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