Although the principles of Hydraulics and Hydrostatics are discussed in "Mechanics," it will be well to review them briefly, showing their application to the various problems under the head of "Water Supply."

If several open vessels containing water are connected by pipes, the water will eventually stand at the same level in all of them, regardless of the length or the size of the connecting pipes.

The pressure exerted by a liquid at any given point is the same in all directions, and is proportional to the depth.

A column of water at 60° temperature having a sectional area of one square inch and a height of one foot, weighs .43 pound, and the pressure exerted by a liquid is usually stated in pounds per square inch, the same as in the case of steam. If a closed vessel is connected, by means of a pipe, with an open vessel at a higher level, so that it is 10 feet, for example, from the bottom of the first vessel to the surface of the water in the second, the pressure on each square inch of the entire bottom of the lower vessel will be 10 X .43 = 4.3 pounds, and the pressure per square inch at any given point in the vessel or connecting pipe will be equal to its distance in feet from the surface of the water in the upper vessel multiplied by .43. If a pipe is carried from a reservoir situated on the top of a hill to a point at the foot of the hill a hundred feet below the surface of the water, a pressure of 100 X .43 = 43 pounds per square inch will be exerted at the lower end of the pipe, provided it is closed. When the pipe is opened and the water begins to flow, the conditions are changed and the pressure in the different parts of the pipe varies with the distance from the open end.

In order for a liquid to flow through a pipe there must be a certain pressure or "head" at the inlet end. The total head causing the flow is divided into three parts, as follows: 1st, the velocity head: the height through which a body must fall in a vacuum to acquire the velocity with which the water enters the pipe. 2d, the entry head: that required to overcome the resistance to entrance into the pipe. 3d, the friction head: due to the frictional resistance to flow within the pipe. In the case of long pipes and low heads the sum of the velocity and entry heads is so small that it may be neglected.

Table I shows the pressure of water in pounds per square inch for elevations varying in height from 1 to 135 feet.

Table II gives the drop in pressure due to friction in pipes of different diameters for varying rates of flow. The figures given are for pipes 100 feet in height. The frictional resistance in smooth pipes having a constant flow of water through them is proportional to the length of pipe. That is, if the friction causes a drop in pressure of 4.07 pounds per square inch in a l 1/4-inch pipe 100 feet long, which is discharging 20 gallons per minute, it will cause a drop of 4.07 X 2= 8.14 pounds in a pipe 200 feet long; or 4.07/ 2 = 2.03 pounds in a pipe 50 feet long, acting under the same conditions. The factors given in the table are for pipes of smooth interior, like lead, brass or wrought iron.

Example. - A 1 1/2-inch pipe 100 feet long connected with a cistern is to discharge 35 gallons per minute. At what elevation above the end of the pipe must the surface of the water in the cistern be to produce this flow?

In Table II we find the friction loss for a 1 1/2-inch pipe discharging 35 gallons per minute to be 5.05 pounds. In Table I we find a pressure of 5.2 pounds corresponds to a head of 12 feet, which is approximately the elevation required.

How many gallons will be discharged through a 2-inch pipe 100 feet long where the inlet is 22 feet above the outlet? In Table I we find a head of 22 feet corresponds to a pressure of 9.53 pounds. Then looking in Table II we find in the column of Friction Loss for a 2-inch pipe that a pressure of 9.46 corresponds to a discharge of 100 gallons per minute.

Tables I and II are commonly used together in examples.

A house requiring a maximum of 10 gallons of water per minute is to be supplied from a spring which is located 600 feet distant, and at an elevation of 50 feet above the point of dis-

charge. What size of pipe will be required? From Table I we find an elevation or head of 50 feet will produce a pressure of 21.65 pounds per square inch. Then if the length of the pipe were only 100 feet, we should have a pressure of 21.65 pounds available to overcome the friction in the pipe, and could follow along the line corresponding to 10 gallons in Table II until we came to the

friction loss corresponding most nearly to 21.65, and take the size of pipe corresponding. But as the length of the pipe is 600 feet, the friction loss will be six times that given in Table II for given sizes of pipe and rates of flow; hence we must divide 21.65 by 6 to obtain the available head to overcome friction, and look for this quantity in the table, 21.65/ 6 = 3.61, and Table II shows us that a 1-inch pipe will discharge 10 gallons per minute with a friction loss of 3.16 pounds, and this is the size we should use.

