Pressure Loss in Liquid Flow

1. Two flow states

The flow state of a liquid can be judged by the Reynolds number Re. When Re<Re is critical, the fluid is laminar flow; when Re>Re is critical, the fluid is turbulent flow.

        Re＝4vr/ν

In the formula: v—liquid flow velocity (cm/second)

        ν—Kinematic viscosity of oil (cm²/sec)

        r—hydraulic radius of liquid flow section (cm)

The hydraulic radius r is equal to the ratio of the effective cross-sectional area F of the liquid flow to the wetted perimeter length W (the perimeter length of the effective cross-section).

        r＝F/W

The hydraulic radii of commonly used sections are as follows:

Circle r=d/4 (d is diameter) Rectangle r=bh/2(b+h) (h is height, b is width)

Concentric rings r=(d₁-d₂)/4 d₁ is the diameter of the outer circle, d₂ is the diameter of the inner circle)

The Reynolds number Re of a circular cross-section duct can be calculated by the following formula

        Re＝vd/ν＝21.23Q/dν

In the formula: 

        Q—the flow rate of liquid through the pipeline (L/min)

        d—pipe inner diameter (cm)

The critical Reynolds numbers of commonly used liquid flow pipelines are as follows:

round smooth pipe	2000~2300	Rough eccentric ring gap	400
Rubber hose with connector	1600~2000	Slide valve port	260
Smooth concentric ring gaps	1100	rotary valve	550~750
Smooth eccentric ring gap	1000	Flat and poppet valves	20~100
Smooth eccentric ring gap	700

2. Pressure loss along the way

        Δp_edge=λ·γ·l/d·v²/2g (kg force/cm²)

In the formula: 

        λ—resistance coefficient along the way

        γ—Liquid weight (kgf/cm³)

        l—pipeline length (cm)

        d—pipe diameter (cm)

        v—average velocity of liquid (cm/s)

        g—acceleration due to gravity (cm/s²)

When the liquid is laminar flow λ = 75/Re

When the liquid is turbulent and the inner wall is smooth, when Re<10⁵, λ=0.3164Re^-0.25;

When 10⁵<Re<3×10⁶, λ=0.0032+0.221Re^-0.237.

3. Local pressure loss

        Δp_edge=ξγv²/2g (kg force/cm²)

In the formula:

         ξ—local resistance coefficient

4. Total pressure loss of hydraulic system

The total pressure loss of a hydraulic system is equal to the sum of all pressure losses along the system and local pressure losses. The pressure loss is proportional to the square of the liquid flow velocity, so the liquid flow velocity is the most important factor affecting the pressure loss. In order to reduce the pressure loss of the system, the flow rate of liquid in the pipeline should not be too high. The following are recommended values for the allowable flow rates of various pipelines in the hydraulic system:

High pressure pipeline	3~6	Control oil circuit	2~3
Low pressure pipeline	≤3~4	Liquid-filled oil circuit	1~2
Oil return line	≤3	local oil circuit	5~9
Suction line	0.6~1.2	unit:	meters/second

When the pressure is high, the pipeline is short, and the oil viscosity is low, a large value can be taken, otherwise a small value should be taken.

Tags: Hydraulic Pressure, Pipeline, Liquid, High Pressure, Low Pressure, Piston Pump Oil, Control Oil Circuit, Open Circuit, Flow State, Hydraulic System