basic hydraulics density, specific gravity math for water technology mth 082 and water works...
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Basic Hydraulics Density, Specific Gravity
Basic Hydraulics Density, Specific Gravity
Math for Water TechnologyMTH 082 and Water Works
Operation WQT 111Lecture 4
Hydraulics Chapter 1(pgs. 205-212)
Math for Water TechnologyMTH 082 and Water Works
Operation WQT 111Lecture 4
Hydraulics Chapter 1(pgs. 205-212)
Objectives/DiscussObjectives/Discuss
• Density
• Specific Gravity
• Bulk Density
• Density of a Fluid
• Density
• Specific Gravity
• Bulk Density
• Density of a Fluid
What is Density?What is Density?• The weight per unit of volume.
Density= Mass/Volumeρ = 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)
• 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?
A substance weighs 378 g and occupies a space of 48 cm3. What
is its density in grams per cubic centimeter?
0.1
3 g
/cm
3
7.9
g/c
m3
18,
144
g/c
m3
378
g/c
m3
7%0%
13%
80%
1. 0.13 g/cm3
2. 7.9 g/cm3
3. 18,144 g/cm3
4. 378 g/cm3
1. 0.13 g/cm3
2. 7.9 g/cm3
3. 18,144 g/cm3
4. 378 g/cm3
What is the density in pounds per gallon of a 1.00 L solution that
weighs 2.29 lb?
What is the density in pounds per gallon of a 1.00 L solution that
weighs 2.29 lb?
2.2
9 lb
/gal
8.6
7 lb
/gal
0.1
2 lb
/gal
0.4
3 lb
/gal
7%0%
14%
79%
1. 2.29 lb/gal
2. 8.67 lb/gal
3. 0.12 lb/gal
4. 0.43 lb/gal
1. 2.29 lb/gal
2. 8.67 lb/gal
3. 0.12 lb/gal
4. 0.43 lb/gal
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?
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?
700
cm
3
0.0
15 c
m3
0.6
5 cm
3
150
0 cm
3
91%
0%0%9%
1. 700 cm3
2. 0.015 cm3
3. 0.65 cm3
4. 1500 cm3
1. 700 cm3
2. 0.015 cm3
3. 0.65 cm3
4. 1500 cm3
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.
The density of a substance changes slightly as the temperature of the
substance changes.
The density of a substance changes slightly as the temperature of the
substance changes.
Tru
e
Fal
se
0%
100%
1. True
2. False
1. True
2. False
(T) Substances increase in size (expand volume) as they become warmer. Density is lower in warm substance but greater in cold substances, cool=condense
(T) Substances increase in size (expand volume) as they become warmer. Density is lower in warm substance but greater in cold substances, cool=condense
What is Density?What is Density?
1 ft3 or 0.1 lb 2 ft3 or 0.1 lb
Cold Higher DensityCold Higher Density
Warm Lower DensityWarm Lower Density
In water supply operations, the density of water varies slightly with
temperature.
In water supply operations, the density of water varies slightly with
temperature.
Tru
e
Fal
se
0%
100%
1. True
2. False
1. True
2. False
(T) However, at the constant temperatures in water supply operations the change is negligible. (T) However, at the constant temperatures in water supply operations the change is negligible.
Water is the most dense at 39.2 oF and becomes less dense when the
temperature rises or falls.
Water is the most dense at 39.2 oF and becomes less dense when the
temperature rises or falls.
Tru
e
Fal
se
13%
88%
1. True
2. False
1. True
2. False
(T) water is an unusual substance that acts differently from everything else.. (T) water is an unusual substance that acts differently from everything else..
What is Bulk Density?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
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.
This physical property is what prevents salt and freshwater from mixing in an aquifer or
underground basin.
Spec
ific
gravi
...
Tem
perat
ure pH
Van
der
waa
ls ..
.
80%
13%
0%7%
1. Specific gravity
2. Temperature
3. pH
4. Van der waals forces
1. Specific gravity
2. Temperature
3. pH
4. Van der waals forces
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.
What is specific gravity of a liquid?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.
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?
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?
62.4 lb/ft3
162 lb/ft3 = 2.6062.4 lb/ft3
162 lb/ft3 = 2.6062.4 lb/ft3
162 lb/ft3162 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?
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?
62.4 lb/ft3
56 lb/ft3 = 0.90; its 9/10 as dense as water!62.4 lb/ft3 THAT’S WHY OIL FLOATS ON H2O56 lb/ft3 = 0.90; its 9/10 as dense as water!62.4 lb/ft3 THAT’S WHY OIL FLOATS ON H2O
56 lb/ft356 lb/ft3
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?
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?
