Heavy-duty hydraulic manipulators exhibit high robustness and an impressive power-to-weight ratio, enabling their application to execute complex and demanding tasks. Evaluating velocity performance is crucial for successful task performance, as it informs trajectory planning, configuration selection, and design optimization. However, assessing the velocity performance of hydraulic manipulators is challenging due to flow coupling between joints, asymmetric actuators, and implicit constraints introduced by complex higher order dynamics. In this article, a flow manipulability polytope is proposed for evaluating hydraulic manipulators. Flow constraints are analyzed and established as linear constraint inequalities in a quasi-steady state. The implicit constraints are avoided by simplifying the dynamic model, and the impact of gravity load variations on the constraints is considered. The proposed method is employed to identify the optimal position in the workspace of the hydraulic manipulator. The optimal position, compared with that obtained by the manipulability ellipsoid, demonstrates superior velocity performance. The average flow is reduced by 11.25%, the pressure fluctuation is reduced by 19.75%, and the maximum joint error is reduced by 35.23%.