Part 4
Fluidics
121
Density review
W
Weight W

Weight density, D 
,
Volume V
D
V
is the weight in pounds (grams) per
unit volume in ft3 or gallons (cm3). Density has units of lb/ft3 or lb/gal or g/cm3.
The greater the density, the more matter per volume
Example:
Answer:
Example:
balloon?
A block has a weight of 16.4 lbs and a volume of 6 ft3. What is the density of the block?
D
W 16.4lb
lb

 2.73 3
3
V
6 ft
ft
A helium filled balloon has a volume of 0.33 ft3. What is the weight of the helium in the
Answer:
Using the circle above, solve for the weight. You will also need the density of helium,
from the table on the next page, DHE=0.011 lbs/ft3.
W  DV  0.011
lb
0.33 ft 3  0.0036lb
ft 3
Example:
grams?
An iron block measure 22 cm by 57 cm by 9 cm. How mcuh does the block wiegh in
Answer:
First we need to find the volume of the block.
Volume  l w h  22cm57cm9cm  11,286cm3
Use the circle above and solve for the weight. You will also need the density of iron in the table
on the next page.
W  DV  7.80
g
11286cm 3  88031g
3
cm
Example:
What is the volume of 2000 lb of oil?
Answer:
Solve the circle above for volume and use the density of oils from the table;
V 
W
2000lb

 36.9 ft 3
lb
D
54.2 3
ft
122
Densities of Common Substances
Substance
Weight Density (lb/ft3)
Mass Density (g/cm3)
Solids
Aluminum
169
2.7
Brass
527
8.44
Concrete
145
2.3
Copper
555
8.89
Cork
15
0.240
Gold
1213
19.4
Ice
57
0.917
Iron
490
7.80
Lead
708
Wood, pine
Zinc
11.3
26
0.420
446
7.133
Liquids
Alcohol
49.4
0.79
Gasoline
42.0
0.680
Mercury
846
13.6
Oil
54.2
0.870
Sea water
64.0
1.025
Water
62.4
2
Gases – At 0 °C (32 °F) and a pressure of 14.7 lb/in ( 1 atm)
1.000
Air
0.081
0.00129
Ammonia
0.047
0.00076
Carbon dioxide
0.123
0.00196
Carbon monoxide
0.078
0.00125
Helium
0.011
0.000178
Hydrogen
0.0056
0.0000899
Nitrogen
0.078
0.00125
Oxygen
0.089
0.00143
Propane
0.126
0.00202
123
Pressure
F
P
F
Pressure is the force per area P 
A
A
or
Example:
The pressure of a phonograph needle on a record.
Weight of needle = 0.02 lbs.
The area of contact = 0.0001 in2.
P
Answer:
F
0.02lbs
lb

 200 2
2
A 0.0001in
in
Example:
Find the pressure of a tire on pavement of a 10 ton truck with weight supported by 6
wheels each with 18 in2 in contact.
Weight of truck = 10 tons = 10 tons x
2000lb
= 20,000 lbs.
1ton
The area of contact = 6 x 18 in2 = 108 in2.
P
F 20000lb
lb

