Basic Hydraulics Density,
Specific Gravity
Math for Water Technology
MTH 082 and Water Works
Operation WQT 111
Lecture 4
Hydraulics Chapter 1
(pgs. 205-212)
Objectives/Discuss
•
•
•
•
Density
Specific Gravity
Bulk Density
Density of a Fluid
What is Density?
• The weight per unit of volume.
Density= Mass/Volume
ρ=m/V
ρ is the object's density (measured in kilograms per cubic
meter)
–m is the object's total mass
(measured in kilograms)
–V is the object's total volume
(measured in cubic meter)
Units:
• lb/ft3 (sand, activated carbon, lime, soda ash, air, chlorine
gas, methane, carbon dioxide)
 lb/gal (water, liquid aluminum, liquid chlorine)
A substance weighs 378 g and
occupies a space of 48 cm3. What
is its density in grams per cubic
centimeter?
80%
0.13 g/cm3
7.9 g/cm3
18,144 g/cm3
378 g/cm3
13%
7%
3
37
8
g/
cm
g/
cm
3
44
18
,1
9
7.
13
g/
cm
3
g/
cm
3
0%
0.
1.
2.
3.
4.
What is the density in pounds per
gallon of a 1.00 L solution that
weighs 2.29 lb?
79%
2.29 lb/gal
8.67 lb/gal
0.12 lb/gal
0.43 lb/gal
14%
7%
ga
l
0.
43
lb
/
ga
l
0.
12
lb
/
ga
l
lb
/
67
8.
29
lb
/
ga
l
0%
2.
1.
2.
3.
4.
The density of an unknown
substance is 2.14 g/cm3. How
much space would this substance
occupy in cubic centimeters if it
weighed 3.3 lb?
We know that 2.14 g of substance occupies 1 cm3 by knowing its density. To get
the space 1,498.2 g occupies, divide by the density.
91%
9%
0%
15
00
cm
3
cm
3
65
0.
0.
01
5
cm
3
cm
3
0%
0
700 cm3
0.015 cm3
0.65 cm3
1500 cm3
70
1.
2.
3.
4.
The density of a substance changes
slightly as the temperature of the
substance changes.
(T) Substances increase in size (expand volume) as they become warmer.
Density is lower in warm substance but greater in cold substances,
cool=condense
100%
1. True
2. False
ls
e
Fa
Tr
ue
0%
What is Density?
1
ft3
or 0.1 lb
2 ft3 or 0.1 lb
Cold Higher Density
Warm Lower Density
In water supply operations, the
density of water varies slightly with
temperature.
(T) However, at the constant temperatures in water supply operations the
change is negligible.
100%
1. True
2. False
ls
e
Fa
Tr
ue
0%
Water is the most dense at 39.2 oF
and becomes less dense when the
temperature rises or falls.
(T) water is an unusual substance that acts differently from everything else..
88%
1. True
2. False
ls
e
Fa
Tr
ue
13%
What is Bulk Density?
Bulk density is the weight of a cubic foot of
material as it would be shipped from the
supplier to the treatment plant. It is the mass
of many particles of the material divided by
the volume they occupy. The volume includes
the space between particles as well as the
space inside the pores of individual particles.
Bulk density is a measure of the weight of the substance per
unit volume (g/cc). Includes volume of the air, amount of air
This physical property is what
prevents salt and freshwater
from mixing in an aquifer or
underground basin.
Specific gravity is related to density. Since the seawater is more dense, it
doesn't mix freely with the freshwater. It's similar to what happens with
water and oil.
80%
13%
7%
...
rw
aa
ls
pH
ra
tu
re
Va
n
de
m
pe
Te
ifi
c
gr
av
i..
.
0%
ec
Specific gravity
Temperature
pH
Van der waals
forces
Sp
1.
2.
3.
4.
What is specific gravity of a liquid?
Specific Gravity- is the density of a substance
relative to the standard density of water which
is 62.4 lb/ft3 or 8.34 lb/gal. It’s a ratio of a
substances density to that of water.
SG= density of substance
62.4 lb/ft3 or 8.34 lb/gal
SG is used as a way to compare to separate
materials.
Its done at a fixed temperature and pressure
for a given substance.
Example 1. The density of granite rock is 162 lb/ft3 and
the density of water is 62.4 lb/ft3. What is the specific
gravity of granite?
