Abstract
This study is a numerical and analytical investigation into the behavior of round orifices
(leaks) in pressurized oval and non-oval steel water pipes. Since ovality is known to induce
bending stresses in a pipe subjected to internal pressure, the overall aim of this study was
to determine whether pipe ovality contributes to an increase in leakage flow rate. This was
achieved by comparing the leakage behavior in round holes within oval and non-oval steel
pipes. The study derived a leakage equation from linear elastic theory, which incorporated
the bending stresses due to ovality. Following this, a regression leakage model based on
simulation data from finite element analysis was also developed. When collecting the FEM
data, several variables, namely the leak size, pressure, and wall thickness were varied. The
simulations were done on a model with a nominal size of 105.1 mm. The study was conservative
in variations of ovality (only up to 2% was considered), as it was assumed that
such ovality can exist even in non-buried pipes, paving the way for comparisons with other
studies. Thickness was varied between 3 mm and 4.92 mm, leak size was varied between 4
mm and 16 mm, and pressure between 0.1 MPa and 1.2 MPa. As ovality was the main focus
of this study, pressure area slopes (𝑚) and leakage exponents (𝑁1) for different ovalities were
investigated for different pipe wall thicknesses and leak sizes. It was observed that with an
increase in thickness, leakage exponents and pressure area slopes for both oval and non-oval
pipes decreased, primarily due to the reduction of stress around the leak opening. However,
it was noted that the oval pipe showed slightly higher values of leakage exponents and pressure
area slopes than the non-oval pipe. On the other hand, across different hole sizes, it
was observed that pressure area slope and leakage exponents increased with increase in hole
size, with oval pipes registering higher values. The differences between the oval and non-oval
pipes are attributed to the additional bending stresses induced by the ovality. The maximum
pressure-area slopes and leakage exponents observed for the oval and non-oval pipes with
respect to change in pipe wall thickness were 0.00208 mm2/m (0% ovality), 0.00264 mm2/m
(2% ovality) , 0.5018 (0% ovality), and 0.5023 (2% ovality). The maximum leakage exponents
and pressure-area slopes registered for the change in hole size were 0.00237 mm2/m
(0% ovality), 0.00293 mm2/m (0% ovality), 0.5012 (0% ovality), 0.5015 (2% ovality). These
results confirm that ovality can indeed affect leakage behavior, with more leakage likely to
occur in oval pipes. The analytical equation and the data-driven model were also compared
to other numerical studies and experimental data, demonstrating generally favorable agreement,
except for the experimental studies which registered negative pressure-area slopes.
Simulational studies were then conducted to assess the impact of the developed model on
v
total annual leakage. Here, 3 cases were considered, i.e., where ovality was completely 0%,
ovality was 0.038%, and the maximum ovality (2%). The case with 0% ovality produced
total annual leakage of 31770.69 m3 , compared to 31781.75 m3 (0.038%) and 31789.66 m3
(2%). These results were only considered for a single leak, and the situation can be worse
for multiple leaks running across several detection periods.
Overall, the study provides valuable insights into the behavior of underground water pipes
across different parameter combinations, facilitating a greater comprehension of leakage behavior
in steel pipes and contributing to the management of non-revenue water. Future
research might consider investigating larger ovalities and pipe sizes than those in this research.