Reynolds number

Introduction to Reynolds number: When measuring the flow rate of a fluid in a pipe, it is often necessary to understand its flow state, velocity distribution, etc. The Reynolds number is an important parameter that characterizes the flow properties of a fluid. 7 H$ H/ q" e2 d9 z7 O$ @ The ratio of the inertial force Fg to the viscous force (internal friction force) Fm during fluid flow is called the Reynolds number. It is denoted by the symbol Re. Re is a dimensionless quantity. In the formula, the dynamic viscosity η is replaced by the kinematic viscosity υ, since η = ρυ. Therefore, in the formula: υ —— the average velocity of the fluid ；  l——Fixed dimension of the beam ； 0 o9 c8 V7 R% j0 \ N& w ρ、η – in operating condition ； Kinematic viscosity and dynamic viscosity of the fluid: λ% „\" L O9 \! z ρ – density of the fluid under test ；  As can be seen from the above equation, the value of the Reynolds number Re depends on three parameters, namely the velocity of the fluid, the characteristic size of the flow stream, and the viscosity under operating conditions. 9 ?( D3 @0 }" I: A( D; When transporting fluid through circular pipes, the characteristic dimension used for calculating the Reynolds number is generally the pipe diameter (D). Thus, $ ]: w, d7 _" y/ }3 {' i4 H5 w ) F( When transporting fluid through square pipes, the characteristic dimension used is the equivalent diameter (Dd). The equivalent diameter is equal to four times the hydraulic radius. For pipes of any cross-sectional shape, the hydraulic radius is equal to the ratio of the pipe’s cross-sectional area to its perimeter. Therefore, for a rectangular pipe with lengths A and B, respectively, its equivalent diameter can be calculated as four times the cross-sectional area divided by the perimeter. Thus, the formula for calculating the Reynolds number is… A low Reynolds number indicates that, during fluid flow, the viscous forces between the various fluid particles play a dominant role; the fluid particles flow in an orderly manner parallel to the inner walls of the pipe, resulting in laminar flow. A high Reynolds number means that inertial forces play a dominant role, and the flow is turbulent. Generally, in pipes, a Reynolds number Re < 2000 indicates laminar flow, Re > 4000 indicates turbulent flow, while Re = 2000–4000 represents a transitional state. Under different flow conditions, the motion patterns of the fluid and the distribution of flow velocities vary; as a result, the ratio of the average flow velocity υ of the fluid in the pipe to its maximum flow velocity υmax also differs. Therefore, the value of the Reynolds number determines the flow properties of viscous fluids. The figure below shows the relationship between the Reynolds number ReD of a smooth pipe and the velocity ratio V/Vmax. The relationship between the pipe Reynolds number Rep of a smooth pipe and the velocity ratio V/Vmax: I0 S- i6 M/ t: o S! A6 z$ h2 a. Experiments show that when the external conditions are geometrically similar (geometrically similar pipes, fluid flowing through geometrically similar objects, etc.), if their Reynolds numbers are equal, then the flow state of the fluid is also geometrically similar (hydrodynamic similarity). This similar principle is precisely the basis for the standardization of throttling devices used in flow measurement. It can be seen that the Reynolds number, which accurately reflects the flow characteristics of a fluid, is a commonly used parameter in flow rate measurement. The formula for the Reynolds number in terms of flow rate is as follows: M – the mass flow rate of the fluid being measured, in kg/h; Q – the volumetric flow rate of the fluid being measured, in m/h ； " U7 H( w: D* _/ ` D——Inner diameter of pipeline in mm ； D7 i1 g; Y1 G4 s& O’ s0 ~ v——The dynamic viscosity of the medium under operation, in Pa•S. p——The kinematic viscosity of the medium under operation, in m2/s. The constant values in the equation vary depending on the units of the various parameters used in it. When units other than those specified in the formula are used, the constant values must be adjusted accordingly. When using the Reynolds number, attention should be paid to the corresponding characteristic size. Generally, a superscript is indicated in the lower right corner of the given Reynolds number Re to indicate the corresponding dimensional size. In the standards for throttling devices, the Reynolds number relative to the pipe diameter D is denoted as ReD, while the Reynolds number relative to the orifice diameter d of the throttling element is denoted as Red. The relationship between the two is ReD = βRed, where β is the diameter ratio of the throttling element, that is, β = d/D; this factor must be taken into account when using such standards.