When there is a pressure difference Δp (Δp = p₁ – p₂, p₁ > p₂) between the two ends of a fluid flow channel (referred to as flow passage), the oil will flow. Symbol description: A – opening; Δp – pressure difference; q – flow rate
Determining factors of flow rate:
Shape and size of the flow passage (mainly the location with the minimum flow cross-sectional area, referred to as “opening”, represented by symbol A; note: A is not a strict geometric area, but an approximately equivalent quantity);
Viscosity of the oil.
Symbol description: Δp – pressure difference; q – flow rate; A – opening
Pattern: The greater the pressure difference, the larger the opening, and the lower the oil viscosity, the greater the flow rate.
Pressure difference – flow rate characteristics of hydraulic valves: The relationship between pressure difference and flow rate determines the working characteristics of hydraulic valves.
From another perspective, the obstruction of the flow passage to oil flow will cause pressure reduction (referred to as pressure drop/pressure loss), which originates from:
Friction between the oil and the flow passage wall;
Mutual friction within the oil itself.
Conditions for increased pressure loss:
Smaller opening;
Rougher flow passage wall and more variable shape;
Higher flow velocity.
2. Hydraulic Resistance
The obstruction of the flow passage to oil flow is called hydraulic resistance.
Hydraulic resistance is similar to “resistance” in electrical engineering, with dual meanings:
Physical quantity: the obstruction characteristic of the flow passage to liquid flow;
Component: components intentionally placed in hydraulic circuits that create obstruction to liquid flow (such as hydraulic valves, throttle orifices, etc.); does not include pumps, cylinders, motors (their main function is energy conversion); connecting pipes, filters and other auxiliary components have relatively small obstruction effects, and are only called hydraulic resistance when considering pressure drop.
Fixed hydraulic resistance — fixed opening.
Heat conversion of hydraulic resistance: The pressure loss when hydraulic resistance flows is ultimately converted into heat energy. Theoretically, 1MPa pressure loss will increase the oil temperature by about 0.57℃ (slightly lower in practice, because part of the heat is transferred to the flow passage wall); unlike electrical resistance, liquid flow carries away heat, so hydraulic resistance does not become particularly hot.
Physical quantity relationship of hydraulic resistance: Analogous to electrical engineering (flow rate corresponds to current, pressure drop corresponds to voltage, hydraulic resistance corresponds to resistance), but in hydraulic technology, hydraulic resistance is nonlinear and uncertain (due to uncertain flow regime).
3. Flow Regime
1) State of fluid flow (laminar and turbulent flow)
Taking domestic tap water as an example:
Laminar flow: When the opening is small and flow rate is small, the water column is stable and transparent (low flow velocity, liquid molecular groups are constrained by viscosity, without vortices, stable and orderly);
Turbulent flow: When the opening is large and flow rate is large, the water column is turbulent with many bubbles (high flow velocity, molecular group inertial force exceeds attraction, mutual collision).
Liquid flow in pipes is also divided into laminar and turbulent flow:
Liquid at the flow passage wall is almost stationary due to viscous constraint, and liquid far from the wall is constrained by it, producing pressure loss;
The higher the flow velocity and viscosity, the greater the constraint and the greater the pressure loss.
Pressure loss patterns of laminar and turbulent flow:
Laminar flow: Pressure loss is slightly lower, roughly proportional to average flow velocity;
Turbulent flow: Pressure loss is relatively higher, roughly proportional to the square of average flow velocity (due to severe molecular group collision).
2) Factors determining flow regime
Main factors are viscosity, flow velocity, pipe diameter, and flow passage shape.
All liquids have viscosity (kinematic viscosity of water at 20℃ is 1mm²/s);
The lower the viscosity, the higher the flow velocity, and the larger the pipe diameter, the easier it is to form turbulent flow;
Influence of flow passage shape:
① Long channel (friction loss along the path): Flow passage area/shape has no abrupt change, pressure gradually decreases (due to friction between liquid and wall), easy to form laminar flow;
② Opening/shape abrupt change (local loss): Such as at small holes and elbows, the liquid flow conflicts with the flow passage wall due to inertia, forming eddy flow and turbulent flow, with significant pressure drop.
3) Transition of flow regime
Determined by Reynolds number (flow velocity × equivalent radius / kinematic viscosity) (determined by British scientist Reynolds in 1883):
Laminar to turbulent flow: Reynolds number reaches approximately 12000 (reaches 40000 in quiet conditions);
Turbulent back to laminar flow: Reynolds number needs to drop below 2300;
Transition zone (Reynolds number 12000~2300): Flow regime is uncertain, pressure loss cannot be theoretically estimated → hydraulic resistance still has no unit to this day.
Modern hydraulic systems: Complex flow passages, high flow velocity, variable pressure, therefore mainly turbulent flow, with laminar flow only appearing in a few long straight pipe sections.
