Water hammer in pipe-line systems

Assumptions 22, 23, 26, 28, 37, 40, 47, 127. 129 Device 47 Blades action 119, 148 guide 115, 148, 327 Bubbles 62 Cavitation 40, 66, 77, 96, 139, 306 Characteristic method 45, 127 pump 85, 102, l7Y, 271, 306, 313, 316 moment 103, 144, 181 motor 103, 145. 182. 316 pressure 102, 180, 273 invariable 106, 145. 179, 181 variable 108, 145, 146, 187, 321. 327 turbine 85, 180. 181 actual 109 interpolation 110, 321, 327 model 107, 108, 187, 321, 327 valve 85, 91, 178. 185, 271, 279 Computer application 120, 216, 226, 234 Conditions initial 127. 133, 149, 250 steady state 43, 133, 151, 154, 258 Data 121, 125, 247 input 121, 125, 163, 216 graphical output 210 junction 165 name 0 1 calculation 163 numerical output 210 parameters 166 section 165 subtitle 215 type of calculation 160, 208 output 125, 223, 250, 258 Density 37, 49, 55, 57, 62, 77, 167 damping 47, 68, 120, 135, 174 air chamber 70, 136, 174, 232, 301 air inlet valve 75, 138, 174, 233, 306 cavitation 77, 139, 174, 306 constant pressure 68, 135, 250 discharge 86, 141, 175, 283 integrated device 79, 139, 174, 316, 321 modification 156 overtlow 73, 137, 174, 306, 3 16 pressure 84, 140, 175, 279, 294, 3 10, 3 I3 reservoir 69, 135, 174, 290 surge tank 72, 137, 174, 231 without damping device 68, 135, 258 pressure 47, 89, 120, 141, 178 butterfly valve 93, 143, 183, 316 closed pipe-line 89, 141 condenser 98, 143, 183, 316 control valve 32, 91, 142, 178, 185, 229, 258, 271, 283 local loss 90, 142, 178, 271, 306 modification 157 non-return flap valve 93, 142, 306 pump 32, 86, 102, 144, 178, 230, 271, 290, turbine controlled by governor 33, 113, 306, 313, 316 146, 193. 327 action blades 119, 204 guide blades 115, 204, 327 178 145, 187, 321 turbine with fixed characteristics 106, 145, turbine with variable characteristics 108, without pressure device 89, 141, 250 Diameter aperture 75, 77, 139, 305 butterfly valve 94 control valve 91 3 59 Index pipe-line 37, 54 pump 109 turbine 109 admissible 145, 150, 151, 155, 158, 160, 167 Differences Direction of section 47, 121, 165 Discharge 68, 86, 127, 141, 165 Diskette 120, 216, 352 Elevation 37, 258 Equations of water hammer 22, 23, 26, 37, 127 derivation 37 continuity 39 motion 37 linearisation 43, 127, 129, 135, 141, 150 methods of solution 43 parameters 37, 49 density of the liquid 49, 55, 57, 62 pipe-line diameter 54 pressure losses due to friction 55, 127, 155 velocity of pressure waves 49, 127, 155 scope of application 40 solution 43, 127 accuracy 48, 150, 151, 160 method of characteristics 45, 127, 149 methods 43 discharge 127 pressure 37, 65 velocity of liquid 37, 57 variables 37 Errors in calculation 240, 249 Examples 32, 247 actual 32, 279, 306, 310, 313, 316, 321, 327 calculations 247 abrupt closing 250, 258 air chamber 301 butterfly valve 316 cavitation 306 characteristics 279, 313, 316, 321, 327 condenser 306, 316 control valves 258, 271, 279 discharge 283, 310 electric motor 316 governor-controlled turbine 327 integrated damping device 316, 321, 327 local losses 271, 294, 306 non-return flap valve 306 overflow 306, 316 periodic variations 294 pipe-line network 290 pressure 279, 283, 294, 310, 313 pump 271, 290, 301, 306, 316 reservoir 290 steady state 258, 271, 290, 327 turbine with variable characteristics 321 valve control regime 271, 283 File 120, 163, 352 input 121, 163, 216, 247, 352 graphical and numerical outputs 210, 251, junctions 165, 251 name of calculation 163, 250 parameters 166 255 accuracy of calculation 167, 321 control valve - alternative method 185, damping devices 174 governor-controlled turbine 193, 327 pressure devices 178 time interval of printing 167, 251, 295 turbine with variable characteristic 187, 27 1 32 1 sections 