TABLE I.

Head in feet.

Pressure pounds per square inch.

Head in feet.

Pressure pounds per square inch.

Head in feet.

Pressure pounds per square inch.

1

.43

46

19.92

91

39.42

2

.86

47

20.35

92

39.85

3

1.30

48

20.79

93

40.28

4

1.73

49

21.22

94

40.72

5

2.16

50

21.65

95

41.15

6

2.59

51

22.09

96

41.58

7

3.03

52

22.52

97

42.01

8

3.46

53

22.95

98

42.45

9

3.89

54

23.39

99

42.88

10

4.33

55

23.82

100

43.31

11

4.76

56

24.26

101

43.75

12

5.20

57

24.69

102

44.18 .

13

5.63

58

25.12

103

44.61

14

6.06

59

25.55

104

45.05

15

6.49

60

25.99

105

45.48

16

6.92

61

26.42

106

45.91

17

7.36

62

26.85

107

46.34

18

7.79

63

27.29

108

46.78

19

8.22

64

27.72

109

47.21

20

8.66

65

28.15

110

47.64

21

9.09

66

28.58

111

48.08

22

9.53

67

29.02

112

48.51

23

9.96

68

29.45

113

48.94

24

10.39

69

29.88

114

49.38

25

10.82

70

30.32

115

49.81

26

11.26

71

30.75

116

50.24

27

11.69

72

31.18

117

50.68

28

12.12

73

31.62

118

51.11

29

12.55

74

32.05

119

51.54

30

12.99

75

32.48

120

51.98

31

13.42

76

32.92

121

52.41

32

13.86

77

33.35

122

52.84

33

14.29

78

33.78

123

53.28

34

14.72

79

34.21

124

53.71

35

15.16

80

34.65

125

54.15

36

15.59

81

35.08

126

54.58

37

16.02

82

35.52

127

55.01

38

16.45

83

35.95

128

55.44

39

16.89

84

36.39

129

55.88

40

17.32

85

36.82

130

56.31

41

17.75

86

37.25

131

56.74

42

18.19

87

37.68

132

57.18

43

18.62

88

38.12

133

57.61

44

19.05

89

38.55

134

58.04

45

19.49

90

38.98

135

58.48

TABLE II.

Gallons discharged per minute.

1/2 in-

3/4 in.

1 in.

1 1/4 in.

1 1/2 in.

2 in.

2 1/2 in.

3 in.

Velocity in feet per second.

Friction loss in pounds.

Velocity in feet per second.

Friction loss in pounds.

Velocity in feet per second.

Friction loss in pounds.

Velocity in feet per second.

Friction loss in pounds.

Velocity in feet per second.

Friction loss in pounds.

Velocity in feet per second.

Friction loss in pounds.

Velocity in feet per second.

Friction loss in pounds.

Velocity in feet per second.

Friction loss in pounds.

