## Total static head

It consists basically of two parts:
1. The pressure difference between discharge side and suction side tank. It is zero for open tanks and closed circulation systems.
2. The height difference between the liquid levels of discharge side and suction side tanks respective the system inlet and outlet. It is zero for closed circulation systems.
This means for circulation systems the static head is always zero, pin, pout = pressures on suction respectively discharge liquid levels ρ = fluid density g = gravity (9.81 m/s2) Hgeo = static height difference between suction and discharge liquid levels

## Calculating the System H-Q Curve

The required pumping head in a branchless pipeline is determined from BERNOULLI’s equation for one-dimensional, stationary flow of incompressible fluids: pin, pout = pressures on suction respectively discharge liquid levels ρ = fluid density g = gravity (9.81 m/s2) Hgeo = static height difference between suction and discharge liquid levels Hl,tot = total pipe friction loss between inlet and outlet areas vin, vout = mean flow velocities at inlet and outlet liquid level areas The mean flow velocities at the inlet and outlet areas are, based on the Continuity Law, mostly insignificantly small and can be neglected, if the tank areas being relatively large compared to those of the pipe work. In this case, above formula will be simplified to: The static portion of the system H-Q curve, that part that is unrelated to the rate of flow, reads: For closed circulating systems this value becomes zero. The total friction losses are the sum of the frictional losses of all components in the suction and delivery piping. They vary, at sufficiently large REYNOLDS numbers, as the square of the flow rate. g = gravity (9.81 m/s2) Hl,tot = total friction loss between inlet and outlet areas vi = mean flow velocities trough pipe cross-section area Ai = characteristic pipe cross-sectional area ζi = friction loss coefficient for pipes, fittings, etc. Q = flow rate k = proportionality factor Under the above stated premises the parabolic system H-Q curve can now be drawn: The proportionality factor k is determined of the specified duty point. The intersection of the system H-Q and the pump H-Q curves defines the actual operating point.

## System Curve

The system performance curve is composed of a static and a dynamic component. Hsystem = Hstat + Hloss(Q) The static component Hstat is independent of the flow velocity (and thus of the flow rate). It contains the geodetic height difference as well as the pressure difference between suction and pressure vessel or inlet and outlet point of the system under consideration. In closed circuits (e.g. heating circulation) the static heed is always zero. The dynamic part of the performance curve describes the piping losses, which depend on the flow rate. In the case of turbulent flow of NEWTON liquids with constant loss coefficients of the system components, the characteristic curve results in a square parabola. If the static head and the duty point are known, the system curve can be shown with sufficient accuracy.