CHE493

FLUID MECHANICS

CHAPTER 3: TYPES OF FLOW

COURSE LEARNING OUTCOMES:

The student should be able to:

Describe each types of flow including pathline, streamline and stream tube

Discuss the differences/characteristics of steady, unsteady, uniform, non-uniform, laminar, transitional and turbulent flow

Calculate Reynolds number & describe the types of flow based on Reynolds Number

INTRODUCTION:

Fluid dynamics

The analysis of fluid in motion

Fluid motion can be predicted in the same way as the motion of solids

By use of the fundamental laws of physics and the physical properties of the fluid

IDEAL AND REAL FLUID

Ideal / perfect fluid the concept of a frictious fluid that can flow in the absence of all frictional effects

For real fluid, all the frictional effects will be considered

FLOW CLASSIFICATIONS

Flow can be classified based on the flow parameters such as velocity and pressure.

Uniform:

Flow conditions (velocity, pressure, cross-section or depth) are the same at every point in the fluid.

Example: flow in a constant diameter pipeline with constant flow rate

Non-uniform:

Flow conditions are not the same at every point

Example: flow with constant flow rate thru a tapered pipe

FLOW CLASSIFICATIONS

Steady

Flow conditions may differ from point to point but DO NOT change with time

Unsteady

Flow conditions change with time at any point

FLOW CLASSIFICATIONS

Combining these four gives:

Steady uniform flow.

Conditions do not change with position in the stream or with time.

E.g. flow of water in a pipe of constant diameter at constant velocity.

Steady non-uniform flow.

Conditions change from point to point in the stream but do not change with time.

E.g. flow in a tapering pipe with constant velocity at the inlet.

FLOW CLASSIFICATIONS

Unsteady uniform flow

At a given instant in time the conditions at every point are the same, but will change with time.

E.g. A pipe of constant diameter connected to a pump - pumping at a constant rate which is then switched off.

Unsteady non-uniform flow

Every condition of the flow may change from point to point and with time at every point.

E.g. Waves in traveling along a channel

COMPRESSIBLE OR INCOMPRESSIBLE

FLOW

Compressibility - measure of the relative volume change of a fluid as a response to a pressure change

All fluids are compressible - density will change as pressure changes

Under steady conditions and small changes in pressure, it is usually possible to simplify analysis of the flow by assuming it is incompressible and has constant density

COMPRESSIBLE OR

INCOMPRESSIBLE FLOW

Liquids are quite difficult to compress - so under most steady conditions they are treated as incompressible

Gasses are very easily compressed, it is essential in most cases to treat these as compressible, taking changes in pressure into account

ONE, TWO & THREE DIMENSIONAL FLOW

Fluids can be classified according to their direction of motion with respect to the three mutually perpendicular axes:

1-dimensional flow

Velocity, pressure and elevation vary only in the direction of flow

2-dimensional flow

Flow parameters vary in two directions

3-dimensional flow

Flow parameters resolved into 3 mutually perpendicular direction

Difficult to analyze

STREAMLINES, STREAKLINES &

PATHLINES

Streamlines

An imaginary curve that is everywhere tangent to the instantaneous local velocity vector

Streamlines are useful as indicators of the instantaneous direction of fluid motion throughout the flow field

Streamlines cannot be directly observed experimentally except in steady flow

Streamtube

consists of a bundle of streamlines

STREAMLINES, STREAKLINES &

PATHLINES Pathlines

the actual path travelled by an individual fluid particle over some time period.

Time-exposed flow path of an individual particle over a time period

Streaklines

the locus of fluid particles that have passed sequentially through a prescribed point in the flow.

Streakline is a pathline that moves more than a single point through the flow

In a streakline, the entire line is moved through the flow.

Instantaneous snapshot of a time-integrated flow pattern

Both are time history associated

If the flow is steady, streamlines, pathlines and streaklines are identical

LAMINAR FLOW

When a fluid flows through a tube, different parts flow at different speeds

The dots in the simulation above show how "parcels" of fluid would move in a tube.

Notice that the fluid moves fastest in the middle of the tube and slowest at the walls.

This type of flow is called laminar because the fluid moves in layers.

TRANSITIONAL FLOW

As the fluid velocity increases the layers of fluid start to become a little unstable. This type of flow is called transitional.

Increasing the flow rate still further leads to a third type of flow.

TURBULENT FLOW

At high velocities, the orderly layers of flow are completely disrupted and turbulence sets in.

Turbulent flow is not as efficient at moving fluid as laminar flow. Some energy is lost as sound, for instance.

Laminar: highly ordered fluid motion with smooth streamlines.

Transitional: a flow that contains both laminar and turbulent regions

Turbulent: highly disordered fluid motion characterized by velocity fluctuations and eddies.

REYNOLDS'S EXPERIMENT

LAMINAR VS. TURBULENT FLOW

Laminar flow: A thin filament of dye injected into a laminar flow appears as a single line. There is no dispersion of dye throughout the flow, except the slow dispersion due to molecular motion

Turbulent flow: If a dye filament injected into a turbulent flow, it disperses quickly throughout the flow field; the line of dye breaks up into myriad entangled threads of dye.

LAMINAR VS. TURBULENT FLOW

REYNOLDS NUMBER

A criteria to determine the flow regime Re < 2000 laminar 2000 Re 4000 transitional Re > 4000 turbulent Re is the ratio of inertial forces to viscous forces

Re =

Where:

= density, kgm-3

u = average velocity , ms-1

d = diameter of the pipe, m

= fluid viscosity, kgm-1s-1

units???

udRe

REYNOLDS NUMBER

EXAMPLE 1

A pipe of 20 mm diameter carries water at an average velocity of 1.5m/s. Calculate the Reynolds number for the flow and determine the flow regime. The absolute viscosity of water at room temperature is about 0.001 Pa.s.

Solutions:

Re = d/

= 1000 (1.5)(0.02)/0.001

= 30,000

Re > 4000, thus, the flow is turbulent

EXAMPLE 2:

A Newtonian fluid having a viscosity of 0.38 N.s/m2 and a specific gravity of 0.91 flows through a 25mm diameter pipe with velocity of 2.6m/s. Determine the value of Reynolds number.

SOLUTIONS:

= SGH2O = 0.91(1000kg/m3) = 910 kg/m3

Re = d/

= [(910 kg/m3)(2.6m/s)(25mm)(10-3m/mm)]/0.38N.s/m2

= 156 (kg.m/s)/N

= 156

Re < 2000, thus laminar flow