When designing hydraulic circuits, whether it’s for a tracked military vehicle, a heavy press line or a forestry arm, something which will often require consideration is how pressure behaves when flow conditions change. This is where Bernoulli’s equation becomes a valuable part of the hydraulic design process.
The Bernoulli equation connects the dots between fluid pressure, flow velocity and elevation. Based on Bernoulli’s principle it’s a simplified version of the conservation of energy applied to fluid mechanics.
The Bernoulli equation is based on the principle of conservation of energy and applies to a moving fluid under specific conditions. It tells us that the total pressure in a fluid flow, made up of pressure energy, kinetic energy and potential energy - stays constant along a streamline, assuming no work is added or lost and there's no friction.
The most common form of Bernoulli’s equation used in hydraulics:
P/ρg + v²/2g + z = constant
Where:
This form of the equation is valid for steady, incompressible, non-viscous fluid flow along a streamline.
Each term in the Bernoulli equation corresponds to a different form of energy per unit weight of the fluid:
The equation implies that an increase in one form must be balanced by a decrease in another. For example, as flow velocity increases, pressure decreases in a region of lower pressure, keeping total energy constant.
In real-world hydraulics, engineers apply the Bernoulli equation to understand how a fluid’s velocity, density, and pressure interact within a system, particularly in mobile and industrial sectors. The equation can be applied to determine how pressure changes in hydraulic components, such as pipe reducers, elbows and control valves.
A construction machine lifting a load with a hydraulic ram might show a pressure drop in the return line when retracting at speed. Using the Bernoulli equation, the engineer can assess the difference in pressure caused by increased fluid speed in narrowed sections.
In industrial presses, understanding the dynamic pressure versus static pressure can prevent uneven stroke movement. The form of Bernoulli’s equation helps evaluate how flowing fluid responds to varying loads.
Renewable energy setups often involve fluid flow at varying heights. The elevation head term in the Bernoulli equation is critical in sizing pumps for vertical transfer lines in ground source systems.
The Bernoulli principle works alongside the continuity equation, which is another key rule in fluid mechanics. The continuity equation states:
A₁v₁ = A₂v₂
Where A is the cross-sectional area, and v is the flow velocity. This tells us that if pipe diameter decreases, velocity of the fluid must increase which, based on Bernoulli’s law, causes a decrease in pressure.
This is seen in fittings like venturi blocks, where the Bernoulli effect is used intentionally to create a region of lower pressure for metering or suction.
The equation is often used as a quick estimation tool but it makes a few assumptions:
In real hydraulic systems, these conditions are seldom fully met. So, Bernoulli’s equation can be modified to include terms for head loss, typically using the Darcy-Weisbach equation. This allows for more accurate analysis, particularly in long pipe runs, turbulent zones, or systems with many bends and fittings.
Let’s go through some real-world applications of Bernoulli’s equation in different hydraulic sectors.
In every case, the equation applied early in the design helps reduce errors later.
Daniel Bernoulli published this principle in 1738. Although Bernoulli deduced it centuries ago, it’s still referred to as Bernoulli’s law and forms the foundation for modern fluid mechanics. Whether it’s sizing a pipe or designing a complete hydraulic power unit, engineers use this energy equation because it works.
Even with simulation software and CAD tools, the equation tells us the fundamentals, how the pressure due to fluid flow can be controlled and harnessed to get the job done.
The Bernoulli equation states that in a steady, incompressible flow of a non-viscous fluid, the sum of pressure energy, kinetic energy, and potential energy per unit weight is constant along a streamline.
Yes. As long as the fluid flow is steady and the oil’s density remains consistent, the equation is valid. For detailed design, you may need to account for viscosity and losses.
The continuity equation focuses on conservation of mass, while the Bernoulli equation focuses on the conservation of energy in a moving fluid.
It helps predict pressure drop, select components, and analyse how fluid velocity changes in fittings, bends, and pipe diameter transitions.
The Bernoulli equation is a key part of any hydraulic engineer’s toolbox. It doesn’t solve every problem on its own but it lays down the groundwork. From fluid pressure changes to flow velocity analysis, from mobile rigs to process plants, this form of Bernoulli’s equation makes a difference where it counts.
Posted by admin in category Hydraulic Systems Advice on Monday, 26th January 2026
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