HYDRAULICS AND

ITS APPLICATIONS

-BY

A. H. GIBSON, M. Sc. Assoc. MEM. INST. C.E.

SENIOR DEMONSTRATOR AND ASSISTANT LECTURER IN ENGINEERING

IN THE UNIVERSITY OF MANCHESTER

NEW YORK

D. VAN NOSTRAND COMPANY

23 MURRAY AND 27 WARREN STREETS

1908

PREFACE.

WERE water a perfectly non-viscous, inelastic fluid, whose

particles, when in motion, always followed sensibly parallel

paths, Hydraulics would be one of the most exact of the sciences.

But water satisfies none of these conditions, and the result is

that in the majority of cases brought before the engineer,

motions and forces of such complexity are introduced as baffle

all attempts at a rigorous solution.

This being so, the best that can be done is to discuss each

phenomenon on the assumption that the fluid in motion is

perfect, and to modify the results so obtained until they fit the

results of experiment, by the introduction of some empirical

constant which shall involve the effect of every disregarded

factor.

It is worth while here impressing on the student of the science

that, apart from these experimentally-deduced constants, his

theoretical results are, at the best, only approximations to the

truth, and may, if care be not taken in their interpretation, be

actually misleading.

On the other hand, it may be well to answer the criticism of

those who would cavil at such theoretical treatment, by pointing

out that the results so obtained provide the only rational

framework on which to erect the more complete structure of

Hydraulics.

In the following pages an attempt has been made to consider

the science, and its application to the design of Hydraulic

174569

vi PREFACE.

Machinery, in a manner suitable for a student who has some

initial knowledge of mechanics.

While written primarily with the needs of a student in view,

it is, however, hoped that the book may prove of value to

such as are actively engaged in the practice and profession of

Hydraulic Engineering. Although it has not been attempted

to elude the largely imaginary difficulties of a mathematical

treatment involving some knowledge of the Differential and

Integral Calculus, the knowledge of this subject which is

necessary for a thorough grasp of the greater part of the book

is very slight.

Where, as in Arts. 23, 24, 35 and 62, a somewhat more

extended mathematical knowledge is required, the work is such

as may safely be left by all but the more advanced student of

the subject.

In the section devoted to Hydraulic Machinery, it has not

been attempted to deal in any way exhaustively with the subject,

and only such machines have been illustrated or described as

are typical of their class, represent good modern design, and

illustrate some definite principle of construction. For many of

these illustrations the Author is indebted to the manufacturers,

and while reference has been made to these in the text, he

would take this opportunity of thanking them collectively for

the help which they have so courteously tendered.

As was essential, reference has been freely made to the

minutes of the proceedings of the various English and American

societies, and to the English and German technical press, as

well as to standard works on the subject. Of these the Author

is particularly indebted to the Councils of the Institution of

Civil Engineers, the Institution of Mechanical Engineers, the

American Society of Civil Engineers, the Zeitschrift des Vereins

deutscher Ingeiiieure, The Engineer, and Engineering.

The greatest debt of all is, however, owing to the teachings

and published papers of his old professor and some time chief,

Osborne Reynolds. Old students of the Professor will readily

PREFACE. vii

recognise to what extent any slight merit which the book may

possess is due, directly or indirectly, to the influence of one

to whom the science of Hydraulics owes so much.

In conclusion, the Author would tender his thanks to Mr. S.

Chapman, to Mr. E. Magson, and to his colleagues, Mr. C. H.

Lander and Mr. F. Pickford, of the Manchester University, each

of whom has revised a portion of the proofs, and to whose kindly

criticism and siiestion the book owes much.

A. H. GIBSON

MAIs T CHESTEl{,

February, 1908.

CONTENTS.

SECTION I.

PHYSICAL PROPERTIES OF WATER HYDROSTATICS.

CHAPTEE I.

ART. PAGE

1. Historical Resume . . , . . . . . . . 1

2. Physical Properties of Water ...... 3

3. Cohesion ; Adhesion ; Capillarity ; Surface Tension 5

4. Viscosity . . . . . . . . . . . . . . . . . . 11

CHAPTEE II.