 185.2 2
2
A 108in
in
Gauge Pressures vs Absolute Pressure
Absolute pressure is the total amount of pressure. This includes the pressureof the atmosphere. If
a gauge is used to measure the pressure, it will only tell you the pressure in the container that is bigger than
atmospheric pressure. Air pressure is 14.7 lb/in2.
Absolute Pressure = Gauge Pressure + Atmospheric Pressure
Pabs  PG  Patmos
or
Example
The gauge pressure of a tire is 30 lb/in2. What is the absolute pressure?
Answer
Absolute pressure is gauge pressure plus atmospheric pressure.
30 lb/in2 + 14.7 lb/in2 = 44.7 lb/in2
Example
A car falls off a bridge and goes under water. The inside pressure is 15 lbs/in2. The outside
pressure is 20 lbs in2. How hard must one push to open a car door which is 3 feet by 3 feet?
Answer
First find the area of the door in square inches. The door is 36 in by 36 in.
Area = l x w = 36 in x 36 in = 1296 in2
Now for each square inch you must push with 5 lbs. Thus 5 lb/in2 x 1296 in2 = 6,480 lb.
Therefore, you must push with 6,480 lbs of force. Is there a better way out of the car?
124
Pressure Increases with Depth
As one goes deeper into a fluid the pressure increases in proportion to the depth. The pressure per
square inch is equal to the weight of fluid over that square inch. Pressure does not depend on area of the
container.
Which dam must be stronger?
The pressure can be calculated using the formula
P
D
h
P = D*h
where D is the density and h is the height of the fluid.
Example:
A tank is filled to a depth of 18 feet with gasoline. What is the pressure on the side of the
tank at the bottom?
Answer:
From the table in the density section, we find that the density of gasoline is 42.0 lb/ft3.
The height of the fluid above the bottom of the tank is 18 feet. So the pressure is
P  D h  42.0
lb
lb
18 ft  756 2
3
ft
ft
Notice that the units on the height cancelled with one of the units on the bottom of the density.
Things work much smoother if the units are converted (if need be) to this this cancellation take place. This
lets you have the right kind of units for the pressure (force units over area units)
Example:
How deep would you need to go in the ocean to find a pressure equal to the atmosphere at
the surface (14.7 lb/in2)?
First do the conversion from lb/in2 to lb/ft2.
14.7
lb  144in 2 
lb
 2116.8 2
2 
2 
in  1 ft 
ft
Using the circle above and solving for h
lb
P
ft 2
h 
 331
. ft
lb
D
64.0 3
ft
2116.8
125
Archimede’s Principle
The buoyant force on an object in a fluid is equal to the weight of the displaced fluid.
Example
A hydrometer is put in battery acid to check the specific gravity (density) of the battery fluid.
Which case represents the most fully charged battery? (Hint: A fully charged battery has the highest
specific gravity.)
Using the same
hydrometer in all cases.
If a fluid is dense, you will not need
as much volume to equal the weight
of the hydrometer. So the fluid where
the hydrometer floats highest has the
highest density.
From this we would determine that
the top battery is the one with the
highest charge.
100 lbs
80 lbs
In the above figure a rock is submerged in water.
The buoyant force is 20 lbs.
(100 lbs - 80 lbs)
Thus the weight of water displaced is 20 lbs
126
From the definition of density, D 
V 
weight

D
Weight
. The volume of water displaced by the rock is
V
20lb
 0.32 ft 3 .
lb
62.4 3
ft
The volume of the water displaced is equal to the volume of the rock because the rock is what
displaces the water.
Therefore we can use the above arrangement to find the volume of a weird shaped object. In this
case
Vobject = 0.32 ft3
But if we know the volume of the object and the weight of the object we can also determine the
density of the object.
D
weight
100lb
lb

307 3
3
V
0.32 ft
ft
127
Pascal's Principle
Pascal’s Principle states "A change in pressure at one point in a confined fluid is transmitted to all
other points of the fluid."
This principle is the basis for hydraulic equipment.
Force out
Force in
-A
-a
The pressure is approximately
the same at all points. Thus, the
pressure on the big piston is the
same as on the little piston, say
20 lbs/in2. If the area of the
little piston, a, is 1 in2 and if
the area of the large piston, A,
is 100 in2 then the force at A is
100 times that at a.
Fout
, and from the formula for pressure, F=PA, so
Fin
A
 out .
Ain
Then the TMA 
TMA 
Fout
PAout

Fin
PAin
Sometime the information is given in terms of the diametrers of the pustons and not in terms of the areas.
The formula for Area = 0.785 D2 , so when we add that to the equation for the TMA,
2
2
Aout 0.785 Dout
Dout
Thus TMA 

 2 .
Ain
0.785 Din2
Din
Therefore the TMA of hydraulic pressure is the ratio of the diameters squared.
Example
Find the TMA of the following hydraulic jack.
TMAlever 
TMApressure
10in
 10
1in
(3in) 2
9


