fluid flow pressure bernoulli principle surface tension flow -- pressure pressure in a moving fluid...
TRANSCRIPT
Fluid flow
L
A v
v is the average speed = L/t
A is the area
Volume V =AL
Flow rate Q is the volume flowing per
unit time (V/t) Q = (V/t)
Q = AL/t = A v
Flow rate Q is the area times the average speed
Relating:
Fluid flow rate to Average speed
Q = A v
Speed of a fluid in a pipe is not the same
as the flow rate
Depends on the radius of the pipe.
example:
Low speed
Large flow rate
Same low speed
Small flow rate
Fluid flow -- Pressure
Pressure in a moving fluid
with low viscosity and laminar flow
Bernoulli Principle
Relates the speed of the fluid to the pressure
Speed of a fluid is high—pressure is low
Speed of a fluid is low—pressure is high
Daniel Bernoulli
(Swiss Scientist 1700-1782)
21
2P v ghr r constant
Bernoulli Equation
Fluid flow -- Pressure
2 2
1 1 1 2 2 2
1 1
2 2P v gh P v ghr r r r
Bernoulli Principle
P1 P2
Fluid
2 2
1 1 2 2
1 1
2 2P v P vr r
1 2if h h
2 2
2 1 1 2
1 1
2 2v v P Pr r
2 2if v is higher then P is lower
v1
v2
Fluid flow
P1 P2
P3
A1
A2
A3 v1 v3 v2
If fluid is incompressible flow rate Q is the
same everywhere along tube
A1 = A2 v1 v2 v2 v1
A1
A2
=
> v2 v1 Since A2 < A1
Thus from Bernoulli’s principle P1 > P2
therefore
Venturi Effect
–constricted tube enhances the Bernoulli effect
Q = A v
Continuity of flow
Fluid flow
Explanation
Speed increases in smaller tube
P1 P2
Potential energy associated with pressure is
employed to increase kinetic energy.
Therefore pressure decreases.
Speed increases pressure decreases
High speed—low pressure
Therefore kinetic energy increases.
(Tube horizontal so no change in gravitational
potential energy)
Bernoulli’s principle:
Fluid
Fluid flow
Applications of Bernoulli principle
Atomiser
(creating a low pressure)
Water aspirator uses the Venturi effect
to produce low pressure
air
Rubber
bulb
Liquid (perfume)
Principle
Increased speed
Lower pressure
Perfume entrained
in air flow
Fluid flow
Example
If the average speed of blood in a capillary of
diameter 4 x10-4cm is 3.5 x10-2cms-1,
calculate the flow rate in litres per second.
Q = A v
Q =flow rate A = area
v =average speed
A = pr2 = (2 x10-4cm)2 p
Q = [(2 x10-4cm)2 p](3.5 x10-2cms-1)
Q = 44 x 10-10 cm3s-1
Q = 44 x10-13 litres.s-1
Fluid flow
Plaque build-up on an artery wall reduces its
diameter from 1.1cm to 0.75cm. If the speed of the blood is
15cms-1 before reaching the region of plaque build-up.
Find the speed of the blood within the plaque region?
Q =flow rate A = area v =average speed
Assume blood is incompressible,
flow rate Q is the same everywhere
along artery
A1 = A2 v1 v2
v2 v1
A1
A2
=
Q = A v
2
211 0.95
2
dA cmp
2
222 0.44
2
dA cmp
1 1
2
0.95 215 32
0.44
cmv cms cms
cms
(a)
Fluid flow
Bernoulli effect not limited to
fluid flow in tubes.
Airplane wing profile
Air moves faster over the
upper side of the wing
Pressure is lower,
resulting in lift
Shower curtain
Curtain is ―sucked inwards‖ when water
is switched on. Why?
Forces between Molecules
Molecules close together: forces repulsive
Otherwise forces are attractive
Molecules close together: forces repulsive
>>>Liquids and solids almost incompressible
Attractive forces
>>>> phenomena such as surface tension
Water droplet spherical shape
why?
Surface is subject to tension
makes surface area as small
as possible
Forces between Molecules
Surface Tension
Molecule at B surrounded
on all sides by other similar
molecules. Net attractive force
is zero since it is attracted
equally in all directions
A
B
Molecule at A, no liquid molecules above,
therefore net force exists which pulls it towards
the interior of the liquid
Net effect of the pull on all molecules at surface
Surface of liquid contracts
>>surface area becomes a minimum
Minimum surface area for a given volume is
when shape is a sphere
Forces between Molecules
Surface Tension g = F/L
Measuring surface tension
Measure force (F) required
to stretch liquid film
L F
Liquid g(Nm-1)
Blood 0.058
Ethyl
Alcohol
0.023
Mercury 0.44
Water
(0oC)
0.076
Water
(20oC)
0.072
Water
(100oC)
0.059
Soapy
Water
0.037
Surface Tension
SI unit of surface tension
Newton per metre Nm-1
Surface Tension Phenomena
Liquid surface behaves like a rubber membrane
under tension
Needle on surface of water
mg
Force due to surface tension
Density of steel rs » rw
Steel needle does not sink
Surface tension results in
Upwards force on needle
Surface Tension Phenomena
Insects can walk on water
Depression in water surface
(increases surface area)
Liquid surface behaves like a rubber membrane
under tension
Surface tension opposes this, which results
in an upwards force that tends to bring back
surface to original flat shape.