5. Hydrostatics .. .. .. .. .. .. .. . 1(>

6. Pressure at a Point . . . . . . 17

7. Pressure Head . . . . . . . . . . . . . . . . IB

8. Transmissibility of Pressure Hydraulic Press . . . . . . 19

9. Eesultant Pressure and Centre of Pressure . . 21

10. Masonry Dams . . . . . . . . . . . . 2s"

11. Equilibrium of Moating Bodies .. 32

12. Oscillations of Ships . . . . . . . . 37

13. Strength of Pipes and Cylinders .. .... 39

SECTION II.

HYDRAULICS.

CHAPTEE III

14. Modes of Motion of a Fluid . . . . . . . . . . . . 4.~>

lo. Vortices . . . . . . . . . . . . . . .-.48

16. Conditions Eegulating the Two Modes of Motion . . . . ' 49

17. Critical Velocity. . . . . . . . . . 51

18. Flow against Viscous Resistances . . 53

19. Steady Flow between Parallel Plates . . 51

20. Steady Flow through Circular Pipe . . . . . . . 5(>

21. Steady Flow through Circular Pipe, assuming Slip at Boundaries 58

x CONTENTS.

CHAPTER IV.

AKT. 1'AUK

22. Motion of Fluids . . 59

23. Equations of Motion for a Viscous Fluid . . (51

24. Application to Stream. Line Motion . . <><>

25. Effect of Heat Motion . . . . (58

26. Bernoulli's Theorem . . . . . . 69

27. Elementary Proof of Bernoulli's Theorem. .. .71

28. Application to Unsteady Motion . . . . 72

29. Experimental Verification of Bernoulli's Theorem .. .. 73

30. Venturi Meter . . 77

31. Sudden Enlargement of Section . . SI

32. Sudden Contraction of Area . . ss

33. Initiation and Stoppage of Motion . . . S9

34. Flow in Converging Passages Eadial Flow . . 92

35. Change of Pressure across a Stream Tube . . . . . . . 94

36. Vortex Motion Forced, Free and Compound Vortices . . . . 9(5

CHAPTER V.

37. Flow from a Small Orifice .. ..103

38. Determination of Coefficients of Velocity, Discharge, and Con-

traction . . 108

39. Equation of Momentum .. .. .. .. ..Ill

40. Borda's Mouthpiece .. .. .. .. ..112

41. Orifice in Flat Plate .. .,115

42. Bell-mouthed Orifice .. ..119

43. Velocity of Approach .. ..120

44. Time of Discharge from Small Orifices .. .121

45. Form of Effluent Streams . . . . . . . . . . 124

46. Large Orifices . . . . . . . . 127

47. Rectangular Orifice .. ..129

48. Circular Orifice . . . . . . 132

49. Submerged Orifice . . . . 134

50. Law of Comparison for Orifices . . . . 13(5

51. Notches and Weirs . . . . ... 137

52. Theoretical Formula for Flow over a Notch . 138

53. Submerged Weirs . . . . . . . . . . 1 54

54. Shape of Weir Sill 155

55. Eise in Surface Level produced by a Dam . . 159

56. Use of Weir as a Measuring Appliance . . . . . . 160

57. Time of Discharge through Orifices and Notches . . . . 1(52

CHAPTER VI.

58. Fluid Friction .. .. ..1(57

59. Resistance of Ships . . . . . . . . . . . . ..173

60. Propulsion of Ships Power Necessary Screw Propellers

Paddle Wheels 17!)

CONTENTS. xi

CHAPTER VII.

ART. PA(;K

01. Pipe Plow 185

62. Critical Velocity.. .. 190

63. Formulae for Pipe Flow Rational and Empirical. . . . 195

64. Flow in Eivetted Pipes .. .. .. 200

65. Values of / in Formula, h = -~^~ . - 202

A (J ftl

66. Accuracy of Determination of v . . ... -Oo

67. Mean Velocity and Distribution of Velocity in Pipe . 205

68. Measurement of Discharge . . . . . . 209

69. Relation between Diameter and Discharge .. .. .212

( Water Hammer in Pipes of Uniform. Bore 1 %) ,

( Rise in Pressure at Gradual Closing of a Valve j

CHAPTER VIII.

