With the rapid development and progress and the urbanization of human society, the demand for water of human activity is increasing. In the development of human society, with the climate changing and human activities increasing, water shortages have become increasingly prominent. The amount of water in some areas cannot be guaranteed, as well as a sharp deterioration in water quality. With the acceleration of urbanization, urban water demand is increasing. The water resources in the natural water cycle which are supplied for the city are not enough. Thus, in various urban water supply and water diversion projects, water is transported to the city, with the purpose of supplying water for the city production and life. Water cycle has also evolved from the original natural water cycle to dualistic nature-social water cycle. The dualistic water cycle theory indicates a new direction for the development of hydrology and water resources disciplines. So far there is still no uniform mathematical formula that can accurately describe the dualistic water cycle. In this study, we try to explore the mathematical and physical foundation of dualistic water cycle. We focused on the cities and did the in-depth analysis of the interference and driving principle of the socio-economic water demand on the water cycle. By analogy in physics Maxwell equations, the urban water demand field-the concept of water field was preliminary defined. According to the concept of electric charge, we define the water charge as the water requirement intensity. In the progressive development of the city, the city is in the analogy of a point electric charge in electric field. The electric field is formed by the point electric charge, while the water demand field is formed by the urban water demand. Point charge electric field can be superimposed over each other, so the electric field strength is also superimposed. Also, the water field strength of each cities which are close can be superimposed, and the city group will attract the water resources more far from their location, for example, the South-North water conversion project. And the formulas for calculating the city water field intensity were proposed. We also defined the constant in the formulas. This study took 22 major cities in the Haihe River Basin as an example, the water demands of every city are consider the city water charge. And the Haihe River Basin water field strength was quantitative described by applying the water field strength calculation formulas, and the trends in water flow were analyzed. The results showed that the water field strength formulas can describe the driving force and the mobility trend of urban water resources. Through the preliminary application, with the distribution of water field, the water cycle of social trends and the direction of water flow in the Haihe River Basin can be more accurately and effectively described. Meanwhile, using the field strength calculation formulas, the water field strength of city can be calculated, which represents the attracting strength of the city for the water resources around the city.