Six Fundamental Laws of Hydraulic Systems: From Pressure Generation to Flow Distribution

The fundamental laws of hydraulic systems originate from the fundamental principles of fluid mechanics. Simplified and refined through engineering practice, they form six core laws unique to the hydraulic industry. These interrelated laws collectively explain fundamental issues such as how pressure is generated, flow is controlled, and energy is transferred and distributed in hydraulic systems. They are: the Pressure Generation Law (P Law), the Flow Generation Law (Q Law), the Pressure Loss Law (ΔP Law), the Multi-Load Pressure Distribution Law, the Flow Distribution Law, and the Flow Loss Law (ΔQ Law).

1. Overview of the Six Fundamental Laws of Hydraulics

2. Pressure Development Law (P-Law): The Source of Hydraulic Force

"Pressure depends on load"—this classic adage in the hydraulics industry accurately summarizes the essence of the Pressure Development Law (P-Law). In a hydraulic system, pressure isn't generated solely by the hydraulic pump; it's the system's response to external load. When hydraulic oil pushes the cylinder piston to overcome external resistance, system pressure naturally increases; when the load decreases, pressure also decreases. This law reveals the fundamental operating logic of hydraulic systems: the pump provides flow, while pressure is the product of the load's resistance to fluid movement.

This principle can be verified with a simple experiment: place a hydraulic jack under cars of varying weights. When lifting a small car, the pressure gauge displays a low reading; when lifting a heavy truck, the gauge reads significantly higher. Although the pump delivers the same amount of oil, the pressure is completely determined by the load. In engineering practice, operators often observe changes in system pressure to determine the load status of the equipment, which is an application of the Pressure Development Law.

The law of pressure development has two important exceptions that deepen our understanding of pressure development:

Dynamic pressure development: When high-speed fluid flow is suddenly obstructed (such as when a valve is rapidly closed), its kinetic energy is converted into pressure energy, generating a surge pressure far exceeding the static pressure. This phenomenon is particularly pronounced during sudden stops or direction changes in construction machinery, potentially causing pipeline vibration or seal failure.

Pressure under leak conditions: In a system with a leak, whether pressure can be built up depends not only on the load but also on the balance between leakage and oil supply. When leakage is excessive, the system may be unable to build sufficient pressure to support the load, a common occurrence in worn hydraulic pumps or cylinders.

3. Flow Development Law (Q-Law): Controller of Motion Speed

3.1 ​​The Relationship between Flow and Speed

The flow development law (Q-Law) reveals the essence of motion speed in a hydraulic system: the speed of an actuator is determined by the flow supplied to it. This law demonstrates a precise mathematical relationship for hydraulic cylinders and hydraulic motors:

• Hydraulic cylinder speed: V = Q / A

(V: piston speed; Q: flow rate; A: piston effective area)

• Hydraulic motor speed: n = Q / q

(n: speed; Q: flow rate; q: motor displacement)

These formulas indicate that increasing cylinder extension speed can be achieved by increasing oil flow or reducing piston area; increasing motor torque requires increasing pressure or selecting a larger-displacement motor. During excavator operation, the displacement of the operating handle effectively controls the valve opening, thereby regulating the flow entering the cylinder and ultimately achieving precise control of bucket speed.

3.2 The Real-World Impact of Leakage

Ideally, the flow output of a hydraulic pump should be fully converted into movement of the actuator. However, in reality, internal and external leakage are inevitable; this is a fundamental characteristic of hydraulic transmission. Internal leakage primarily occurs in the clearances between the friction pairs of the pump, valve, and motor, such as the clearance between the plunger and cylinder bore of a plunger pump and the clearance between the valve core and sleeve of a spool valve. While these leaks reduce volumetric efficiency, they are necessary for lubricating and maintaining hydrostatic bearings.

Internal leakage in modern hydraulic components has been effectively controlled. For example, advanced threaded cartridge valves have an internal leakage rate of only 3-6 drops/hour (approximately 1 ml). However, external leakage in the system still requires significant attention, especially at pipe joints and seals. With the development of technologies such as 12.9-grade high-strength bolts, this external leakage problem has been significantly improved.

The conservation of power is another important manifestation of the flow law: N = P × Q / 60 (kW). This quantitative relationship states that, given constant power, pressure and flow are mutually constrained—increasing pressure requires decreasing flow, and vice versa. Constant-power variable displacement pumps utilize this principle, automatically reducing displacement as load pressure increases to maintain constant power.

4. Pressure Loss Law (ΔP Law): The Root Cause of System Heating

4.1 Causes and Quantification of Pressure Loss

As hydraulic oil flows through a system, it inevitably encounters resistance, causing a pressure drop along the way. This pressure loss (ΔP) is the primary cause of heating in hydraulic systems. Pressure loss primarily stems from two factors:

• Longitudinal resistance: friction between oil and pipe walls as it flows through a pipeline, proportional to the length and roughness of the inner wall.
• Local resistance: generated when flowing through local obstacles such as valves, elbows, and joints, typically accounting for over 70% of total pressure loss.