71. Pipe Line Losses Hydraulic Gradient .. .. 228

72. Losses at Valves Bends Elbows Tees, etc. . 231

73. Flow in Long Pipes . . . . . . . . . 241

74. Time of Discharge through Long Pipe Line . . . 242

75. Equivalent Diameter of Uniform Main . . 243

76. Branch Mains ...... . 244

77. Multiple Supply. ... . . . . 246

78. Flow along a Bye-Pass. . . . 247

79. Pipes Coupled in Parallel . . . . 248

80. Flow through Xozzles Conditions for Maximum Delivery of

Energy .... . . 250

81. Syphons . . . . 259

82. Inverted Syphons .... .... 264

CHAPTER IX.

83. Flow in an Open Channel . . . 267

84. Most suitable Form of Channel . . . . . . .277

85. General Equation of Flow in an Open Channel . . . . 287

86. Non-uniform Flow . . . . . . . . .291

87. Channel with Horizontal Bed .. .. .. 307

88. Effect of Bridge Piers, etc . . 308

89. Radial Flow over Horizontal Bed . . . . 309

90. Change of Level produced by Passage of Boat through Canal . . 310

91. Flow around River Bends . . . . r . 312

92. Distribution of Velocity in an Open Channel . 313

93. Distribution of Velocity along a Vertical . . . 316

94. Erosion of Channels . . . . . . . . . . . 320

95. Gauging of Flow in Rivers or Open Channels . 322

xii CONTENTS.

CHAPTER X.

A KT.

96. Impact of Jets on Fixed Vanes

97. Actual Force of Impact

98. Distribution of Pressure across a Jet

99. Hate near to Orifice of Nozzle Ball Xozzle

100. Impact on Moving Vanes

101. Graphical Construction for Pressure on Vane and for Centre of

Pressure

102. Compounding of Jets .

103. Jet Propulsion . .

10-L Hydraulic Mining

105. Resistance to Motion of Submerged Plane*

106. Rudder Action

107. Resistance to Motion of Submerged Bodies

SECTION III.

HYDRAULIC MACHINERY.

CHAPTER XI.

108. Hydraulic Prime Movers

109. Utilization of Water Powers '

110. Overshot Water Wheel

111. Breast Wheel ..

112. Sagebien Wheel

113. Undershot Wheel

114. Poncelet Wheel

115. Pelton Wheel Form Construction Form of Buckets

Xumber of Buckets Speed Regulation . . . . . . 39(>

CHAPTER XII.

116. Turbines Classification of . . 417

117. Impulse Turbines .. .. .. .. .. .. .. 419

118. Girard and Haenel " Limit " Turbine . . i21

119. Pressure Turbines Barker's Mill .. .. 42(5

120. Borda Turbine .. .. .. .... 431

121. Fourneyron Turbine . . . . .... 432

122. Jonvul Turbine .. 436

123. Suction Tube . . . . . . 4-i2

124. Francis Turbine .. 446

125. Thomson Vortex Turbine . . . . . . 456

126. Compound Turbine . . . . 46S

127. American Mixed Flow Turbine . . . . . . . 469

128. Governing of Turbine Plants Stand Pipes Relief Valves

Relays Gates and Connections . . .... 473

129. Design of Head and Tail-Races .. .. .. .. 485

CONTENTS. xiii

CHAPTER XIII.

ART.

130. General Considerations of Turbine Design . . . . 489

/ General Case of Inward Radial Plow Pressure Turbine \

131. Inward Radial Flow Turbine with Radial Vanes Limitations of > 492

( Theory

132. Losses in Turbine . . . . 508

133. Vane Thickness 513

134. Curvature of Vanes . . . . . . . . . . 515

135. Outward Radial Flow Pressure Turbine .. ..518

136. Axial Flow Pressure Turbine 519

137. Mixed Flow American Type . . 520

138. Impulse Wheel Girard Type . . 522

139. Centrifugal Action .. ..527

140. General Comparison of Impulse and Pressure Turbines . . . . 528

141. Stand Pipe Theory .. . . 529

142. Flywheel Effect of Rotors . . . . 532

CHAPTER XIV.

143. The Hydraulic Engine . . . . . . . . . 537

144. Theory of the Hydraulic Engine Port Areas . . . . . . 541

CHAPTER XV.

