A Numerical Exploration of Transient Decay Mechanisms in Water Distribution Systems - Advances in Control and Automation of Water Systems - page 5

a- The independent variable contains non-positive values. The minimum value is .00.
The Logarithmic and Power models cannot be calculated.
b- The independent variable contains values of zero. The Inverse and S models cannot
be calculated. Regression Equation defined in stages (2-3-7-8) is meaningless. Stages
(1-4-5-6-9-10-11) are accepted, because their coefficients are meaningful:

Linear function \ =+

\ = +
\ =- +
\

pressure 6.062 .571Flow ,

Quadratic function pressure 6.216 - .365Flow

4

.468Flow ,

3

Cubic function pressure 6.239 .057Flow

2

.174Flow,

Compound function pressure = 1.089(1 + Flow) , n

n

= compoundin g period

(3)

Growth function \ =

\ =
\ =+

pressure 1.804(.085)

Flow / .05

,

Exponential function pressure 6.076e

FlowLn.085

,

Logitic function pressure 1 / (1 e

- Flow

) or pressure =+ .165 .918Flow

figure 1.1 Scatter diagram for Tests for Water Transmission Lines (Field Tests Model).

Assumption (2): p = f (V, T, L), V-velocity (flow) and T-time and L-distance, are
the most important variables.
Input data are in relation with water hammer condition. Regression software fits
the function curve (Figure 1.2-1.4) with regression analysis.

tABle 1.2 Model Summary and Parameter Estimates (Water hammer condition).

Model Un-standardized Coefficients Standardized Coefficients t Sig.

Std. Error Beta

1 (Constant) 28.762 29.73 - 0.967 0.346

flow 0.031 0.01 0.399 2.944 0.009

distance -0.005 0.001 -0.588 -4.356 0

time 0.731 0.464 0.117 1.574 0.133