Calculating the System H-Q Curve

The system H-Q curve depicts the dependency of the Total Head HA on the Flow Q.

The required pumping head in a branchless pipeline is determined from BERNOULLI’s equation for one-dimensional, stationary flow of incompressible fluids:




p_a,p_e = pressures on suction or delivery liquid levels respectively

p = fluid density
g = gravity (9.81 m/s2)

H_geo = Static height difference between suction and delivery liquid levels respectively.

H_v,ges. = Total friction loss between inlet and outlet areas.

v²_a,v²_e, = Mean flow velocities at inlet and outlet areas.



The mean flow velocities at the inlet and outlet areas are, based on the Continuity Law, mostly insignificantly small and can be neglected; the tank areas being relatively large compared to those of the pipe work.
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)

H_v,ges. = total friction loss between inlet and outlet areas

v_i² = mean flow velocities trough area

A_i = characteristic cross-sectional area

ζi = friction loss coefficient for 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 duty point.