How to Determine the System Load Curve

The system load curve of a hydraulic setup can be determined theoretically using Bernoulli’s Equation of Energy Conservation or experimentally by measuring the pump pressure at various flow rates.

Experimental Determination

Watch the Levitronix Design Guideline Video and see how the system load curve can be determined experimentally by measuring the pressure at various flow rates.

Since the system load curve represents the demand of the hydraulic setup, one can use any type of pump to determine the load curve. When using a Levitronix pump, only the flow needs to be actively measured, the pressure can be read from the pump speed + flow.

Theoretical Determination (Bernoulli)

In many applications of Bernoulli’s equation, internal energy can be neglected resulting in a simplified equation. This allows looking at kinetic (and potential) energy only, which can be used to calculate the pressure drop.

Since the system load curve represents the pressure drop at various flow rates, one can determine the system load curve by calculating the required pressure to move liquid through a fixed setup. The total pressure drop equals the sum of distributed dynamic pressure drop due to tube friction, localized dynamic pressure losses such as valves or tube bends, and static (vertical) pressure drop.

Online pressure drop calculator tools (e.g. Pressure Drop Online-Calculator (pressure-drop.com)) offer an easy way to quickly determine multiple points on the system load curve.

*Extended Information on Bernoulli: Pressure Drop Calculation

Distributed pressure loss of tubing (ID, length, roughness)

All pipes produce a distributed pressure loss, due to the friction between the fluid and the wall of the pipe.

The pressure loss can be estimated with the Darcy-Weisbach equation:

In this formula we find different parameters of the hydraulic system, among which:

From this formula we can derive a few key pieces of information on how to minimize the pressure losses in the system:

• The Pressure losses are proportional to the pipe length –> minimizing the pipe length will proportionally reduce the pressure losses
• The diameter has an enormous influence on the pressure loss –> E.g., doubling the pipe diameter will cause a reduction of the pressure loss by a factor 32.
• The coefficient fd depends on the pipe’s relative roughness (affected by diameter, surface quality, degradation, abrasion, corrosion, cleanliness), fluid and flow regime (Reynold’s number). In turbulent flows (the most common case), fd depends uniquely on the pipe’s relative roughness –> using large pipes, with good surface quality and cleanliness, will help reduce the pressure losses.
• Once the hydraulic circuit is defined, the pressure losses will be proportional to the square of the flowrate.

Localized pressure loss of tubing (bends, valves, filters…)

All items in a hydraulic circuit cause a pressure loss due to the energy lost in redirecting the fluid (in the case of elbows), vortexes generation (in the case of fittings) or by causing a resistance to the flow (filters). The nature and geometry of these items define the local pressure loss coefficient$$\xi$$This coefficient is tabulated for all most common components, or it is provided by the supplier.

The pressure drop caused by these elements can be expressed by this formula:

For static components (e.g. elbows, T-junctions, filters, orifices), the equivalent diameter is fixed, fluid properties and loss coefficient are fixed too, therefore the pressure loss is proportional to the square of the flowrate flowing through the component.

For dynamic components (valves in particular) the equivalent diameter changes depending on how closed the valve is. This causes the pressure loss to depend on the square of the flowrate and on the stroke of the valve. This is the reason why many applications use control valves to reduce the flowrate.

To minimize the localized pressure losses in the system, it is important to simplify the circuit as much as possible (reduce the number of elbows, fittings, expansions and reductions…) and to use components of sufficient diameter.

Static pressure drop

The pressure difference due to elevation can be calculated as the product of elevation change, gravity, and density. By elevation change it is meant the difference in meters between the free surface levels of the fluid in the downstream and upstream tanks.

In the rare case where the up- and downstream tanks are pressurized, the pressure difference constitutes another element in the static pressure drop term.