The relationship between ΔP and the square of the flow velocity (ΔP ∝ v²) is the core of the pressure loss law. This means that when the flow velocity doubles, the pressure loss quadruples. Therefore, controlling flow velocity is a key principle in hydraulic system design:

• Pump suction line: Flow velocity should be <1 m/s (to prevent cavitation).
• Return line: 1-3 m/s
• Pressure line: 3-6 m/s
• Local area of ​​the valve port: <10 m/s

5. Multi-Load Pressure Distribution Law: Coordination of Complex Systems

In multi-actuator hydraulic systems, the pressure distribution law reveals a key principle: different loads cannot directly share the same pressure source. This is because pressure in a hydraulic system is uniform—the pressure at each point in the same pipeline is equal under steady-state conditions. When multiple loads are connected in parallel, the system pressure will first meet the requirements of the smallest load, while those of higher loads will remain unmet.

This phenomenon can be observed through a simple experiment: when two cylinders requiring different pressures (e.g., 5 MPa and 10 MPa) operate simultaneously, if the system pressure is set to 10 MPa, the low-pressure cylinder will actuate rapidly due to excessive pressure, even exceeding its safe speed; whereas if the system pressure is set to 5 MPa, the high-pressure cylinder will not actuate. This pressure distribution conflict is particularly prominent during complex movements of construction machinery.

6. Flow Distribution Principle: The Key to Coordinating Multiple Actuators

6.1 Traditional Distribution Methods and Their Limitations

Flow distribution in a hydraulic system is like "dividing a pie." Limited flow resources must be rationally allocated according to the needs of different actuators. Traditional flow distribution methods primarily include two methods:

• Damping Distribution (Throttling): Flow is distributed by adjusting the opening of the throttle valves in each branch. This method is simple and economical, but it suffers from significant energy losses and poor flow stability when load pressures fluctuate. Especially when multiple actuators operate simultaneously, flow will preferentially flow to the actuator with the smaller load, resulting in uncoordinated operation.
• Volume distribution: Output flow is directly controlled by varying pump displacement (variable pump) or motor speed (variable frequency drive). This method is highly efficient, but significantly increases cost and technical complexity.

The speed regulation effect of a throttle valve relies on the "hydraulic half-bridge" principle. A single throttle valve cannot stably control flow; it must work with upstream and downstream resistance to create a pressure differential. Understanding this principle is crucial for analyzing system failures. When throttle valve flow is abnormal, it's important to check not only the valve itself but also the system pressure stability.

6.2 Innovative Solution: LUDV System

To address the shortcomings of traditional flow distribution, the innovative LUDV system (load-independent flow distribution system) has been developed in the construction machinery industry. This system achieves true on-demand flow distribution through a series of ingenious design features:

• Shuttle valve network: Detects the maximum pressure of multiple loads in the system (PLs = max(PL1, PL2, ... PLn))
• Pressure-compensating valve group: Ensures equal pressure differentials across each orifice (ΔP1 = ΔP2 = ... = ΔPn)
• Proportional orifice: Precisely controls opening angles using electrical signals from the operating handle

In the LUDV system, flow to each actuator is proportional solely to the orifice opening area, unaffected by load pressure differences. For example, an operator can simultaneously control boom lift (high load) and bucket tilt (low load), with the system automatically distributing appropriate flow to ensure coordinated operation, avoiding the "small load rushing" phenomenon common in traditional systems.

The more advanced electronic flow distribution solution uses an ECU (electronic control unit) to independently adjust the orifice area of ​​each orifice, integrating sensor feedback for intelligent flow distribution. For example, a new loader hydraulic system features an independently controllable orifice (OR31) between the pump outlet and the return line. This allows for non-coordinated regulation with the working orifices (OR32, OR33, etc.), achieving more precise flow control while minimizing energy loss.

The six fundamental laws of hydraulics—pressure formation, flow formation, pressure loss, pressure distribution, flow distribution, and flow loss—form the theoretical foundation of hydraulic technology. These laws not only explain the operating principles of hydraulic systems but also guide system design and troubleshooting. In today's rapidly evolving technology, innovative directions such as high pressure, intelligentization, and electro-hydraulic integration are still based on these fundamental laws.

A deep understanding of these laws enables hydraulic engineers to advance from "knowing the phenomenon" to "understanding the essence," and from "relying on experience" to "scientific design." Whether analyzing the root cause of uncoordinated complex movements in an excavator, designing the hydraulic system for a high-precision injection molding machine, or addressing the temperature rise problem of a 10,000-ton press, the six laws provide fundamental solutions. Mastering these laws means mastering the essence of hydraulic technology.