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## FLUID

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### FLUID Characteristics of Fluid Flow (1) Steady flow (lamina flow, streamline flow) The fluid velocity (both magnitude and direction) at any given point is constant in ... – PowerPoint PPT presentation

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Title: FLUID

1
FLUID
2
Characteristics of Fluid Flow (1)
• Steady flow (lamina flow, streamline flow)
• The fluid velocity (both magnitude and direction)
at any given point is constant in time
• The flow pattern does not change with time
• Velocities vary irregularly with time
• e.g. rapids, waterfall

3
Characteristics of Fluid Flow (2)
• Rotational and irrotational flow
• The element of fluid at each point has a net
• Otherwise it is irrotational
• Example whirlpools
• Compressible and incompressible fluid
• Liquids are usually considered as incompressible
• Gas are usually considered as highly compressible

4
Characteristics of Fluid Flow (3)
• Viscous and non-viscous fluid
• Viscosity in fluid motion is the analog of
friction in the motion of solids
• It introduces tangential forces between layers of
fluid in relative motion and results in
dissipation of mechanical energy

5
Streamline
• A streamline is a curve whose tangent at any
point is along the velocity of the fluid particle
at that point
• It is parallel to the velocity of the fluid
particles at every point
• No two streamlines can cross one another
• In steady flow the pattern of streamlines in a
flow is stationary with time

6
Change of speed of flow with cross-sectional area
• If the same mass of fluid is to pass through
every section at any time, the fluid speed must
be higher in the narrower region
• Therefore, within a constriction the streamlines
must get closer together

7
Kinematics (1)
• Mass of fluid flowing past area Aa ?ava?tAa
• Mass of the fluid flowing past area Ab ?bvb?tAb

8
Kinematics (2)
• In a steady flow, the total mass in the bundle
must be the same
• ? ?avaAa ?t ?bvbAb ?t
• i.e. ?avaAa ?bvbAb
• or ?vA constant
• The above equation is called the continuity
equation
• For incompressible fluids
• vA constant

9
Static liquid pressure
• The pressure at a point within a liquid acts in
all directions
• The pressure depends on the density of the liquid
and the depth below the surface
• P ?gh

10
Bernoullis equation
• Bernoullis equation
• This states that for an incompressible,
non-viscous fluid undergoing steady lamina flow,
the pressure plus the kinetic energy per unit
volume plus the potential energy per unit volume
is constant at all points on a streamline
• i.e.

11
Derivation of Bernoullis equation (1)
• The pressure is the same at all points on the
same horizontal level in a fluid at rest
• In a flowing fluid, a decrease of pressure
accompanies an increase of velocity

12
Derivation of Bernoullis equation (2)
• In a small time interval ?t, fluid XY has moved
to a position XY
• At X, work done on the fluid XY by the pushing
pressure
• force ? distance moved
• force ? velocity ? time
• p1A1 ? v1 ? ?t

figure
13
Derivation of Bernoullis equation (3)
• At Y, work done by the fluid XY emerging from the
tube against the pressure
• p2A2 ? v2 ? ?t
• Net work done on the fluid
• W (p1A1 ? v1 - p2A2 ? v2)?t
• For incompressible fluid, A1v1 A2v2
• ? W (p1 - p2)A1 v1 ?t

figure
14
Derivation of Bernoullis equation (4)
• Gain of p.e. when XY moves to XY
• p.e. of XY - p.e. of XY
• p.e. of XY p.e. of YY - p.e. of XX - p.e.
of XY
• p.e. of YY - p.e. of XX
• (A2 v2 ?t?)gh2 - (A1 v1 ?t?)gh1
• A1 v1 ?t?g(h2 - h1)

figure
15
Derivation of Bernoullis equation (5)
• Gain of k.e. when XY moves to XY
• k.e. of YY - k.e. of XX

figure
16
Derivation of Bernoullis equation (6)
• For non-viscous fluid
• net work done on fluid gain of p.e. gain of
k.e.
• (p1 - p2)A1 v1 ?t A1 v1 ?t?g(h2 - h1)

figure
17
Derivation of Bernoullis equation (7)
• or

figure
18
Derivation of Bernoullis equation (8)
• Assumptions made in deriving the equation
• Negligible viscous force
• The fluid is incompressible
• There is no source of energy
• The pressure and velocity are uniform over any
cross-section of the tube

