear mathematical form as Similar to the expression for viscous shear, J. In case of turbulent flow there is huge order intermission fluid particles and due to this, various properties of the fluid are going to change with space and time.Īverage velocity and fluctuating velocity in turbulent flow Turbulent flow is a flow regime characterized by the following points as given below From the above we can that the value of correction factor for Laminar flow is more than that for turbulent flow.It is defined as the ratio of kinetic energy of flow per second based on actual velocity to the kinetic energy of the flow per second based on average velocity across a same section.įor flow through pipes values of α and β: It is defined as the ratio of momentum per second based on actual velocity to the momentum per second based on average velocity across a section. Pressure difference between two parallel fixed plates Ratio of Maximum velocity to average velocity: The average velocity is obtained by dividing the discharge (Q) across the section by the area of the section t × 1. Velocity and shear stress profile for turbulent flowĭischarge (Q) between two parallel fixed plates: Thus, velocity varies parabolically as we move in y-direction as shown in Figure. Laminar Flow Between Two Fixed Parallel Platesįor steady and uniform flow, there is no acceleration and hence the resultant force in the direction of flow is zero. Radial distance from the pipe axis at which the velocity equals the average velocity Head loss in Laminar flow through a pipe over length LĪbove equation is hagen poiseuille equation. On integrating the above equation on both sides: Pressure variation in Laminar flow through a pipe over length L Thus, the Average velocity for Laminar flow through a pipe is half of the maximum velocity of the fluid which occurs at the centre of the pipe. Ratio of maximum velocity to average velocity Shear stress and velocity distribution in laminar flow through a pipe As there is no acceleration hence:Īs ∂P/∂x across a section is constant, thus the shear stress τ varies linearly with the radius r as shown in the Figure. The shear force, τ × 2πr∆x on the surface of the fluid element. Now, forces acting on the fluid element are: Ν = Kinematic viscosity of the liquid (m 2/s) Μ = dynamic viscosity of the liquid (N – s /m 2) It is referred to as Re, is used to determine whether the fluid flow is laminar or turbulent.ĭ = Characteristic length of the geometry The dimensionless Reynolds number plays a prominent role in foreseeing the patterns in a fluid’s behaviour.In case of turbulent flow there is continuous inter mixing of fluid particles.Laminar flow is also referred to as streamline or viscous flow.Laminar flow is the flow which occurs in the form of lamina or layers with no intermixing between the layers.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |