Water Flow Sensors with Wide Range of laminar Flow Rate

Xiang Zheng Tu 

The thermal flow sensors provided by POSIFA Microsystems Company are based on the linear relationship between the fluid flow rate and temperature difference dependence voltage or thermoelectric effect. The criteria for the operation of the sensors are to create and maintain laminar flow through the sensitive surface of the sensors.

Osborne Reynolds in 1883 proposed a concept relating to fluid flow properties through pipes of different diameter as well as the determination of boundary layers where the transition between laminar flow to turbulent flow occurs. The regimes where laminar or turbulent flow prevails are prescribed by a dimensionless parameter known as the Reynolds number, defined as

{\displaystyle \mathrm {Re} ={\frac {\rho uL}{\mu }}={\frac {uL}{\nu }}}

R_e = ρ u L / μ = u L / υ      (1)

Where:

ρ is the density of the fluid (SI units: kg/m³)

u is the average velocity of the fluid with respect to the object (m/s)

L is a characteristic length (m)

μ is the dynamic viscosity of the fluid (Pa·s or N·s/m² or kg/m·s)

ν is the kinematic viscosity of the fluid (m²/s).

The characteristic length can be calculated with the generic equation as

d_h = 4 A / p                            (2)

Where

d_h = hydraulic diameter (m)

A = area section of the duct or pipe (m2)

p = "wetted" perimeter of the duct or pipe (m)

Based on equation (2) the characteristic length of a circular duct can be expressed as:

d_h = 4 π r² / 2 π r  = 2 r                              (3)

Where

r = pipe or duct inside radius  (m)

d = pipe or duct inside diameter  (m)

As expect the hydraulic diameter of a standard circular tube or duct is the inner diameter or two times the inner radius.

Based on equation (2) the characteristic length of an annulus duct or tube with an inside duct or tube can be expressed as

dh = 4 (π r_o² - π r_i²) / (2 π r_o + 2 π r_i) = 2 (r_o - r_i)               (4)

Where

r_o = inside radius of the outside tube (m)

r_i = outside radius of the inside tube (m)

Based on equation (2) the characteristic length of a rectangular duct or pipe with very length width can be calculated as

d_h = 4 a b / 2 (a + b) = 2 a                                 (5)

Where

a = height of the duct (m)

b = width of the duct (m)

b >> a

Generally, laminar flow occurs at Reynolds numbers of less than 2,000, but in practice Reynolds numbers of less than 1,000 are used to ensure laminar flow under all conditions (e.g., viscosity and density variations with temperature).

As can be seen from the above equations:

• The laminar flow rate of the circular duct or tube is only limited by the Reynolds number.
• The laminar flow rate of the annular duct or tube can be extended by increasing the radius of inside tube and outside tube simultaneously without changing the Reynolds number.
• The laminar flow rate of the rectangular duct or tube can be extended by increasing the width of the rectangular duct or tube without changing the Reynolds number.

POSIFA Microsystems preferred rectangular duct or tube. The following water flow ranges are available:

• 0 – 10 mL / min for medical application
• 0 – 40 mL / min for medical application
• 0 – 120 mL / min for medical application
• 0 – 1000 mL / min for Coffee Makers
• 0 – 3000 mL / min for Water Dispensers
• 0 – 10 L / min for  Liquid Cooling CPU Systems