19
Applications of Bernoulli principle (1)
• Jets and nozzles
• Bernoullis equation suggests that for fluid flow
where the potential energy change h?g is very
small or zero, as in a horizontal pipe, the
pressure falls when the velocity rises
• The velocity increases at a constriction and this
creates a pressure drop. The following devices
make use of this effect in their action

20
Applications of Bernoulli principle (2)
• Bunsen burner
• The coal gas is made to pass a constriction
before entering the burner
• The decrease in cross-sectional area causes a
sudden increase in flow speed
• The reduction in pressure causes air to be sucked
in from the air hole
• The coal gas is well mixed with air before
leaving the barrel and this enables complete
combustion

21
Applications of Bernoulli principle (3)
• Carburettor of a car engine
• The air first flows through a filter which
removes dust and particles
• It then enters a narrow region where the flow
velocity increases
• The reduced pressure sucks the fuel vapour from
the fuel reservoir, and so the proper air-fuel
mixture is produced for the internal combustion
engine

22
Applications of Bernoulli principle (4)
• Filter pump
• The velocity of the running water increases at
the constriction
• The surrounding air is dragged along by the water
jet and this causes a drop in pressure
• Air is then sucked in from the vessel to be
evacuated

23
Spinning ball
• If a tennis ball is cut it spins as it travels
through the air and experiences a sideways force
which causes it to curve in flight
• This is due to air being dragged round by the
spinning ball, thereby increasing the air flow on
one side and decreasing it on the other
• A pressure difference is thus created

figure
24
Aerofoil
• A device which is shaped so that the relative
motion between it and a fluid produces a force
perpendicular to the flow
• Fluid flows faster over the top surface than over
the bottom. It follows that the pressure
underneath is increased and that above reduced. A
resultant upwards force is thus created, normal
to the flow
• e.g. aircraft wings, turbine blades, sails of a
yacht

25
Pitot tube (1)
• a device for measuring flow velocity and in
essence is a manometer with one limb parallel to
the flow and open to the oncoming fluid
• The pressure within a flowing fluid is measured
at two points, A and B. At A, the fluid is
flowing freely with velocity va. At B where the
Pitot tube is placed, the flow has been stopped

26
Pitot tube (2)
• By Bernoullis equation

where P0 atmospheric pressure
27
Pitot tube (3)
• ?
• Note
• In real cases, v varies across the diameter of
the pipe carrying the fluid (because of the
viscosity) but if the open end of the Pitot tube
is offset from the axis by 0.7 ? radius of the
pipe, then v is the average flow velocity
• The total pressure can be considered as the sum
of two components the static and dynamic
pressures

28
Pitot tube (4)
• A moving fluid exerts its total pressure in the
direction of flow. In directions at right angles
to the flow, the fluid exerts its static pressure
only
• figures

Further reading paragraph of Pitot Static
System near the bottom of the page
29
Venturi meter (1)
• This consists of a horizontal tube with a
constriction. Two vertical tubes serving as
manometers are placed perpendicular to the
direction of flow, one in the normal part and the
other in the constriction
• In steady flow the liquid level in the manometer
connected to the wider part of the tube is higher
than that in the narrower part

figure
30
Venturi meter (2)
• From Bernoullis principle

(h1 h2)
For an incompressible fluid, A1v1 A2v2 ?
31
Venturi meter (3)
• Hence

? v1 can be deduced
32
EXAMPLES
33
Streamline
Q
P
34
Change of speed in a constriction
Streamlines are closer when the fluid flows faster
35
Derivation of Bernoullis equation
v2
Y
v1
Y
p2A2
X
v2?t
X
Area A2
p1A1
h2
v1?t
h1
Area A1
36
Bunsen burner
37
Carburettor
air
filter
fuel
to engine cylinder
38
Filter pump
39
Spinning ball
40
Aerofoil
41
Pitot tube (1)
42
Pitot tube (2)
Pitot is here
43
Pitot tube fluid velocity measurement (1)
Fast moving air, lower pressure inside chamber
Static pressure holes
Stagnant air, higher pressure inside tube
Flow of air
Static tube
P1 total pressure P2 static pressure P2 P1
½(?v2)
Total tube
44
Pitot tube fluid velocity measurement (2)
45
Ventri meter (1)
46
Venturi meter (2)
47
Venturi meter (3)
Density of liquid ?
v1
v2
A2
A1