Water Hammer in Pipe-Line Systems

Abstract

1. Water Hammer. The origin of water hammer. Physical principles. Actual cases. Causes of water hammer. Examples of water hammer. 2. Basic Equations Derivation. Scope of application. 3. Solution of the Basic Equations. Methods of solution. Application of the method of characteristics. Schematization of the pipe-line system. 4. Parameters of the Basic Equations. Velocity of propagation of the pressure wave. Pipe-line diameter. Density of the liquid. Pressure losses due to friction. Velocity of the liquid. Solid particles in the pipe-line. Gas in the pipe-line. Pressure in the pipe-line. Cavitation. 5. Damping Devices. Junction without a damping device. Constant pressure. Reservoir. Air chamber. Surge tank. Overflow. Air inlet valve. Cavitation. Integrated damping device. Pressure. Discharge. 6. Pressure Devices. Attachment without a pressure device. Closed pipe-line. Local loss. Control valve. Non-return valve flap. Butterfly valve. Condenser. Pump. Turbine with fixed characteristics. Turbine with variable characteristics. Turbine controlled by a governor. 7. Calculation of Water Hammer. Computer application. Preparation. Input data. Data input and output of the results. Solution for the sections. Solution for the junctions. The initial state. Calculations for the damping devices. Calculation for the pressure devices. Calculation procedure. Iterative solution for the junctions. Checking whether a steady state was attained. Maximum and minimum values. Submission for several calculations. 8. Calculation of the Steady State. Abridged calculation of the steady state. Modification of the pipe-line sections. Modification of the damping devices. Modification of the pressure devices. Submitting the calculation. 9. Input Data File. Name of the calculation. Sections. Junctions. Parameters. Type of calculation. Graphical and numerical outputs. Subtitle of the calculation. 10. WTHD Program for Creating the Input Data File. Starting work with the WTHD program. Adding a data line to the end of the file. Inserting a data line into the file. Deleting a data line from the file. Modifying a data line. Adding a further data line. Formal checking of the file. Listing of a data file. Plotting of fuctions. Terminating the WTHD program. 11. Output of the Results. Main output. Graphical output. Numerical output. WRHG program for plotting the numerical output. 12. Reduction of Water Hammer. Adjustment regime of a valve. Pump. Surge tank. Air chamber. Other methods of protection. 13. WTHM Program for the Calculation of Water Hammer. Basic layout of the program. The main program. Subprograms. Errors in the calculation. Denotation of the variables. 14. Examples of the Calculation of Water Hammer. Abrupt closing of a pipe-line without considering the effect of pressure losses due to friction. Abrupt closing of a pipe-line with the effect of pressure losses taken into account. Control valves in the delivery pipe-line of a pump. (Part Contents).