Abstract. This paper develops a novel mathematical formulation for geothermal well flow. Non-isothermal flow would implicate the effectiveness of gravity as a body force term regulated by viscosity and density as well. Consequently it is a critical concept in practice that a dome-shaped water head surface would be present in its equilibrium-state water potential, as a proper observation needed to understand geothermal flow fields. Tabulation and formula are compiled on water density and viscosity as a function of temperatures and pressures to facilitate calculations. The derived formulas were applied to the field study site in a deep fault zone at a geothermal field in coastal Guangdong province, China, based on observations from a thousand-meter-depth borehole drilling project. The deep fault is unique in having a steep plane that emerges at the ground surface, and constitutes fast flow path for deep thermal water up to 115 °C and static water pressure up to 10 MPa at the borehole bottom. The fault is conceptualized as an inclined thin aquifer, and formula are derived for thermal outflows for the sloped aquifer to quantify the flow in the fault plane. Results showed that the deep fault has permeability equivalent to clean sands and lower end of unconsolidated gravels. Deep faults could provide useful information on pathways of preferential fluid flows. The deep fault study has several implications in deep geothermal environments and pressure characterizations, regional groundwater circulation limits, and pressure wave propagations in earthquake prediction in the deep crust.