165, 251 subtitle 215, 259 type of calculation 208, 258 graphical 210, 225, 255, 262, 268, 277 main 210, 223, 252, 264, 274, 293, 296 numerical 210, 226, 256, 286 output 223 Gas 62 Governor 113, 146, 193, 327 Grid of characteristics 127 Interval calculation 123, 127, 149, 155, 162, 210, 251 printing 124, 167, 208, 210 Iteration 130, 150, 208 Junction 47, 165, 210 number 47, 121 solution 129 iterative 130, 150 Liquid 40, 55, 57, 62, 66 compressible 23, 26, 37 incompressible 22 Modulus of elasticity 50 bulk 49, 58, 62 360 Index Moment inertial butterfly valvc 96, 316 motor 105, 306 pump 105, 144 turbine 113, 146, 193, 327 butterfly valve 95, 316 generator 114, 144, 146, 182, 193,321, 327 motor 103, 144, 182, 316 pump 103, 144, 181, 306, 316 torsional Momentum 22 Particles 57 concentration 58 settled 60 Period 26, 32, 176, 258, 294 Pipe-linc 40, 47 closing 32. 86, 271, 283, 310 abrupt 23, 86, 250. 258 linear 22, 26, 86 diameter 37. 54 expansion bends 51 length 47. 128, 155, 165, 251, 252 modulus of elasticity 50 non-circular 53, 54 scction modification 127, 155 support conditions 51 system 47 thick-walled 52 reference 37, 65, 121, 250, 258 schematisation 47, 120, 247 Plane Poisson’s ratio 51 Pressure 37, 65, 84 absolute 65. 70, 75, 77, 82, 121, 136, 138, 303 actual 37, 65, 121, 263 atmospheric 65, 76, 77, 138 converted 37, 68, 84, 127, 129, 140 initial 133, 149, 251 losses 37, 55, 90, 91, 128, 142 slow variations 26. 43 wave 23, 26, 40, 49. 155 zero 121, 250 deleting data lines 218 inserting data lines 217 listing data files 219 modifying data lines 218 plotting of functions 220 starting work 216 terminating the WTHD program 222 put 120,226, 352 WTHG for plotting the numerical out- WTHM for the calculation of water hammer 120, 125, 153, 234, 352 basic layout 234 denotation of variables 243 main program 234 subprograms 238, 333 errors 240 Reduction of water hammer 229 adjustment regime of a valve 229, 283 air chamber 232, 301 other methods 232 pump 230 surge tank 231 References 353, 356 Roughness 55 Section 47, 165, 210 direction 47, 121, 165 length 47, 128, 155 modification 47, 128, 155 number 47, 121 parameters 47, 165 solution 127 Sediment 60 State initial 133, 135, 141, 149, 250 steady 43, 133, 151, 154 calculation 159, 208 checking 151, 155, 156, 157 abridged calculation 159, 208 several calculations 152, 208 Submission Subprograms 238, 333 Symbols 13, 243 Thickness of pipe-line wall 50 Time 37, 127, 149, 161, 210, 260 Type of calculation 160, 208 Program 120, 333, 352 WTHD for creating the input data file 120, 163, 216, 352 adding data files 219 adding data lines 217 Values checking data files 219 maximum 151, 254, 256, 257, 300 361 Index minimum 151, 254, 256, 257, 300 air inlet 75, 138, 174, 306 butterfly 93, 143, 183, 316 control 32, 91, 142, 178, 250, 258, 271, 283 liquid 37, 57 mean cross-sectional 38 pressure wave 24,37,40,49,62, 127,155, 160, 165, 2 10, 260, 290 profile 57 Valve Velocity Viscosity 37, 47, 55, 127, 155, 165, 258, 312 Water hammer 21, 28, 247 actual cases 28, 32, 279, 306, 310, 312, 313, basic equations 37, 127 calculation 22, 23, 26, 43, 120, 125, 149, 154 abridged 154. 258 submission 159 time interval of calculation 161 velocity of pressure waves 160 316, 327 computer application 120 damping devices 68, 135, 156, 174 examples 247 initial state 133, 135, 141, 149, 154 input 121, 125, 159, 163, 216 junctions 47, 129, 150, 165 output 125, 208, 210, 223 preparation 120 pressure devices 89, 141, 150, 157, 178 procedure 149 sections 47, 127, 149, 165 several 152, 208 causes 30 estimating 21, 22, 23, 26 examples 32, 247 measurement 32 methods of solution 43 origin 21, 30 physical principles 22 reduction 229 characteristics 45, 127, 149, 150, 154 362