The distribution of chilled water flow rate in terminal unit is a major factor used to evaluate the performance of central air conditioning unit. In this work, a theoretical chilled water distribution in the terminal units has been studied to predict the optimum heat performance of terminal unit. The central Air-conditioning unit model consists of cooling/ heating coil (three units), chilled water source (chiller), three-way and two-way valve with bypass, piping network, and pump. The term of optimization in terminal unit ingredient has two categories, the first is the uniform of the water flow rate representing in statically permanents standard deviation (minimum value) and the second category is the maximum heat transfer rate from all terminal units. The hydraulic and energy equations governing the performance of unit solved with the aid of FORTRAN code with considering the following parameters: total water flow rate, chilled water supply temperature, and variable valve opening. It was found that the optimum solution of three-way valve case at 8°C water supply temperature, 0.12 kg/s total water flow rate and valve opening order (valve 1: 100%, valve 2: 100% and valve 3: 75%) with total heat rate (987.92 Watt) and standard deviation (1.181E-3). Also, for the two-way valve case the results showed that the optimum condition at 8°C water supply temperature, 0.12 kg/s total water flow rate and valve opening order (valve 1: 75%, valve 2: 75% and valve 3: 50%) with total heat rate and standard deviation (717Watt) and (5.69E-4) respectively.