laminar and Turbulent flow

laminar and Turbulent flow

1. 1 Unit-5: Laminar and Turbulent Flow BY TIWARE V.S. ASSISTANT PROFESSOR BVCOE KOLHAPUR

2. Content A. Laminar Flow and Turbulent Flow: Reynold's Experiment, Hazen Poisulle's Equation for Viscous Flow through Circular Pipes, Prandtl Mixing Length Theory, Introduction to Moody's Chart. B. Boundary Layer Theory: Concept, Various Thicknesses (Nominal, Displacement, Momentum, Energy), Hydraulically Smooth and Rough Boundaries, Separation of Boundary Layer, Control of Separation.

3. LAMINAR FLOW:

4. LOSS OF HEAD DUE TO FRICTION IN PIPE FLOW–DARCY EQUATION

5. Moodys Chart In engineering, the Moody chart or Moody diagram is a graph in non-dimensional form that relates the Darcy-Weisbach friction factor fD, Reynolds number Re, and surface roughness for fully developed flow in a circular pipe. It can be used to predict pressure drop or flow rate down such a pipe.

6. BOUNDARY LAYER THEORY The concept of boundary layer was first introduced by L. Prandtl in 1904 and since then it has been applied to several fluid flow problems. When a real fluid (viscous fluid) flows past a stationary solid boundary, a layer of fluid which comes in contact with the boundary surface, adheres to it (on account of viscosity) and condition of no slip occurs (The no-slip condition implies that the velocity of fluid at a solid boundary must be same as that of boundary itself). Thus the layer of fluid which cannot slip away from the boundary surface undergoes retardation; this retarded layer further causes retardation for the adjacent layers of the fluid, thereby developing a small region in the immediate vicinity of the boundary surface in which the velocity of the flowing fluid increases rapidly from zero at the boundary surface and approaches the velocity of main stream. The layer adjacent to the boundary is known as boundary layer. Boundary layer is formed whenever there is relative motion between the boundary and the fluid.

7. the fluid exerts a shear stress on the boundary and boundary exerts an equal and opposite force on fluid known as the shear resistance. According to boundary layer theory the extensive fluid medium around bodies moving in fluids can be divided into following two regions: (i) A thin layer adjoining the boundary is called the boundary layer where the viscous shear takes place. (ii) A region outside the boundary layer where the flow behaviour is quite like that of an ideal fluid and the potential flow theory is applicable

8. BOUNDARY LAYER DEFINITIONS AND CHARACTERISTICS: Consider the boundary layer formed on a flat plate kept parallel to flow of fluid of velocity U (Though the growth of a boundary layer depends upon the body shape, flow over a flat plate aligned in the direction of flow is considered, since most of the flow surfaces can be approximated to a flat plate and for simplicity). — The edge facing the direction of flow is called leading edge. — The rear edge is called the trailing edge. — Near the leading edge of a flat plate, the boundary layer is wholly laminar. For a laminar boundary layer, the velocity distribution is parabolic. — The thickness of the boundary layer (δ) increases with distance from the leading edge x, as more and more fluid is slowed down by the viscous boundary, becomes unstable and breaks into turbulent boundary layer over a transition region.

9. Boundary Layer Thickness (δ) The velocity within the boundary layer increases from zero at the boundary surface to the velocity of the main stream asymptotically. Therefore the thickness of the boundary layer is arbitrarily defined as that distance from the boundary in which the velocity reaches 99 per cent of the velocity of the free stream (u = 0.99U). It is denoted by the symbol δ. This definition however gives an approximate value of the boundary layer thickness and hence δ is generally termed as nominal thickness of the boundary layer. The boundary layer thickness for greater accuracy is defined in terms of certain mathematical expressions which are the measure of the boundary layer on the flow. The commonly adopted definitions of the boundary layer thickness are: 1. Displacement thickness (δ*) 2. Momentum thickness (θ) 3. Energy thickness (δe)