145. Pumping Machinery . . . . . . 547

146. The Scoop Wheel * .547

147. The Screw Pump . . . . 548

148. The Reciprocating Pump Types . . 549

149. Valves Leakage Slip . . . . . . ... 557

150. Displacement Curves . . . . . . . . . . . . . . 567

151. Variation of Pressure in Cylinder Coefficient of Discharge-

Separation or Cavitation . . . . . . . . 570

152. Rise in Pressure following Separation .. .. .. 579

153. Effect of Elasticity of Suction Column . . . . . . 583

1 54. Air Vessels on Suction Side .... . . 586

155. Air Vessels on Delivery Side ... . . '591

156. Summary .... . . .... 592

157. Air-charging Devices .... .. .. '596

158. Efficiency of Reciprocating Pumps .. .... 597

159. Positive Rotary Pumps . . k . . . . . . . . 597

CHAPTER XVI.

160. The Centrifugal Pump .. 600

161. Losses in the Centrifugal Pump Volute Chamber Vortex or

Whirlpool Chamber Guide Vanes . . . . . . . . 602

162. Theory of Action (510

xiv CONTENTS.

163. Pump with Inefficient Collecting Chamber . . . . . . 612

164. Pump with Whirlpool Chamber . . .621

165. Pump with Guide Yanes . . . . . . . . 623

166. Most suitable Peripheral Speed in Practice . . 624

167. Compound Multiple Chamber High-Lift Pumps .. .. 625

168. Speed at which Pumping commences . . . . 626

169. Size of Pump for given Discharge Similar Pumps . . . . 627

170. Suction and Delivery Pipes . . . . 628

171. Examples of Design .. ',. 630

172. Types of Pump .. .. 634

173. Balancing of End Thrust on Impeller Shaft . . (540

CHAPTEE XVII.

174. Water Hoisting from Mines . . . . . . . . . . . . 648

175. The Hydraulic Earn Types Theory ^-the Pearsall Earn Earn

for Air Compression . . . . . , . . . . . 649

176. The Jet Pump . . . . 661

177. The Injector Hydrant. . .. .. 666

178. The Air Lift Pump . . . . 668

179. !The Hydraulic Air Compressor .. .... 674

CHAPTEE XVIII.

180. Hydraulic Power Transmission .. .. .. .. .. 677

181. Accumulators .. .. .. .. .. 686

182. Intensifies .... . . .... 692

183. Friction of Leather Collars for Earns and Pistons Hemp

Packings . . . . . . , . . . 693

184. Water Meters . 695

CHAPTEE XIX.

185. Hydraulic Lifts and Hoists . . . . . . . . 704

186. The Hydraulic Jigger . . . . 711

187. Hydraulic Cranes . . . . . . 712

188. The Hydraulic Jack . . 715

189. The Hydraulic Press . . . . . . 717

190. The Hydraulic Forging Press . . . . 721

191. Hydraulic Eivetters .. ..723

192. Hydraulic Brakes and Buffer Stops .. .. ,'. 727

193. Hydraulic Dynamometers .. .. .. ... . . 735

APPENDIX ...... . . 745

INDEX . . 751

LIST OF SYMBOLS AS GENERALLY ADOPTED

THROUGHOUT THE BOOK.

Wlicre, for any reason, thin notation las been departed from, special notice

is given.

i- . . . . Linear velocity in feet per second.

P T .. .. Kelative

ir .. .. Tangential ,, ,, ,, I in case of a turbine or >

/' . . . Eadial ,, ,, ,, ( centrifugal pump. >

/ . . . Coefficient of friction (in pipe flow).

. . . . Angular velocity in radians per second.

r . . . . Eadius in feet.

Pipe diameters in feet. ^

Areas in square feet.

a . . . . )

/ . . . . Length in feet.

m . . . . Hydraulic mean depth.

/ . . . Slope of a channel.

Head in feet of water.

// . . . . i

j> . . . . Pressure usually in Ibs. per square foot.

II . . . . Weight of 1 cubic foot of water = 62*4 Ibs.

<l . . . . 32 - 2 feet per second per second.

p . . . . Density of water - H' -f- u.

Q . . . . Quantity in cubic feet per second.

fj. . . . . Coefficient of viscosity.

?? . . . . Efficiency.

I' Work done.

CORRIGENDA.

Page 14. Footnote. Substitute Proc. Roy. Soc.. Vol. 80. 1!>08. p. 114.

