This is a static model of a flow fuse (excess flow valve). The valve is normally fully open. When the pressure drop across the valve exceeds pMin (indicating high flow rate), the valve starts to close. At a pressure drop of pMax, the valve is fully closed. When the flow drops and the pressure drop decreases, the valve reopens automatically.

Since the pressure drop across a turbulent orifice is proportional to the square of the flow rate, the closing pressure thresholds correspond to flow rate thresholds.

The valve element has second-order dynamics characterized by mass m, spring stiffness k, and damping d. These determine the natural frequency ω_n = √(k/m) and damping ratio ζ = d/(2√(km)). In a hydraulic ram, these correspond to the weight and inertia of the clack valve.

Limitations

This model does not contain lumped volumes, so it does not integrate the flow and compute the pressure at the ports.