162 lb/ft3
62.4 lb/ft3
162 lb/ft3 = 2.60
62.4 lb/ft3
Example 2. The density of SAE motor oil is 56 lb/ft3 and
the density of water is 62.4 lb/ft3. What is the specific
gravity of the motor oil?
56 lb/ft3
62.4 lb/ft3
56 lb/ft3 =
62.4 lb/ft3
0.90; its 9/10 as dense as water!
THAT’S WHY OIL FLOATS ON H2O
Example 3. The density of aluminum is 168 lb/ft3 and the
density of water is 62.4 lb/ft3. What is the specific gravity
of the aluminum?
168 lb/ft3
62.4 lb/ft3
168 lb/ft3 =
62.4 lb/ft3
2.69
Example 4. The specific gravity of SAE motor oil is 0.92
and the density of water is 62.4 lb/ft3. What is the
density of the motor oil?
0.92= ??? lb/ft3
62.4 lb/ft3
(X) lb/ft3 =
62.4 lb/ft3
0.92;
(X lb/ft3) = 62.4 lb/ft3 (0.92)
3
(X) = 57.41 lb/ft
Example 5. Suppose you wish to pump a certain liquid at
the rate of 25 gpm. How many lb per day will be
pumping if the liquid weighs 74.9 lb/ft3?
74.9 lb/ft3
74.9 lb/ft3 =
62.4 lb/ft3
1.20
H20 Specific Gravity
8.34 lb/gal (1.20) =10.01 lb/gal
Pumped Conversion Rate
(25 gpm) (10.01 lb/gal) (1,440 min/day) = 360,360 lb/d pumped
A fluid with a specific gravity of
1.05 weighs _____ lb/gal.
25%
8.
5
25%
7.
2
8.4
8.8
7.2
8.5
25%
8.
8
a)
b)
c)
d)
25%
8.
4
Given : Sg= 1.05 Need lb/gal
Conversions 8.34 lb/1gal
8.34 lb (1.05) = 8.75 lb/gal
gal
If water weighs 8.34 lbs/gal,
how much will 7.5 gal weigh?
lb
s
.3
77
.5
.6
62
25%
lb
s
25%
lb
s
25%
lb
s
.8
50.8 lbs
62.6 lbs
75.5 lbs
77.3 lbs
50
a)
b)
c)
d)
25%
75
Given : 8.43 lbs/gal and 7.5 gal
Conversions 8.34 lb/1gal
8.34 lb (7.5 gallons) = 63 lbs
gal
Example 6. There are 1,240 gal of a certain liquid in a
tank. If the specific gravity of the liquid is 0.93, how
many pounds of liquid are in the tank?
1240 gal
0.93 SG
SG=0.93
H20 Specific Gravity
8.34 lb/gal (0.93) =7.76 lb/gal
Conversion Rate
(7.761 lb/gal) (1240 gal) = 9,622 lb
A liquid has a specific gravity of
1.16 How much would 300
gallons of this liquid weigh?
un
ds
21
56
po
un
ds
02
25
8
34
25% 25%
po
po
u
un
ds
po
02
2902 pounds
348 pounds
2502 pounds
2156 pounds
29
a)
b)
c)
d)
nd
s
Given : Sg= 1.16 and 300 gallons?? Need weight
Conversions 8.34 lb/1gal
25% 25%
8.34 lb (300 gallons) = 2502 lbs
gal
2502 lbs (1.16) = 2902 lbs
What is specific gravity of a gas?
Specific Gravity- is the density of a gas
substance relative to the standard density of
air which is 0.075 lb/ft3 at 20oC and a pressure
of 14.7 psia (pounds per square inch
absolute)
Example 7. The density of chlorine gas is 0.187 lb/ft3.
What is the specific gravity of this gas?
Specific gravity of Cl2 gas= (density of Cl2 gas)
density of air
Cl2 Specific Gravity = 0.187 lb/ft3 / 0.075 lb/ft3
= 2.49
Chlorine gas is about 2.5 times as dense as air
Today’s objective: to discuss the
concept of density and specific
gravity has been met.
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Strongly Agree
Agree
Neutral
Disagree
Strongly Disagree
St
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20% 20% 20% 20% 20%