4."). Line 3,y> " three points not in the same straight line ''for ' two point;

60. Insert " incompressible " before " fluid," on line 18.

.. 90. Line S.jmt (~ a + A \ for ( * + A \

... 11)5.. Art. 63, line 3. After " Reynolds " Insert " and may be obtained."

., 400. On last line put plus sign for minus before /.' (r ) cos

a.

401. On top line insert the factor before (r w) (I - 7^ cos a).

OF THE

UNIVERSITY;?

OF < J

HYDKAULICS AND ITS

APPLICATIONS.

SECTION I.

CHAPTEE I.

Introductory Historical Jle*ume Physical Properties of Water Density Com-

pressibility Cohesion Adhesion Capillarity Surface Tension Viscosity.

INTRODUCTORY PHYSICAL PROPERTIES OF WATER.

ART. 1. HYDROMECHANICS.

.

THE science which deals with liquids at rest or in motion may

be divided into two branches : Hydrostatics, which deals with

the equilibrium of liquids at rest ; and Hydrodynamics, which

deals with the problems connected with their motion. The term

Hydraulics is usually broadly applied to that portion of the

latter branch which deals with the motion of water in so far as

this is of importance in the problems brought directly under the

notice of the engineer.

A knowledge of the fundamentals of Hydrostatics is however

so essential to a thorough grasp of the principles of Hydro-

dynamics, and is of such direct importance to the hydraulic

engineer, that a treatise on Hydraulics would not be complete

without some preliminary treatment of this branch of the

subject.

The origin of the science is of great antiquity, and no attempt

will be made to give a detailed historical resume of its growth.

Some few of the principles of Hydrostatics were enunciated by

H.A. B

2 HYDRAULICS AND ITS APPLICATIONS.

Archimedes (B.&.. 250) and it is a remarkable fact that for 1,800

years from this date until the time of Stevinus, Galileo, and

Torricelli practically no further progress was made.

The construction of the elaborate series of aqueducts and of

service pipes for supplying Rome with water indeed shows that

the Romans possessed some knowledge of the properties of water

when at rest and when in motion in pipes and open channels,

but we have no record that this knowledge was based on any

quantitative laws.

A treatise by Stevinus, written about 1585, would appear to

follow historically that of Archimedes. In this the method of

obtaining the pressure of a liquid on the sides and base of a

containing vessel was first demonstrated.

Galileo, in a treatise published in 1612, discussed the

Hydrostatic Paradox and also the flotation of bodies in

water.

Shortly afterwards Torricelli made an important investigation

into the behaviour of a jet when issuing vertically from an orifice,

while, since the middle of the seventeenth century, numerous

investigators have been at work deducing by experimental

observation and theoretical reasoning the laws governing the

various manners of motion of liquids, and applying these laws to

the development of the science of Hydraulics. Of these

experimentalists perhaps Mariotte, Bernoulli, and D'Alembert,

with Poiseuille, Darcy, and Bazin in France ; Rankine, Froude,

Osborne Reynolds and James Thomson in England ; Eytelwein,

Weisbach, and Hagen in Germany ; Venturi in Italy, with Francis

and Hamilton Smith in America, are most worthy of note.

In spite however of all the work which has been so ably

accomplished by these and other observers, Hydraulics cannot

yet be classed as an exact science. The laws governing many of

its phenomena are still imperfectly understood, and the difficulties

chiefly analytical to be overcome before all the disturbing

factors can be taken fully into account, are very great. In such

cases, experience, based on the results of experiment, forms

the only safe guide. In other cases, however, the deductions

of theory are found to be perfectly in accord with observed

phenomena, and an attempt will be made in the course of this

PHYSICAL PEOPEKTIES OF WATEE.

work to indicate to what extent our knowledge of the forces con-

trolling any phenomenon is sufficiently accurate and compre-

hensive to enable theory to be an exact guide, and where, on

the other hand, theory, based on insufficient data, is only useful

as indicating in what direction a true solution is to be found.

ART. 2. PHYSICAL PROPERTIES OF WATER.

Im its pure state water is an almost colourless, transparent,

odourless liquid and one of the best solvents to be found in

Nature. Its maximum density occurs at 4 C., or 39*1 F.,

and under atmospheric pressure it freezes at 32 F. and boils

at 212 F. The freezing point is lowered, and the boiling point

raised by an increase in pressure, the opposite being true of a

reduction of pressure. The specific gravity at maximum density

is unity, and the specific heat varies slightly with temperature,

increasing from TOGO at 32 F. to 1/013 at 212 F.