Surfactant (surface active) substances (soaps)
When added to liquid will lower its surface tension
Soapy water can penetrate the fine structure
of clothes or skin more easily than water
and hence clean better
Temperature of liquid increases:
Surface tension of liquids decreases
Surface Tension Phenomena
Uses
Molecules moving faster
–bound together less tightly
Surface Tension Phenomena
Lungs
Similar effect occurs
Surface tissue of air sacs (alveoli) has a liquid
with large surface tension that would result in
difficulty in lungs expanding during inhalation
As lungs expand (push against the liquid’s
surface tension) during inhalation, the body
secretes a fluid (surfactant) into the tissue of the
air sacs that gradually lowers the surface tension
of the liquid and allows easy inflation of the air
sacs
This surfactant produced late on in the
development of the fetus
Result-
premature infant suffer respiratory distress
Premature birth
Surface Tension
Capillary action
Forces between like molecules are
called cohesive forces
Forces between unlike molecules are
called adhesive forces
e.g. between water molecules
e.g. between water and glass
H2O
F F
Adhesive forces
(between water and glass)
greater than the cohesive forces
between waters molecules
Result: water rises in the capillary tube
until the weight of the water column supported
= the upward force
h qq
Capillary tube in water
meniscus
Surface Tension
Capillary action
H2O
Therefore small radius (r) → large h
h
h = 2g
rgr Cosq
F F
Surface Tension g = F/L
F = gL = g2pr
Vertical component of force Fv = FCosq
q F Fv
Fv = g2prCosq
This force must equal the weight w of the liquid
which rises to height h,
w = mg = rVg = rpr2h g
Thereforerpr2h g = g2prCosq
Surface Tension
Hg
F F
When adhesive forces between liquid and
glass are less than the cohesive forces
between liquid molecules
Capillary action
q
h = 2g
rgr Cosq
h
Mercury
Surface Tension
Capillary action
Applications
•Used to draw samples of blood
•Plants: feed using capillary action
•Kitchen towels: absorb using capillary action
Surface Tension
Dental application: filling
Adhesion of material to tooth surface
Mechanical interlock
Chemical bond
Mechanical (amalgam) no bonding
•undercutting required: chamber that is
smaller at the surface and wider inside.
Adhesion:
interaction force between two materials at their
contact interface
Advantage
conserves tooth structure
Alternative
Surface Tension
Contact angles
Important characteristic is the way in which the
adhesive wets the surface
Effectiveness of adhesion
Wetting characterised by the way in which the
substance spreads out:
f>90o large surface tension
f<90o small surface tension
f
Water drop
f
Water drop
+wetting agent f
wetting agent reduces surface tension
Adhesion
•good intimate contact
•Large area
Enamel normally covered with thin layer of pellicle
(organic substance deposited from saliva)
Clean surface to achieve good adhesion
Low surface tension (good wetting ability)
adhesive is desirable in promoting adhesion
Surface Tension
Dental application:
Chemical Adhesion
Bond strength depends on contact area
Rough surfaces>>>small contact area
Small force >>large stress at local points
>>result failure
Smooth surface –large contact area –lower stress
Use fluid that flows into irregularities to provide
intimate contact over larger surface area
Example- glass slides with water
Rough surfaces when
viewed on atomic scale
Surface Tension
Dental restoration
Bonding to tooth surfaces impaired by
contamination
-Etching debris and saliva
Viscosity
Adhesive should spread out (wet)
therefore a low viscosity adhesive is important
Wetting of enamel and dentine surfaces reduced
by application of aqueous fluoride solution
less plaque adheres to enamel surface treated
with fluoride
Fluid must flow easily (wetting) to achieve bonding
Wetting of enamel and dentine
Surface Tension
Chemical Adhesion Dental restoration
Forces between Molecules
Like water droplets,
Bubbles are also spherical
Inward force due to surface tension
increases pressure of the gas inside
to a value greater than atmospheric
pressure
Excess pressure DP inside bubble given by
DP = 4g/r
Surface Tension
Example
Calculate the excess pressure in (a) SI units
and (b) in mm Hg inside a water bubble of
radius 0.25mm
DP = 4g/r
DP = 4 (0.072N/m)/(0.25 x10-3m)
(a)
DP = 1.152 x103 Nm-2
(b) P = rgh
h = P/rg
h = 1.152 x103 Pa
(13.6 x103 kgm-3)(9.8ms-2)
h = 8.6 x10-3m
h = 8.6 mm Hg
DP = 1.152 x103 Pa
Surface Tension
Calculate the pressures inside bubbles of water
and soapy water each of diameter 1.5cm.
Surface tension of water(gw) is 0.072Nm-1
Surface tension of soapy water (gsw) is 0.037Nm-1
Pressure inside a bubble is given by
P =(4g)/r
Water
Pressure (P) = (4 x 0.072Nm-1)/(0.75 x10-2m)
P = 38.4Nm-2
Soapy water
Pressure (P) = (4 x 0.037Nm-1)/(0.75 x10-2m)
P = 19.6Nm-2