The flow of water over an obstacle is a fundamental problem in fluid mechanics.
Transcritical flow means the wave phenomenon near the exact criticality. The transcriti-
cal flow cannot be handled by linear solutions as the energy is unable to propagate away
from the obstacle. Thus, it is important to carry out a study to identify suitable model
to analyse the transcritical flow. The aim of this study is to analyse the transcritical
flow over a bump as localized obstacles where the bump consequently generates upstream
and downstream flows. Nonlinear shallow water forced Korteweg-de Vries (fKdV) model
is used to analyse the flow over the bump. This theoretical model, containing forcing
functions represents bottom topography is considered as the simplified model to describe
water flows over a bump. The effect of water dispersion over the forcing region is in-
vestigated using the fKdV model. Homotopy Analysis Method (HAM) is used to solve
this theoretical fKdV model. The HAM solution which is chosen with a special choice
of }-value describes the physical flow of waves and the significance of dispersion over a
bump is elaborated.