FLUID KINETICS- ENERGY CORRECTION FACTOR 'α' |Sumam Miss| FLUID MECHANICS Lecture Videos:M3 – L19

Описание: #EnergyCorectionFactor-α #LaminarFlow #TurbulentFlow
The discussion on the Energy Correction factor alpha α, connected with the definition of Bernoulli's equation, which states that for a steady irrotational flow of incompressible fluid, total energy at any point is constant. That is, the summation of velocity head and pressure head and position head, equal to constant and this constant is valid along the streamline. Bernoulli’s equation is valid under certain assumptions. The first assumption is flow is steady, that is, flow and fluid characteristics are constant with respect to time. Second is, fluid/flow is ideal, that means, fluid possess no viscosity, there is no frictional resistance or there is no loss. Third one is fluid/flow is incompressible, that means the density of the flowing fluid is constant. Fourth, is flow is one dimensional, that means this equation is derived for the motion of the fluid element along the streamline. Fifth, is flow is continuous and velocity is uniform over the section. Energy Correction factor alpha α, arise based on the concept of uniform velocity over the section. Based on Bernoulli's equation, the total energy at any point is constant.
Based on Newton's seconds law of motion, Bernoulli's equation can be viewed as work done by pressure force and gravity force on the fluid particle, equal to increase in kinetic energy of the fluid particle. If Bernoulli's equation is applied at two sections, p1/ρg +V1^2/ 2g +z1, total energy at the section 1, equal to total energy at the section 2. But, for real fluid, we must consider the losses, that take place when the fluid moves from section 1 to section 2. So, for real fluid, this equation is modified as p1/ρg +V1^2/2g +z1, equal to p2/ρ g +V2^2/2g +z2 +hL, hL is the head loss. V1 and V2, at the section 1 and the section 2, is the average velocity, obtained by the equation, V equal to Q / A.
One of the assumption used for the derivation of Bernoulli's equation is the concept of uniform velocity over the section. If you are considering the flow through a pipe, then the velocity is uniform throughout or the velocity V = Q /A. This velocity is considered uniform across a section. But, for real fluid, velocity = 0 at the boundary. The velocity of the fluid particle increases from 0 at the boundary to the maximum value at the centre. So, if you are taking a cross section, velocity of the fluid particle is changing from the boundary. All the fluid particles have different velocity at that section. That is, along any cross section, the velocity of the flow will be different at different points and the total kinetic energy possessed by the flowing fluid at any section will be obtained by integrating the kinetic energy possessed by different fluid particle. But, if you are calculating the Kinetic Energy based on the average velocity, V, Kinetic Energy = m V ^2/ 2. Which Kinetic Energy will be higher? Definitely, the kinetic energy calculated by integrating the Kinetic Energy of the individual fluid particle is higher than the Kinetic Energy, based on average velocity or we can equate these two Kinetic Energy by using the term alpha α, called Energy Correction factor. That is, the Kinetic Energy calculated by integrating the kinetic energy of the individual fluid particle = (alpha) α into the Kinetic Energy calculated based on the average velocity V.
The value of α is different for laminar flow and turbulent flow. What is laminar flow? In laminar flow Reynolds number is very less or it is less than two thousand for pipe flow and another characteristic of laminar flow is that, fluid is moving in layers. Each layer is having its own velocity or across the section, there is a huge velocity gradient, that is zero velocity at the boundary and it is increasing to the maximum value at the centre, whereas in turbulent flow Reynolds number is high. It is more than four thousand for pipe flow. In turbulent flow the fluid particles are moving in random manner and there is a momentum transfer taking place between the adjacent layers. The variation of velocity is very less across the section or it is more or less close to the average velocity V. So, if you are considering the value of α for laminar flow and turbulent flow, for laminar flow, the value of α is 2 compared to turbulent flow, where α is 1.03 to 1.06. What is the role of alpha, α in Bernoulli's equation? If you are accounting this Energy Correction factor α, Bernoulli's equation can be written as p1/ρ g +α1 * V1^2/ 2g +z1 equal to p2/ρg +α2*V2^2/2g +z2 +hL. That is total energy at the section 1 equal to total energy at the section 2 +hL, where α1 is the energy correction factor at the section 1 and α2, energy correction factor at the section 2. But, unless otherwise specified we need not consider the value of α.
Timestamps:
00:00 Introduction
03:44 Derivation of α
07:34 Laminar vs Turbulent flow