TYPES OF FLUID FLOW. Laminar or streamline flow. Turbulent flow

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1 FLUID DYNAMICS

2 We will deal with Intrinsic properties of fluids Fluids behavior under various conditions Methods by which we can manipulate and utilize the fluids to produce desired results

3 TYPES OF FLUID FLOW Laminar or streamline flow Turbulent flow

4 LAMINAR FLOW Laminar or Streamline Flow, is a well-ordered flow and is characterized by the smooth sliding of adjacent fluid layers (or lamina) over one another, with mixing between layers occurring only on a molecular level.

5 TURBULENT FLOW Turbulent Flow, is an erratic (irregular) flow and is characterized by the transfer of small packets of fluid particles between layers. Thus it is accompanied by fluctuations in velocity. In turbulent flow the speed of the fluid at a point is continuously undergoing changes in both magnitude and direction.

6 Transition from Laminar to Turbulent Flow When fluid flow is intensified, it tends to switch from laminar to turbulent flow. The transition from laminar to turbulent flow was studied by Reynolds in He suggested a parameter (i.e., Reynolds number) as the criterion for predicting the type of flow in round tubes.

7 Reynolds Number (N RE ) Re D = DV = DVρ μ D = pipe diameter (m), V= the average fluid velocity (m/s), = the kinematic viscosity (m2/s), ρ= fluid density, η = fluid or dynamic viscosity V If N RE < 2100 then laminar flow If N RE > 4000 then turbulent flow External factors such as surface roughness and initial disturbances in the fluid may change the critical Reynolds number!!!

8 Velocity Profiles for Laminar and Turbulent Flows For laminar flow the velocity profile is parabolic; in turbulent flow, the curve is somewhat flattened in the middle. Notice that for both cases the velocity is zero at the fluid-wall interface, this is known as the no-slip boundary condition.

9 Newton s Law of Viscosity-I At steady state, for plates of area A, and laminar flow, the force is expressed by F/A=η(V/Y) where Y is the distance between plates and η=constant of proportionality (viscosity).

10 Newton s Law of Viscosity-I Shear stress F/A=η(V/Y) Force: Shear

11 Newton s Law of Viscosity-I At steady state, for plates of area A, and laminar flow, the force is expressed by F/A=η(V/Y) where Y is the distance between plates and η=constant of proportionality (viscosity).

12 Newton s Law of Viscosity Viscosity-II F/A = shear stress = τ = momentum flux (V/Y) = the constant velocity gradient = d x /dy when the velocity profile is linear at steady state. τ yx = d x dy Direction of momentum transport Direction of velocity coponent Flux of x-momentum in the y direction Reflects the momentum is transferred from the lower layers of fluid to the upper layers in the positive y- direction. In this case, d x /dy is negative.

13 Facts about Newton s Law of Viscosity It is only valid in the regime of laminar flow not in the regime of turbulent flow. Fluids that obey Newton s law of viscosity are called Newtonian Fluids. All gases and simple liquids (e.g., water, molten metals, molten semiconductors, and many molten salts) are Newtonian, while pastes, slurries and polymeric melts are non-newtonian. On the other hand the fluids, whose viscosities depend on the rate of applied shear are called non-newtonian; clays, sullaries, pastes and polymer solutions belong to the class of non-newtonian fluids.

14 Fluid (or Dynamic) Viscosity (η) Dynamic viscosity is the ratio of shear stress to velocity gradient. When force is applied perpendicular to the surface of a liquid, it deforms sideways, or shears. The ease or difficulty of this deformation is the dynamic viscosity, sometimes referred to simply as viscosity. It measures the resistance of a fluid to flow in other words, the internal friction of the fluid The cgs (centimeter-gram-second) unit of stress is dyn.cm-2 or g.cm- 1.s-2. Therefore, the cgs unit of viscosity is g/cm.s= Poise (P) 1 Centipoise (cp) = the viscosity of water at 20 C and 1 atm. 1cP = 0.01 P In mks system, the corresponding unit of viscosity is Pa.s (N.s/m 2 ) or kg/m.s, and is equivalent to 10 3 cp (or 10 P).

15 Kinematic Viscosity Kinematic viscosity, measures the resistance of the liquid to flow in the presence of gravity. This measure is obtained by taking the liquid s dynamic viscosity and dividing it by the liquid s density. The higher the viscosity of the liquid, the less easily it will flow under the force of gravity and the higher its kinematic viscosity will be. In mks system, the unit of kinematic viscosity is m 2 /s, while in the cgs system it is usually cm 2 /s, sometimes called the stoke.

16 Dynamic and Kinematic Viscosity Dynamic and kinematic viscosity are expressed in different units of measurement. The International System of Units (SI) measurement units for dynamic viscosity :pascal-seconds or poise (another measure relating pressure versus time) Pascals are a measurement of pressure in this case, the shear stress applied to the liquid while seconds measure the time it takes to deform. The common unit used to measure kinematic viscosity is the stokes, or square centimeters per second, although sometimes the SI unit of square meters per second is used.

17 Viscosity of Gases-I (Mean Free Path Approach) Based on the collision theory of gases; τ yx = 2 m T 1 / 2 d B x 3 3/ 2 d 2 dy = 2 m T 1 / 2 B 3 3/ 2 d 2 where m, mass of fluid molecules, KB, the Boltzmann constant, T, absolute temperature, d, the center to center distance of two molecules. Viscosity of a gas is independent of pressure and depends only on temperature. This conclusion is valid up to about ten atmospheres ( x 10 5 Pa). usually for real gases, η α T n ; n= rather than 0.5

18 Viscosity of Gases-II (Molecular Force Field Approach) Based on the force of attraction and repulsion between molecules; the potential energy of interaction,lennard-jones potential,between a pair of molecules in the gas is used to predict the η. = / 1 5 MT 2 σ 2 where M, gram-molecular weight, σ, the characteristic diameter of the molecule in Å, T, absolute temperature ( K), Ωη, the collision integral of the Chapman-Enskog theory which is a function of a dimensionless parameter K B T/ε, This equation is applicable only for the viscosity of nonpolar liquids at low pressures.

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