The author solves analytically a boundary-value problem [cf. formulae (1)-(7), or (1), (2)', (3)-(7)] on 2-dimensional and 2-phase flow of incompressible fluids, when reservoir is extensive, dipping and plane, and when only one water injection well with constant injection rate or with constant pressure is penetrated into the reservoir, and when the pressure at each point on reservoir boundary is kept its initial value proportional to its depth [cf. Fig. 1].
The results obtained by this study are as follows:
1. velocity potential in injected water zone and oil zone [cf. formulae (12), (13), or (12)', (13)']
2. stream-function in those zones [cf. (15), (16), (15a), (16a), or (15)', (16)', (15a)', (16a)']
3. complex velocity potential in those zones [cf. (17), (18), or (17)', (18)']
4. pressure distribution in those zones [cf. (19), (20), (19a), (20a), or (19)', (20)', (19a)', (20a)']
5. time variation of injection well pressure when injection rate is constant [cf. (21), (21a)]
6.time variation of injection rate when injection well pressure is constant [cf. (21)', (21a)']
7. the fact that the form of water-oil interface is a generalized cardioid [cf. formulae (14), (14a), Fig. 2, or (14)', (14a)', Fig. 2']
8. influences on the form of time elapsed, angle of dip of oil reservoir, water injection rate or pressure-difference, mobilities and density-difference [cf. Fig. 3, 4, 5, 6, or Fig. 3', 4', 5', 6']