62.4 lb/ft3
168 lb/ft3 = 2.6962.4 lb/ft3
168 lb/ft3 = 2.6962.4 lb/ft3
168 lb/ft3168 lb/ft3
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?
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?
62.4 lb/ft3
(X) lb/ft3 = 0.92; (X lb/ft3) = 62.4 lb/ft3 (0.92)
62.4 lb/ft3 (X) = 57.41 lb/ft3
(X) lb/ft3 = 0.92; (X lb/ft3) = 62.4 lb/ft3 (0.92)
62.4 lb/ft3 (X) = 57.41 lb/ft3
0.92= ??? lb/ft30.92= ??? lb/ft3
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?
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/ft374.9 lb/ft3 74.9 lb/ft3 = 1.2062.4 lb/ft3
74.9 lb/ft3 = 1.2062.4 lb/ft3
Pumped Conversion Rate(25 gpm) (10.01 lb/gal) (1,440 min/day) = 360,360 lb/d pumpedPumped Conversion Rate(25 gpm) (10.01 lb/gal) (1,440 min/day) = 360,360 lb/d pumped
H20 Specific Gravity8.34 lb/gal (1.20) =10.01 lb/gal
H20 Specific Gravity8.34 lb/gal (1.20) =10.01 lb/gal
A fluid with a specific gravity of 1.05 weighs _____ lb/gal.
A fluid with a specific gravity of 1.05 weighs _____ lb/gal.
8.4
8.8
7.2
8.5
25% 25%25%25%
Given : Sg= 1.05 Need lb/galConversions 8.34 lb/1gal8.34 lb (1.05) = 8.75 lb/gal gal
Given : Sg= 1.05 Need lb/galConversions 8.34 lb/1gal8.34 lb (1.05) = 8.75 lb/gal gal
a) 8.4
b) 8.8
c) 7.2
d) 8.5
a) 8.4
b) 8.8
c) 7.2
d) 8.5
If water weighs 8.34 lbs/gal, how much will 7.5 gal weigh?If water weighs 8.34 lbs/gal,
how much will 7.5 gal weigh?
50.
8 lb
s
62.
6 lb
s
75.
5 lb
s
77.
3 lb
s
25% 25%25%25%
Given : 8.43 lbs/gal and 7.5 galConversions 8.34 lb/1gal8.34 lb (7.5 gallons) = 63 lbs gal
Given : 8.43 lbs/gal and 7.5 galConversions 8.34 lb/1gal8.34 lb (7.5 gallons) = 63 lbs gal
a) 50.8 lbs
b) 62.6 lbs
c) 75.5 lbs
d) 77.3 lbs
a) 50.8 lbs
b) 62.6 lbs
c) 75.5 lbs
d) 77.3 lbs
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?
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 gal0.93 SG1240 gal0.93 SG
SG=0.93SG=0.93
Conversion Rate(7.761 lb/gal) (1240 gal) = 9,622 lbConversion Rate(7.761 lb/gal) (1240 gal) = 9,622 lb
H20 Specific Gravity8.34 lb/gal (0.93) =7.76 lb/gal
H20 Specific Gravity8.34 lb/gal (0.93) =7.76 lb/gal
A liquid has a specific gravity of 1.16 How much would 300 gallons of this liquid weigh?
A liquid has a specific gravity of 1.16 How much would 300 gallons of this liquid weigh?
290
2 pound
s
348
pounds
250
2 pound
s
215
6 pound
s
25% 25%25%25%
Given : Sg= 1.16 and 300 gallons?? Need weightConversions 8.34 lb/1gal8.34 lb (300 gallons) = 2502 lbs gal2502 lbs (1.16) = 2902 lbs
Given : Sg= 1.16 and 300 gallons?? Need weightConversions 8.34 lb/1gal8.34 lb (300 gallons) = 2502 lbs gal2502 lbs (1.16) = 2902 lbs
a) 2902 pounds
b) 348 pounds
c) 2502 pounds
d) 2156 pounds
a) 2902 pounds
b) 348 pounds
c) 2502 pounds
d) 2156 pounds
What is specific gravity of a gas?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)
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? 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
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
Cl2 Specific Gravity = 0.187 lb/ft3 / 0.075 lb/ft3
= 2.49
Chlorine gas is about 2.5 times as dense as airChlorine 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.
Today’s objective: to discuss the concept of density and specific
gravity has been met.
Stro
ngly A
gree
Agre
e
Neu
tral
Dis
agre
e
Stro
ngly D
isag
...
20% 20% 20%20%20%
1. Strongly Agree
2. Agree
3. Neutral
4. Disagree
5. Strongly Disagree
1. Strongly Agree
2. Agree
3. Neutral
4. Disagree
5. Strongly Disagree
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