TYPES OF FLUIDS

Types of Fluids: Ideal fluid Real fluid Newtonian fluid Non-Newtonian fluid Ideal plastic fluid

Newtonian Fluids and Non-Newtonian Fluids The study of the deformation and flow characteristics of substances is called rheology, which is the field from which we learn about the viscosity of fluids. One important distinction is between a Newtonian fluid and a non-Newtonian fluid. Any fluid that behaves in accordance with Eq. (2–1) is called a Newtonian fluid. Conversely, a fluid that does not behave in accordance with Eq. (2–1) is called a non-Newtonian fluid.

Newtonian Fluids and Non-Newtonian Fluids

Newtonian Fluids and Non-Newtonian Fluids Two major classifications of non-Newtonian fluids are time-independent and time-dependent fluids. As their name implies, time-independent fluids have a viscosity at any given shear stress that does not vary with time. The viscosity of time-dependent fluids, however, changes with time.

Newtonian Fluids and Non-Newtonian Fluids Three types of time-independent fluids can be defined: Pseudoplastic or Thixotropic The plot of shear stress versus velocity gradient lies above the straight, constant sloped line for Newtonian fluids, as shown in Fig. 2.2. The curve begins steeply, indicating a high apparent viscosity. Then the slope decreases with increasing velocity gradient. Eg. Blood plasma, latex, inks

Newtonian Fluids and Non-Newtonian Fluids Dilatant Fluids The plot of shear stress versus velocity gradient lies below the straight line for Newtonian fluids. The curve begins with a low slope, indicating a low apparent viscosity. Then, the slope increases with increasing velocity gradient. E. Starch in water, TiO2 Bingham Fluids Sometimes called plug-flow fluids, Bingham fluids require the development of a significant level of shear stress before flow will begin, as illustrated in Fig. 2.2. Once flow starts, there is an essentially linear slope to the curve indicating a constant apparent viscosity. Eg. Chocolate, mayonnaise, toothpaste

Variation of Viscosity with Temperature the viscosity for different fluids.

The viscosity of liquids decreases and the viscosity of gases increase with temperature.

Types of fluid Flow 1. Real and Ideal Flow: If the fluid is considered frictionless with zero viscosity it is called ideal. In real fluids the viscosity is considered and shear stresses occur causing conversion of mechanical energy into thermal energy Ideal Real Friction = 0 Ideal Flow ( μ =0) Energy loss =0 Friction ≠ o Real Flow ( μ ≠0) Energy loss ≠ 0

2. Steady and Unsteady Flow Steady flow occurs when conditions of a point in a flow field don’t change with respect to time ( v, p, H…..changes w.r.t. time steady unsteady H=constant V=constant H ≠ constant V ≠ constant Steady Flow with respect to time Velocity is constant at certain position w.r.t. time Unsteady Flow with respect to time Velocity changes at certain position w.r.t. time

3. Uniform and Non uniform Flow Y Y x x Non- uniform Flow means velocity changes at certain time in different positions ( depends on dimension x or y or z( Uniform Flow means that the velocity is constant at certain time in different positions (doesn’t depend on any dimension x or y or z( uniform Non-uniform

4. One , Two and three Dimensional Flow : y 4. One , Two and three Dimensional Flow : x One dimensional flow means that the flow velocity is function of one coordinate V = f( X or Y or Z ) Two dimensional flow means that the flow velocity is function of two coordinates V = f( X,Y or X,Z or Y,Z ) Three dimensional flow means that the flow velocity is function of there coordinates V = f( X,Y,Z) 17

4. One , Two and three Dimensional Flow (cont.) A flow field is best characterized by its velocity distribution. A flow is said to be one-, two-, or three-dimensional if the flow velocity varies in one, two, or three dimensions, respectively. However, the variation of velocity in certain directions can be small relative to the variation in other directions and can be ignored. The development of the velocity profile in a circular pipe. V = V(r, z) and thus the flow is two-dimensional in the entrance region, and becomes one-dimensional downstream when the velocity profile fully develops and remains unchanged in the flow direction, V = V(r).

5. Laminar and Turbulent Flow: In Laminar Flow: Fluid flows in separate layers No mass mixing between fluid layers Friction mainly between fluid layers Reynolds’ Number (NRe) < 2000 Vmax.= 2Vmean In Turbulent Flow: No separate layers Continuous mass mixing Friction mainly between fluid and pipe walls Reynolds’ Number (NRe) > 4000 Vmax.= 1.2 Vmean Vmean Vmean Vmax Vmax

5. Laminar and Turbulent Flow (cont.):

6. Rotational and irrotational flows: The rotation is the average value of rotation of two lines in the flow. (i) If this average = 0 then there is no rotation and the flow is called irrotational flow

rotational flow Irrotational flow

u velocity component in -X- direction 7. Streamline: A Streamline is a curve that is everywhere tangent to it at any instant represents the instantaneous local velocity vector. Stream line equation Where : u velocity component in -X- direction v velocity component in-Y- direction w velocity component in -Z- direction z w V x v u y 23

Airplane surface pressure contours, volume streamlines, and surface streamlines NASCAR surface pressure contours and streamlines

8. Stream tube: Stream tube is bounded by an infinite number of stream lines forming a finite surface across which there is no flow. Is a bundle of streamlines fluid within a stream tube remain constant and cannot cross the boundary of the stream tube. (mass in = mass out)

Types of motion or deformation of fluid element Linear translation Rotational translation Linear deformation angular deformation

Reynolds Experiment

Flow Reynolds’ Number (NRe) Reynold’s experiments involved injecting a dye streak into fluid moving at constant velocity through a transparent tube. Fluid type, tube diameter and the velocity of the flow through the tube were varied.

Reynolds’ experiment Dye followed a straight path. Dye followed a wavy path with streak intact. Dye rapidly mixed through the fluid in the tube

Reynolds classified the flow type according to the motion of the fluid. Laminar Flow: every fluid molecule followed a straight path that was parallel to the boundaries of the tube. Transitional Flow: every fluid molecule followed wavy but parallel path that was not parallel to the boundaries of the tube. Turbulent Flow: every fluid molecule followed very complex path that led to a mixing of the dye.

Reynolds found that conditions for each of the flow types depended on: 1. The velocity of the flow (U) 2. The diameter of the tube (D) 3. The density of the fluid (r). 4. The fluid’s dynamic viscosity (m). He combined these variables into a dimensionless combination now known as the Flow Reynolds’ Number (NRe) where:

Flow Reynolds’ number is often expressed in terms of the fluid’s kinematic viscosity (n; lower case Greek letter nu), where: (units are m2/s) Rearranging: Substituting into R: NRe

The value of R determined the type of flow in the experimental tubes: < 2100 2100-4000 > 4000

Laminar Transitional Turbulent

In laminar flows, Frictional losses vary directly as the flow velocity, i.e., ΔP α u. In turbulent flows, Frictional losses vary as about 1.7 to 2 power of the velocity , i.e., ΔP α (u)1.7-2.0

Example: Given two pipes, one with a diameter of 10 cm and the other with a diameter of 1 m, at what velocities will the flows in each pipe become turbulent? What is the critical velocity for R = 2000? Solve for U: Given: Distilled water at 20°C. Solve for D = 0.1 m and D = 1.0 m.

For a 0.1 m diameter pipe: For a 1.0 m diameter pipe:

FLUID HEAD: P be the pressure of the fluid at a point under consideration, P0 be the atmospheric pressure, and h be the height of the liquid in the tube P = P0 + r g h