The problem of a potential flow discharge through a two-dimensional horizontal duct under the influence of gravitation is examined by the method of hodograph transformation. The stream function is considered and established in the hodograph plane, and the solution in the physical plane is established through additional integrations. The unknown boundary functions of the free jet must be determined as part of the solution. The initial pressure level and the discharge characteristics between the total head and the flow rate, have been established. Results are compared with those obtained previously by other method.

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