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The fundamental laws of hydraulic systems originate from the fundamental principles of fluid mechanics. Simplified and refined through engineering practice, these laws have evolved into six core laws unique to the hydraulic industry. These interrelated laws collectively explain fundamental issues such as how pressure is generated, how flow is controlled, and how energy is transmitted and distributed in hydraulic systems. These laws are: the pressure development law (P law), the flow development law (Q law), the pressure loss law (△P law), the multi-load pressure distribution law, the flow distribution law, and the flow loss law (△Q law).
01. Overview of the six basic laws of hydraulics
02. Pressure Formation 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 workings of hydraulic systems: the pump provides flow, while pressure is the product of the load’s resistance to fluid motion.
This principle can be verified through a simple experiment: place a hydraulic jack under cars of varying weights. When lifting a small car, the pressure gauge displays a low value; when lifting a heavy truck, the gauge reading rises significantly. 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 equipment, which is an application of the pressure development law.
The pressure development law 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 noticeable when construction machinery stops suddenly or changes direction, potentially causing pipeline vibration or seal failure.
Pressure under Leakage: In a system with a leak, whether pressure can be built up depends not only on the load but also on the balance between the leakage volume and the oil supply. When the leakage volume is excessive, the system may be unable to build sufficient pressure to support the load. This is common with worn hydraulic pumps or cylinders.
03. Flow Formation Law (Q Law): Controller of Movement Speed
3.1 Relationship between Flow and Speed
The flow-forming law (Q-law) reveals the essence of motion speed in hydraulic systems: the speed of an actuator is determined by the flow supplied to it. This law expresses a precise mathematical relationship for hydraulic cylinders and 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 rate entering the cylinder and ultimately achieving precise control of bucket speed.
3.2 The Real-World Impact of Leakage
Ideally, the flow rate output by a hydraulic pump should be fully converted into movement of the actuator. However, in reality, internal and external leakage are inevitable and are a fundamental characteristic of hydraulic transmission. Internal leakage primarily occurs in the clearances between friction pairs within pumps, valves, and motors, such as the clearance between the plunger and cylinder bore of a plunger pump and the clearance between the spool and sleeve of a spool valve. While these leaks reduce volumetric efficiency, they are also 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 demonstrates that, given constant power, pressure and flow are mutually constrained—increasing pressure requires decreasing flow, and vice versa. The constant power variable displacement pump applies this principle, automatically reducing the displacement when the load pressure increases to maintain constant power.
04. Pressure Loss Law (△P Law): The Root 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 source of heat generation in hydraulic systems. Pressure loss primarily arises from two factors:
- Along-the-line resistance: This occurs when oil flows through a pipeline due to friction with the pipe wall. It is proportional to the length of the pipe and the roughness of the inner wall.
- Local resistance: This occurs when oil flows through local obstructions such as valves, elbows, and joints, and typically accounts for over 70% of total losses.
The relationship between ΔP and the square of the flow rate (ΔP ∝ v²) is the core of the pressure loss law. This means that when the flow rate doubles, the pressure loss will increase by four times. Therefore, controlling the flow rate becomes a key principle in hydraulic system design:
- Pump suction line: Flow rate should be <1 m/s (to prevent cavitation)
- Return line: 1-3 m/s
- Pressure line: 3-6 m/s
- Valve port area: <10 m/s
05. 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 all points in the same pipeline is equal under steady-state conditions. When multiple loads are connected in parallel, the system pressure will prioritize meeting the smallest load’s requirements, while higher loads will be unable to meet them.
This phenomenon can be observed in a simple experiment: when two cylinders requiring different pressures (e.g., 5MPa and 10MPa) operate simultaneously, if the system pressure is set to 10MPa, the low-pressure cylinder will actuate rapidly due to the excessive pressure, even exceeding the safe speed. If the system pressure is set to 5MPa, the high-pressure cylinder will not actuate. This pressure distribution conflict is particularly prominent during complex movements of construction machinery.
06. Flow Distribution Rule: Coordination of Multiple Actuators
6.1 Traditional Distribution Methods and Their Limitations
Flow distribution in a hydraulic system is like dividing a cake. Limited flow resources must be allocated rationally based on the needs of different actuators. Traditional flow distribution methods primarily include:
- Damping distribution (throttling): Flow is distributed by adjusting the opening of each branch throttle valve. This method is simple and economical, but it suffers from significant energy loss and poor flow stability when the load pressure fluctuates. Especially when multiple actuators are operating simultaneously, flow will preferentially flow to the actuator with the lower 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 in conjunction with upstream and downstream resistance to create a pressure differential. Understanding this principle is crucial for analyzing system failures. When a throttle valve’s flow rate is abnormal, it’s important to check not only the valve itself but also the stability of system pressure.
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 for 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 compensation valve group: Ensures equal pressure differentials across each orifice (ΔP1 = ΔP2 = … = ΔPn)
- Proportional orifice: Opening is precisely controlled by an electrical signal from the operating handle
In the LUDV system, the flow to each actuator is proportional only to the orifice opening area, completely unaffected by load pressure differences. For example, in an excavator, the operator can simultaneously control boom lift (high load) and bucket tilt (low load). The system automatically distributes the appropriate flow to ensure coordinated operation of these two actions, avoiding the “small load flow grabbing” phenomenon common in traditional systems.
Cutting-edge electronic flow distribution solutions use an ECU (electronic control unit) to independently adjust the area of each throttle orifice, incorporating sensor feedback for intelligent flow distribution. For example, a new loader hydraulic system incorporates an independently controllable throttle orifice (OR31) between the pump outlet and the return line. This is independently regulated from the working orifices (OR32, OR33, etc.), achieving more precise flow control while minimizing energy loss.
Conclusion: The Enduring Value of Fundamental Laws
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, intelligent systems, and electro-hydraulic integration remain grounded in 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 temperature rise issues in a 10,000-ton press, these six laws provide fundamental solutions. Mastering these laws means mastering the essence of hydraulic technology.