List of symbols

Symbol Name of the symbol Unit
$A$cross-sectional area of the conduit$\mathrm{m^2}$
$A_1$minimum cross-sectional area between upstream face of the gate and upstream wall of the gate chamber$\mathrm{mm^2}$
$A_2$cross-sectional area of the contracted jet issuing from the gap between the downstream face of the gate and the downstream wall of the gate chamber$\mathrm{mm^2}$
$A_s$area of the horizontal projection of the top seal$\mathrm{m^2}$
$A_{air-pipe}$the flow area of the aerated pipeline$\mathrm{m^2}$
$A_{air}$the flow area of the aerated hole$\mathrm{m^2}$
$B$width of the gate$\mathrm{mm}$
$C_c$coefficient of contraction$\mathrm{ }$
$F_c$Froude number$\mathrm{ }$
$H$total head in the reservoir$\mathrm{m}$
$H_L$loss of pressure on the gate$\mathrm{m}$
$H_v$pressure on the gate$\mathrm{m}$
$K_B$coefficient $K_B$ $\mathrm{ }$
$K_Q$flow coefficient$\mathrm{ }$
$K_T$coefficient $K_T$ $\mathrm{ }$
$K_{Qmax}$max flow coefficient$\mathrm{ }$
$L$pipe length behind the gate$\mathrm{m}$
$P$downpull force$\mathrm{kN}$
$P_1$downpull resulting from the difference between the pressures acting on the top and bottom surfaces of the gate$\mathrm{kN}$
$P_2$downpull resulting from the pressure differential acting on the horizontal protrusions of the gate$\mathrm{kN}$
$P_3$downpull resulting from the lip$\mathrm{kN}$
$P_T$saturated vapor pressure$\mathrm{Pa}$
$P_{u}$under-pressure behind the gate$\mathrm{m}$
$Q$flow of water before the gate$\mathrm{m^3/s}$
$Q_p$relative flow$\mathrm{ }$
$Q_{air}$air flow$\mathrm{m^3/s}$
$Q_{max}$flow$\mathrm{m^3/s}$
$T$the water temperature$\mathrm{°C}$
$W$force on gate$\mathrm{kN}$
$a_1$width of clearance between upstream face of the gate and upstream wall of the gate chamber$\mathrm{mm}$
$a_2$width of clearance between the downstream face of the gate and the downstream wall of the gate chamber$\mathrm{mm}$
$b$clear width of the conduit at the gate section$\mathrm{mm}$
$c_{ef}$effective closing time factor$\mathrm{ }$
$d$gate thickness$\mathrm{mm}$
$d^´$thickness of the skinplate$\mathrm{mm}$
$e$projection of the skinplate$\mathrm{mm}$
$e/d$ratio $e/d$ $\mathrm{ }$
$f_r$reduced free flow area in the throttle control system$\mathrm{ }$
$f_{air}$coefficient of under-pressure of aerated hole$\mathrm{ }$
$g$gravitational acceleration$\mathrm{m/s^2}$
$h$gate axis position to sea level$\mathrm{m}$
$h_c$depth of water at vena contracta$\mathrm{m}$
$p$pressure parameter$\mathrm{ }$
$p_{air}$under-pressure in the aerated pipeline$\mathrm{Pa}$
$p_{a}$atmospheric pressure$\mathrm{Pa}$
$r$radius of curvature for the rounding of the gate lip$\mathrm{mm}$
$s$gate opening$\mathrm{mm}$
$s/s_0$gate position$\mathrm{ }$
$s_0$conduit height immediately upstream from the gate$\mathrm{mm}$
$s_s$gate sealing height$\mathrm{mm}$
$t$closing time$\mathrm{s}$
$v$water velocity before the gate$\mathrm{m/s}$
$v_j$velocity in the contracted jet issuing from underneath the gate$\mathrm{m/s}$
$v_{air}$air velocity$\mathrm{m/s}$
$v_{max}$velocity before the gate$\mathrm{m/s}$
$ΔP$water hammer$\mathrm{m}$
$Δ_h$theoretical pressure in the gate at full opening$\mathrm{m}$
$β$aerated coefficient$\mathrm{ }$
$ζ$loss coefficient$\mathrm{ }$
$θ$angle of inclination of the bottom surface of the gate$\mathrm{°}$
$ρ$density$\mathrm{kg/m^3}$
$ρ_{air}$air density$\mathrm{kg/m^3}$
$σ$cavitation number$\mathrm{ }$