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.    


The head for the duty point of the pump is composed of
  • the static head (static = independent of the flow rate)
    • height difference between suction side and discharge side liquid level (geodetic head)
    • pressure difference between discharge side and suction side tank (for closed tanks)
    • the required outlet pressure, if any
  • the friction loss head from the pressure losses in the piping system as a function of the flow rate
The useable mechanical work transferred from the pump to the fluid being pumped, related to the weight force, is called head H of the pump. At constant speed n and constant flow Q, it is independent of the density of the pumped liquid, but dependent on its viscosity. It can be calculated by the pressure difference divided by the density of the pumped fluid and the local gravitational constant. For Newtonian fluids one can consider the head independent from the pumped fluid for kinematic viscosities less than 20 mm²/s. By this reason it is especially suitable to present the characteristic curve of centrifugal pumps. For pumping water the value is equal to the pressure given in meters of water column.