Design of optimal operation and control of a run-of-river hydro power plant depends on good models for the elements of the plant. River reaches are often considered to be shallow channels with free surface flow. A typical model for such reaches thus use the Saint Venant model, which is a 1D model based on the mass and momentum balances. This combination of free surface and momentum balance makes the problem numerically challenging to solve. Here, the finite volume method with staggered grid is used to illustrate the dynamics of the river upstream from the Grønvollfoss run-of-river power plant in Telemark, Norway, operated by Skagerak Energi. A model of the same river in the Grønvollfoss power plant has been studied previously, but here the geometry of the river is changed due to new information from Skagerak Energi. The numerical scheme for solving the model has been further developed. In addition, the behavior of the dynamic model is compared to data from experiments, carried out on the Grønvollfoss run-of-river power plant. The essence of the experiments is to consider the time taken from an increase in the input volumetric flow, to a measured change in level in front of the dam at Grønvollfoss. The model is manually tuned by changing the Strickler friction factor, the river length and the type of river slope/width (constant/varying) in order to fit the water level ahead of the Grønvollfoss dam from experimental data. Least squares model fitting is also used for the model with the constant slope and width of the river and this model shows good fitting after the manual tuning. The results of the improved model (numerically, tuned to experiments), is a model that can be further used for control synthesis and analysis.