The latent heat of fusion of ice at 32 F. is about 142 B.T.U.,

while the latent heat of evaporation at 212 F. is 966'6

B.T.U.

Weight of Water. Authorities differ as to the precise value of

the weight at maximum density, the lowest value given being

about 62-379 Ibs. per cubic foot and the highest 62'425 Ibs. The

latter value that of Eankine is commonly adopted as being

most nearly correct. The following table, calculated from

Temp.

Fahr.

Weight per

cubic foot.

Temp.

Fahr.

Weight per

cubic foot.

Temp.

Fahr.

Weight per i

cubic foot.

Temp.

Fahr.

Weight per

cubic foot.

32

62-42

80

62-23

130

61-56 ;

180

60-55

40

62-42

90

62-13

140

61-37

190

60-32

50

62-41

100

62-02

150

61-18 (

200

60-07

60

62-37

110

61-89

160

60-98 I

210

59-82

70

62-31

120

61-74

170

60-77

Eankine's formula, gives the weight per cubic foot at different

temperatures. At 212 F. values by different experimenters

vary from 59'56 Ibs. to 59'84 Ibs. Above this temperature the

B 2

4 HYDBAULICS AND ITS APPLICATIONS.

exact values are not so well known and are unimportant to the

engineer. For the purpose of all calculations relating to

Hydraulics it is sufficiently accurate to take the weight per cubic

foot at 62'4 Ibs., more especially as the water with which the

engineer has to deal is never perfectly pure, but contains more

or less of the soluble salts. Unless otherwise stated, the above

value will be adopted throughout this treatise.

The density of sea water varies slightly with the locality, but

is about 1*026 times that of fresh water. Its weight, at the

temperatures commonly met with in practice, may be taken as

64'0 Ibs. per cubic foot.

Compressibility. Water is very slightly compressible, the

compressibility varying with the temperature and with the

amount of air in solution. When pure, the decrease in volume 6 V,

due to an increment in pressure 8 P, of one atmosphere, increases

from '000040 to "000051 as the temperature decreases from

212 F. to 35 F. (Grassi).

b P

This gives values of the bulk modulus K, which equals ^-p ,

~V

varying from 368,000 to 288,000 Ibs. per square inch under this

temperature variation, the modulus increasing with an increase

in temperature.

The value of K at 50 F. may be taken as approximately

300,000 Ibs. per square inch.

The compressibility is so slight that in all practical calculations

concerning water at rest or in a state of steady motion it may

be assumed to be an incompressible fluid. In certain important

phenomena, however, notably those involving a sudden initia-

tion or stoppage of motion, this compressibility becomes an

important, and often the predominating factor, and in the

treatment of such cases the above mean value of K will be

adopted.

At ordinary temperatures and pressures, water is capable of dis-

solving comparatively large volumes of air. As the temperature is

raised this is set free, and at atmospheric pressure a temperature of

180 F. is sufficiently high to liberate almost all the dissolved gases.

Any reduction in pressure also tends to the same end, and the

PHYSICAL PEOPEETIES OF WATEE. 5

hissing which is so often noticeable in jet pumps and injectors,

or where water is escaping at high velocities past the restricted

area of a valve seat, is due to the reduction of pressure and

subsequent liberation of bubbles of air, which occurs under these

circumstances.

In common with all other liquids water also possesses the

properties of Cohesion, Adhesion, and Viscosity.

ART. 3. COHESION

is that property of a liquid, or solid, which enables neigh-

bouring molecules to resist any stress of the nature of a tension.

Adhesion is that property which enables it to adhere to a solid

body with which it may be in contact. Thus a drop of water

exhibits cohesion in its hanging together, and adhesion in virtue

of its clinging to a solid body, the force of gravity being overcome

both by cohesion and by adhesion. Both phenomena are due to

molecular attraction, cohesion between neighbouring molecules

of the liquid, and adhesion between those of the solid and liquid.

A consideration of the molecular theory of matter indicates that

if a is the distance between any two molecules, their mutual

7

attractive force is approximately equal to 6 ; and it follows

that a rise in temperature, by increasing the molecular distance,