The unsteady flow by pumping up in unconfined Aquifer is exprssed as in Eq, (1).
Where k: hydraulic conductivity, β: effective porocity, h the water level at a distance r from the center of pumping well, t: time.
The existing solutions are almost approximative ones because Eq. (1) cannot be solve dexactly. And the radius of well is negrected in these ones.
In this paper, the authors chage the Eq. (1) into the non-ditnensional simultaneous ordinary differential equation, and calculate numerically by means of Runge-Kutta method. In this case. the numerical calculation is done under the condition that the radius of well is finite. The calculated value is described as a diagram (this is called the equidischarge type-curves diagram), and a graphical method which calculate formation constants is proposed (this is called the equi-discharge type-curves method). The equidischarge type-curves method is compared With existing methods and discussed using datas by model tests and field tests. Using this equi-discharge type-curves method, analysis become simple, and more uniform result is obtained in comparison with the resultusing existing methods.

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This paper describes the applicability of the set of equations exprssing free-surfacegroundwater profiles over an impermeable layer.
The theoretical steady free-surface-groundwater profiles are given by equation (5), (6), (7) and (10). The unsteady state profile is given by the finite difference equation (17) which was derived from equation (3). The steps in equation (17) must satisfy condition (23).
The theoretical equations for free-surface-groundwater profiles satisfied the experimental data which were obtained by using a model sand slope for Re< 4 and y< 0.1. Re is Reynolds number and y is an average hydraulic gradient by equation (26).

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