We propose a sensorimotor dynamical system model for pouring unknown liquids. With our system, a robot holds and shakes a bottle to estimate the characteristics of the contained liquid, such as viscosity and fill level, without calculating to determine their parameters. Next, the robot pours a specified amount of the liquid into another container. The system needs to integrate information on the robot's actions, the liquids, the container, and the surrounding environment to perform the estimation and execute a continuous pouring motion using the same model. We use deep neural networks (DNN) to construct the system. The DNN model repeats prediction and execution of the actions to be taken in the next time step based on the input sensorimotor data, including camera images, force sensor data, and joint angles. At the same time, the DNN model acquires liquid characteristics in the internal state. We confirmed that the DNN model can control the robot to pour a desired amount of liquid with unknown viscosity and fill level.