Module 5. Fluid flow

Lesson 11

CLASSIFICATION, STEADY, UNIFORM AND NON UNIFORM FLOW, LAMINAR AND TURBULENT

11.1  Introduction

In Fluid Mechanics, the knowledge of flow behavior is important as the analysis and calculations depends on the flow conditions.

11.2  Types of flow

1.     Steady flow

 In steady flow fluid parameters such as velocity, density, pressure, acceleration etc. at a point do not change with time.

 

      Where v: velocity; P: Pressure; ρ: Density; a: acceleration; t: time

2.     Unsteady flow

In unsteady flow fluid parameters such as velocity, density, pressure, acceleration etc. at a point changes with time.

    

3.     Uniform flow

 In uniform flow if the velocity at a given instant of time is same in both magnitude and direction at all points in the flow, the flow is said to be uniform flow.

4.     Non-uniform flow

 When the velocity changes from point to point in a flow at any given instant of time, the flow is described as non-uniform flow.

5.     Compressible flow

The flow in which density of the fluid varies during the flow is called compressible fluid flow. (i. e.  ). This is applicable in gas flow.

6.     Incompressible flow

In case of in compressible fluid flow, the density of the fluid remains constant during the flow. (i. e.  ). Practically, all liquids are treated as incompressible.

7.     Pressurized flow

 Flow under pressure. e..g. liquid flowing in pipes with pressure.

8.     Gravity flow

 Flow of fluid due to gravity.

9.     One, two and three dimensional flow

a.     One Dimensional: When the flow properties (e.g. velocity, density pressure etc) vary only in one direction.

b.     Two Dimensional flows:  When the flow properties (e.g. velocity, density pressure etc) vary in only two directions.

c.      Three Dimensional flows: When the flow properties (e.g. velocity, density pressure etc) vary in all the three directions.

10.            Rotational and irrotational flows:

Rotational flow: The fluid particles while flowing also rotate about their own axis.

Irrotational flow: The fluid particles while flowing do not rotate about their own axis.

11.            Laminar flow

 In this type of fluid flow, particles move along well defied paths or steam lines. The fluid layers moves smoothly over the adjacent layer. The fluid particles move in a definite path and their  paths do not cross each other (Fig. 11.1).

Fig. 11.1 Laminar flow

12.            Turbulent Flow

In turbulent fluid flow, fluid particles move in a random and zigzag way (Fig. 11.2). Turbulence is characterized by the formation of eddies.

 

Fig. 11.2 Turbulent  flow

    The type of flow is determined by Reynold’s Number.

11.3  Reynold’s Number

It is defined as the ratio of inertia force of the flowing fluid to the viscosity force of the fluid. In case of pipe flow, it is determined by using the following equation.

           

Where, Re=Reynold’s Number

              ρ= Density of fluid

             V= Velocity of fluid

             D= Diameter of pipe

             μ= Viscosity of fluid

Reynold’s Number (Re)

Flow type

Re < 2100

Laminar flow

2100 < Re < 4000

Transitional (flow can be laminar or turbulent)

Re > 4000

Turbulent

11.4  Streamline, Path Line and Streakline

Streamline: Is an imaginary line and velocity vector at any point on a stream line is tangent to the streamline (Fig. 11.3).

Fig. 11.3 Streamline

 

Path line  is the path traced by a fluid particles.

Streaklines are obtained by joining the locus of points of all the fluid particles that have passed continuously through a fixed point during time t. Dye steadily injected into the fluid at a fixed point extends along a streakline.

11.5  Numericals

Q.1 Predict whether the flow would be laminar or turbulent in a pipe of diameter 5 cm. Consider density of liquid to be 950 kg/m3, viscosity 0.2 Ns/m2 and flow velocity 20 m/s.

 Q.2 Calculate the Reynlod’s number if pipe diameter is 4 cm, liquid density 900 kg/cm3, viscosity 0.5 Ns/m2 and flow velocity 10 m/s.