<p>Fluid-powered hose-type robots offer innovative potential for diverse applications. However, existing research lacks a comprehensive modeling of these systems, hindering accurate representation of their dynamics. This study addresses this gap by aiming to develop a fluid-based model for hose-type robots. Our approach involves leveraging quaternions as generalized coordinates and formulating kinematic constraints governing robot motion. We utilize the Reynolds transport theorem for a control volume analysis to delineate fluid-induced forces and moments. Additionally, structural aspects, including stiffness and damping effects, are integrated into the model. By synthesizing dynamic equations and kinematic constraints, we derive a set of differential-algebraic equations, eventually reduced to ordinary differential equations solely reliant on quaternions. This modeling framework is expected to significantly advance control system design and elucidate the complex behaviors of these fluid-driven robots.</p>