fluid in motion

8/3/2019 Fluid in Motion

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FLUID IN MOTION

By Ahmed YASHAR

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Types of flow

1.Laminar andturbulent

2.Compressibleand incompressible

3.Flow of Ideal andReal Fluids

4.Steady andunsteady flow

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1.Laminar and turbulent flow

Laminar flow Turbulent flow

1 Re < 2000 Re > 4000

2 'low' velocity 'high' velocity

3 Dye does not mix with water Dye mixes rapidly and completely

4 Fluid particles move in straight lines Particle paths completely irregular,

Average motion is in the direction of the

flow.

5 Simple mathematical analysis possible Mathematical analysis very difficult - so

experimental measures are used

6 Rare in practice in water systems. Most common type of flow.

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2.Compressible and incompressible

If the density of the flowing fluid is thesame all over the flow field, then such flow is calledincompressible flow. Flow of liquids can be considered as

incompressible even if the density varies a little due totemperature difference between locations. Low velocityflow of gases with small changes in pressure andtemperature can also be considered as incompressibleflow. Flow through fans and blowers is considered

incompressible as long as the density variation is below5%. If the density varies with location, the flow is calledcompressible flow.

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3.Flow of Ideal and Real Fluids

Ideal fluid is nonviscous and incompressible. Shear forcebetween the boundary surface and fluid or between thefluid layers is absent and only pressure forces and body

forces are controlling.Real fluids have viscosity and surface shear forces areinvolved during flow. However the flow after a shortdistance from the surface is not affected by the viscouseffects and approximates to ideal fluid flow. The results

of ideal fluid flow analysis are found applicable in thestudy of flow of real fluids when viscosity values aresmall.

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4.Steady and Unsteady flow

When all the time derivatives of a flow field

vanish, the flow is considered to be a steady flow.

Steady-state flow refers to the condition where the

fluid properties at a point in the system do not changeover time. Otherwise, flow is called unsteady.

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Conservation of Mass

1

2

S1

u1 u2

S2

Consider flow through the pipe-work shown in figure, in which the fluid

occupies the whole cross section of the pipe. A mass balance can be written for the

fixed section between planes 1 and 2, which are normal to the axis of the pipe.

Mass Flow Rate In = Mass Flow Rate Out + Rate of Accumulation within section

Volume is constant so,

Where

= mass density (kg/m3)

Q = volumetric flow rate (m3/sec)

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Conservation of Mass

if the flow is

1. incompressible the density constant. derivative of const.=zero

2. steady no change in properties with time. derivative = zero

So the equation became

The simply states that the mass flow rate into the section is equal to the mass flow rate

out of the section.

In general, the velocity of the fluid varies across the diameter of the pipe but an

average velocity can be defined. If the cross-section area of the pipe at a particular

location is S , then the volumetric flow rate Q is given by

By substituting . (4) in (3) the zero accumulation mass balance becomes

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Energy relationships and the Bernoulli equation

Internal energy :- the energy of the atoms and molecules resulting from their

motion and configuration. The internal energy is a function of temperature.

The internal energy per unit mass of fluid is denoted by U.

Potential energy :- the work required to raise a unit mass of fluid to a height z

above an arbitrarily chosen datum is zg. This work is equal to the potentialenergy of unit mass of fluid above the datum.

Pressure energy :- if P is the pressure and V is the volume of mass m of fluid,

then PV/m is the pressure energy per unit mass of fluid the ratio m/V is the

fluid density . Thus the pressure energy per unit mass of fluid is equal to

P/.Kinetic energy :- this is the energy of fluid motion. The kinetic energy of unit

mass of the fluid is v2/2, where v is the velocity of the fluid relative to some

fixed body.

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1 2

E1 E2

Wi Wo

q


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Application of Bernoulli equation.

1.Pitot tube

2.Venturi meter

3.Orfice meter4.Nozzle

5.Weirs

6. Rotometer

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1.Pitot tube

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1

2

v1= the flow velocity m/s

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Flow direction

h

h

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1.Pitot tube

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5

K

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2.Venturi meter

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2

2

1

R

k

h

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2.Venturi meter

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3.Orifice meter

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H

1

2

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3.Orifice meter

B) Used In Close System

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WHERE

Cc= Coefficient of contraction

Cv=Coefficient of velocity

Cd=coefficient of discharge

V = Cv V2 ,

Q = Cv Cc A V = Cd Q ideal ,


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fluid in motion

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