 144
2
0.0625
(0.25in)
Total TMA = 10 x 144 = 1440
Thus to lift 2880 lb object it only takes 2 lbs of force on the handle.
128
Bernoulli's Principle
For the horizontal flow of a fluid through a tube, the sum of the pressure and energy of motion
(kinetic energy) per unit volume of the fluid is constant, i.e., where the fluid moves fast the pressure is
lower than where the fluid moves slow. Note a fluid is either a liquid or a gas.
Examples of Bernoulli's Principle
Low
pressure
a
High pressure
no flow.
b.
129
Surface Tension
The cohesive forces between water molecules can act as a kind of safety net for tiny objects (such
as a needle or razor blade) placed on the surface of water. This is an example of the surface tension of
water. Another example of the surface tension of water is the way water beads when placed on a glass plate
(the cohesive forces of attraction between the water molecules pull them together into a spherical blob).
The surface tension of water can be reduced by adding soap to the water. This reduced surface
tension reduces the cohesion between the water molecules and thus makes it easier for the water to penetrate
the fabric when washing clothes. The surface tension of most liquids decrease as the temperature increases.
This is because the cohesive force of attraction is not as effective at hold the molecules together when they
vibrate faster at higher temperatures.
It is preferable for oil to have a fairly low surface tension so that it can spread evenly over the
surfaces of the engine parts. Notice that if you place a drop of oil on a glass surface it does not bead up
nearly as much as water does. It is also desirable to have an oil with a high enough surface tension to
prevent oil film penetration.
Viscosity
The viscosity of a fluid (liquid or gas) is the measure of a fluids resistance to something traveling
through it. Molasses has a high viscosity and rubbing alcohol has a low viscosity. The greater the
molecular attraction between the liquid molecules the greater the viscosity. In addition the viscosity of a
liquid also determines how long it will take a liquid to flow out of a hole in the bottom of a tank. We could
thus say that viscosity is a measure of a fluids resistance to flow. The viscosity of a fluid normally
decreases with increasing temperature. This is because as the temperature of a fluid increases the molecules
vibrate more rapidly and hence the molecular forces of attraction are not as great. The viscosity of oil must
be low enough to flow but high enough to resist oil film penetration. Multigrade (10W–40) oils have the
characteristic that the viscosity of the oil does not vary nearly as much for a given temperature change as
does a single grade oil (30W).
Capillary Action
The ability of water to climb up a small glass tube is an example of capillary action. The capillary
action of water can be explained by the fact that the adhesive forces between water and glass are greater
than the cohesive forces between the water molecules. Thus the water climbs up the glass until the cohesive
forces between the water molecules can no longer support a higher column of water. The smaller the tube
diameter the higher the water column can rise in the tube due to capillary action. This is easy to see since
the weight of an 1 inch high column of water in a small diameter tube is much less than the weight of an 1
inch high column of water in a large diameter tube. The height that water rises in a capillary tube decreases
with increasing temperature since the surface tension decreases with increasing temperature.
130
Important Functions of Oil
1.
Provides protective film on metal surfaces to prevent metal to metal contact thus reducing heat
generated by friction.
2.
Transfers heat from inside the engine to the oil pan where it is given off to the surrounding air.
3.
Cleans engine parts. Dirt and "crud" tend to settle to bottom of oil pan.
4.
Provides a protective cushion between metal so as to absorb shock between bearings and other
engine parts.
5.
Forms a good seal between piston rings and the cylinder wall.
Important Properties of Oil
1.
2.
3.
4.
Proper viscosity over the expected temperature ranges
i)
low enough to flow
ii)
high enough to resist oil film penetration and to provide good sealing properties
Surface Tension
i)
low enough to permit even spreading over metal
ii)
high enough to prevent oil film penetration
Stability
i)
resist carbon formation, oxidation, foaming
Detergency
131
Exercises
Density Review
1.
What is the density of a 150 g rock that occupies a volume of 60 cm3?
D = ____________
2.
What is the volume of a piece of gold that has a weight of 1 lb? (the density of gold is 1223 lb/ft 3)
V = _____________
3.
Water has a density of 62.4 lb/ft3 or 8.3 lb/gal. How many lbs of water can a 55 gal drum hold?
Weight = _________________
132
Pressure Review
1.
A 150 lb lady stands on only one heel of her shoe. If the heel is square and has dimensions
1
of 4 in  41 in , what is the pressure that she exerts on the floor?
P=___________
2.
Find the pressure at the bottom of a water filled drum that is filled 6.0 ft high?
