The Piloted Check Valve component is a check valve with a pilot pressure that can be used to assist in opening or closing the valve.

The valve orifice area is assumed to be a piecewise linear function of the pressure difference between port A and port B.

Based on the orifice area, the pressure vs. flow rate relationship is calculated by the formulation used in the Orifice component.

The boolean parameters Use volume A and Use volume B, when true, add optional volumes $V_A$  and $V_B$ to ports A and B, respectively. See Port Volumes for details.

If two orifices or valves are connected, enabling a volume at the common port reduces the the stiffness of the system and improves the solvability.

$\{\begin{array}{cc}\left\{A_{\mathrm{cs}}\=A_i\,A_i\=A_t\right\}& \mathrm{Exact}\\ \left\{A_{\mathrm{cs}}\=\min \left(A_{\mathrm{open}}\,\max \left(A_{\mathrm{close}}\,A_i\right)\right)\,t_c\frac{\mathrm{d}{A}_i}{\mathrm{d}t}\+A_i\=A_t\right\}& \mathrm{otherwise}\end{array}$

$A_t\&equals;\{\begin{array}{cc}{A}_{\mathrm{close}}& p_{\mathrm{tot}}\le p_{\mathrm{close}}\\ A_{\mathrm{close}}\&plus;\left(p_{\mathrm{tot}}-p_{\mathrm{close}}\right)\frac{A_{\mathrm{open}}-A_{\mathrm{close}}}{p_{\mathrm{open}}-p_{\mathrm{close}}}& p_{\mathrm{tot}}<p_{\mathrm{open}}\\ A_{\mathrm{open}}& \mathrm{otherwise}\end{array}$

$V_{f_A}\&equals;\{\begin{array}{cc}\mathrm{Va}\left(1\&plus;\frac{p_A}{\mathrm{El}}\right)& \mathrm{useVolumeA}\\ 0& \mathrm{otherwise}\end{array}{V}_{f_B}\&equals;\{\begin{array}{cc}\mathrm{Vb}\left(1\&plus;\frac{p_B}{\mathrm{El}}\right)& \mathrm{useVolumeB}\\ 0& \mathrm{otherwise}\end{array}$

$p\&equals;p_A-p_B$

$p_{\mathrm{tot}}\&equals;p\&plus;\{\begin{array}{cc}{k}_p{p}_C& \mathrm{dir}\&equals;1\\ -k_p{p}_C& \mathrm{otherwise}\end{array}$

$q_C\&equals;0$

$q\&equals;q_A-q_{V_A}$

$q_{V_A}\&equals;\{\begin{array}{cc}\frac{\mathrm{d}{V}_{f_A}}{\mathrm{d}t}& \mathrm{useVolumeA}\\ 0& \mathrm{otherwise}\end{array}{q}_{V_B}\&equals;\{\begin{array}{cc}\frac{\mathrm{d}{V}_{f_B}}{\mathrm{d}t}& \mathrm{useVolumeB}\\ 0& \mathrm{otherwise}\end{array}$

$q_A\&plus;q_B-q_{V_A}-q_{V_B}\&equals;0$