vi Contents
3.3.1.1 Gauss-Siedel iterative method
for solution of linear algebraic
system of equations 33
3.3.1.2 Approximation of boundary conditions 34
3.3.2 Solution of a parabolic partial differential
equation (diffusion equation) 39
3.3.2.1 Forward in time, central in space
(FTCS) numerical scheme 39
3.3.2.2 Crank-Nicolson numerical scheme 41
3.3.3 Solution of a hyperbolic partial
differential equation (wave equation) 45
3.3.3.1 Euler’s unstable numerical scheme 46
3.3.3.2 Godunov’s numerical scheme 47
3.3.3.3 Lax numerical scheme 50
3.3.3.4 Fromm’s numerical scheme 51
3.3.3.5 Total variation diminishing
(TVD) scheme 52
4 Flow in pressurized conduits
57
4.1 Fundamentals of pipe flow 57
4.2 Pipe network 59
4.2.1 Continuity (junction) equation 60
4.2.2 Energy (loop) equation 60
4.2.3 Hardy Cross method 62
4.3 Unsteady flow in a closed conduit 67
4.3.1 Continuity equation for water hammer 68
4.3.2 Momentum equation for water hammer 70
4.3.3 Linearization of water hammer equations 71
4.3.4 Numerical treatment of water hammer equations 71
4.3.4.1 Initial conditions 72
4.3.4.2 Boundary conditions 72
4.3.4.3 Numerical algorithm 72
5 Free surface flows
79
5.1 Quasi-horizontal free surface flows 79
5.2 One-dimensional open channel flow 79
5.2.1 Steady-state gradually varied non-uniform flow 81
5.2.1.1 Newton-Raphson method
for estimation of the normal
and critical depths 83
5.2.1.2 Water surface profiles 84