5

8.17

24.6

3.63

33

2.04

.84

1.31

.31

.91

.12

10

16.3

96.0

7.25

13.0

4.08

3.16

2.61

1.05

1.82

.47

1.02

.12

15

10.9

28.7

6.13

6.98

3.92

2.38

2.73

.97

1.53

.27

20

14.5

50.4

8.17

12.3

5.22

4.07

3.63

1.66

204

.42

25

18.1

78.0

10.2

19.0

6.53

6.40

4.54

2.62

2.55

.67

1.63

.21

1.13

.10

30

12.3

27.5

7.84

9.15

5.45

3.75

3.06

.91

35

14.3

37.0

9.14

12 04

6.36

5.05

3.57

1.25

40

16.3

48.0

10.4

16.10

7.26

6.52

4.09

1.60

45

11.7

20.2

8.17

8.15

4.60

2.02

50

13.1

24.9

9.08

10.0

5.11

2.44

3 26

.81

2.27

.35

75

19.6

56.1

13.6

22.4

7.66

5.32

4.90

1.80

3.40

.74

100

18.2

39.0

10.2

9.46

6.53

3.20

4.54

1.31

125

12.8

14.9

8.16

4.89

5.67

1.99

150

15.3

21.2

9.80

7.00

6.81

2.85

175

17.1

28.1

11.4

9.46

7.94

3.85

200

20.4

37.5

13.1

12.47

9.08

5.02

Examples For Practice

1. What size pipe will be required to discharge 40 gallons per minute, a distance of 50 feet, with a pressure head of 19 feet?

Ans. 1 1/4 inch.

2. What head will be required to discharge 100 gallons per minute through a 21-inch pipe 700 feet long?

Ans. 52 feet.

Piping

Wrought iron, lead and brass are the principal materials used for water pipes. Wrought-iron pipe is the cheapest and easiest to lay, but is objectionable on account of rust and the consequent discoloration of water passing through it. When it

TABLE III.

Nominal inside diameter.

Actual outside diameter.

Thickness.

Actual inside diameter.

Internal circumference.

External circumference.

Length of pipe per square foot of inside surface.

Length of pipe per square foot of outside surface.

Internal area.

External area.

Length of pipe containing 1 cubic foot.

Weight per foot.

Number of threads per inch of screw.

Gallons per foot of length.

in.

in.

in.

in.

in.

in.

feet

feet

in.

in.

feet

pounds

27

.0006

1/8

.40

.068

.27

.85

1.27

14.1

9.44

.05

.13

2500.

.24

18

.0026

1/4

.54

.088

.36

1.14

1.69

105

7.05

.10

.23

1385.

.42

18

.0057

3/8

.67

.091

.49

1.55

2.12

7.67

5.65

.19

.36

751.5

.56

14

.0102

1/2

.84

.1C9

.62

1.95

2.65

6.13

4.50

.30

.55

472.4

.84

14

.0230

3/4

1.05

.113

.82

2 59

3.29

4.63

3.63

.53

.86

270.0

1.12

11 1/2

.0408

1

1.31

.134

1.05

3.29

4.13

3.68

2.90

.86

1.35

166 9

1.67

11 1/2

.0638

1 1/4

1 66

.140

1.38

4.33

5.21

2.77

2 30

1.49

2.16

96.2

2.26

11 1/2

.0918

1 1/2

1.90

.145

1.61

5.06

5.96

2.37

2.01

2.04

2.83

70.6

2.69

11 1/2

.1632

2

2.37

.154

2.06

6.49

7.46

1.85

1.61

3.35

4.43

42.3

3.66

8

.2550

2 1/2

2 87

.204

2 47

7.75

9.03

1.54

1 33

4.78

6 49

30 1

5.77

8

.3673

3

3 50

.217

3.06

9.63

10.1

1.24

1.09

7.39

9.62

19.5

7.54

8

.4998

3 1/2

4.00

.226

3.55

11.1

12.5

1.07

.95

9 88

12.5

14.5

9.05

8

.6528

4

4.50

.237

4 02

12.6

14.1

.95

.85

12.7

15.9

11.3

10.7

8

.8263

5

5.56

.259

5.04

15.8

17.4

.75

.63

20.0

24.3

7.2

14.5

8

1.469

6

6.62

.280

6.06

19.0

20.8

.63

.57

28.9

34.4

4.9

18.7

8

1.999

is employed for this purpose it is customary to use galvanized pipe, that is, pipe which has been covered with a thin coating of zinc or zinc and tin. This prevents rust from forming where the zinc is unbroken, but at the joints where threads are cut, and at other places where the zinc becomes loosened, as by bending, the pipe is likely to be eaten away more or less rapidly, depending upon the quality of the water. Zinc, when taken into the system, is poisonous, and for this reason galvanized pipes should not ordinarily be used for drinking water.