P=____________
3.
Find the depth in a lake at which the pressure would be 80.0 lb/in2. Hint First change 80 lb/in2 to
units of lb/ft2.
h=____________
4.
The weather channel reports that the atmospheric pressure is 28.5 in of mercury (28.5 in Hg) in
central Nebraska. Find the atmospheric pressure in psi in Nebraska.
P=_____________
5.
20 psi is how many mm of Hg?
P=_____________
6.
The atmospheric pressure at the surface of the earth is due to what?
7.
What is the maximum height that water can be raised with a suction pump?
133
h=_____________
8.
Atmospheric pressure drops with altitude. There are several consequences of this.
(a) How would this account for the lower temeprature at higher altitudes?
(b) When cooking at higher altitudes, recipes often call for a pressure cooker,
which is a sealed pot. Why would this be necessary to cook at temperatures near
or above 100C ?
9.
Jet aircraft require air to fly and routinely fly at altitudes of 30-40 thousand feet.
If the atmospheric pressure was 14.7 psi all the way to the “top”, how deep would
the atmosphere be? Would the jets be able to fly at their usual altitude?
134
Buoyancy Review
1.
A balloon is buoyed up with a force equal to the
a.
weight of air it displaces.
b.
density of the surrounding air
c.
atmospheric pressure
d.
weight of the balloon and contents
e.
all of these
2.
What is the weight of water displaced by a 100 ton floating ship?
a.
less than 100 tons
b.
100 tons
c.
more than 100 tons
d.
100 cubic feet
e.
depends on the ship's shape
3.
Pumice is a volcanic rock that floats in water. Its density is
a.
less than the density of water.
b.
equal to the density of water.
c.
more than the density of water.
4.
A metal alloy weighs 150 lbs in air and 120 lbs when completely submerged in water. What is the
buoyant force acting on the object?
FB = ______________
5.
What is the weight of water displaced by the object? What is the volume of water displaced by the
object? What is the volume of the object
Vwater=___________
Vobject=___________
135
6.
Find the density of the object. (from problems 4 and 5)
D = _______________
7.
If a ship is in a closed lock and sinks will the water level be higher, lower, or at the same level on
the sides of the lock compared to what it was before the ship sank?
136
Pascal's Principle Review
P1 = P2
F1
F
 2 or F1A2 = F2A1
A1 A2
1.
The area of the small piston in a hydraulic jack is 1.5 in2 and the area of the large piston is 75 in2.
If a force of 20 lb is applied to the small piston, what weight can be lifted by the large one?
Fout = ___________
137
Bernoulli's Principle Review
1.
The faster a fluid moves, the
a.
greater its internal pressure.
b.
lower its internal pressure.
2.
On a windy day, atmospheric pressure
a.
increases.
b.
decreases.
c.
remains unchanged.
3.
with
When water is turned on in a shower, the shower curtain moves towards the water. This has to do
a.
b.
c.
d.
e.
4.
capillary action.
surface tension.
heat capacity.
pressure in a moving fluid.
none of these.
An umbrella tends to move upwards on a windy day because
a.
air gets trapped under the umbrella and pushes it up.
b.
buoyancy increases with increasing wind speed.
c.
a low pressure area is created on top of the umbrella.
d.
a and c above.
e.
all of these.
5.
The Bernoulli effect causes passing ships to be drawn together when the ships are close and
moving in the
a.
same direction.
b.
opposite direction.
c.
either the same direction or opposite direction.
6.
Give an example of where Bernoulli's Principle is used in the gasoline engine. If you are
unfamiliar with gasoline engines, explain how the Bernoulli effect works to let airplanes fly.
138
Surface Tension and Viscosity Review
1.
The height that water raises in a capillary tube
a.
increases as the diameter of the tube increases.
b.
decreases as the diameter of the tube decreases.
c.
does not depend on the size of the tube.
d.
none of these.
2.
The surface tension of water is caused by
a.
cohesive forces between water molecules.
b.
adhesive forces between water molecules.
c.
neither of these.
3.
As the water temperature increases, the height water raises in a capillary tube
a.
decreases.
b.
increases.
c.
stays the same.
4.
A consequence of surface tension of water is
a.
capillary action.
b.
wet sand being firmer than dry sand.
c.
hot oily soup tasting different than cold oily soup.
d.
all of the above.
e.
none of the above.
5.
When you put a stick in water and remove it, the stick is wet. When you put a stick in mercury and
remove it, the stick is dry. The reason for this is the adhesive forces are greater between the stick and
a.
water.
b.
mercury.
c.
not enough information given.
6.
Is it possible for a solid piece of metal to float? Explain.
7.
What is viscosity?
139
8.
Give an example of a high viscosity liquid and a low viscosity liquid.
High viscosity : ______________
Low Viscosity : ______________
9.
Does the viscosity of a liquid increase or decrease as the temperature increases?
10.
Why will hot water leak more readily through small leaks in a car radiator than cold water?
140