Flow sensors are precision instruments used to measure the flow rate of fluids (liquids or gases) by converting fluid flow parameters into measurable electrical signals for flow monitoring. Modern flow sensors integrate multidisciplinary technologies such as fluid mechanics, electronics, and materials science to meet various measurement needs, from laboratory micro-flows to industrial large flows.
1. Turbine Flow Meter
The turbine flow meter is a velocity-type flow measurement instrument. When fluid passes through the flow meter, it impacts the turbine blades, causing the turbine to rotate. The angular velocity of the turbine’s rotation is proportional to the fluid flow rate, and by detecting the turbine’s rotational speed, the fluid flow can be calculated. This type of sensor features high measurement accuracy (up to ±0.5%), good repeatability, and a wide range ratio (10:1), making it widely used in the petroleum, chemical, and water supply industries.
Calculation Formula:
Basic flow equation:
Q = f/K
Where:
Q – Volume flow rate (m³/h)
f – Pulse frequency (Hz)
K – Instrument coefficient (pulses/m³)
Reynolds number correction:
When Re < 4000, viscosity correction is required:
K_μ = K_0[1 + 0.01(μ/μ_0 – 1)]
2. Electromagnetic Flow Meter
The electromagnetic flow meter operates based on Faraday’s law of electromagnetic induction. When a conductive liquid flows in a magnetic field, it generates an induced electromotive force proportional to the flow velocity. This sensor has no moving parts and no pressure loss, making it particularly suitable for measuring corrosive liquids and slurries containing solid particles, with a measurement accuracy of up to ±0.3%.
Calculation Formula:
Induced electromotive force:
E = kBDv×10⁻⁸
Flow calculation:
Q = (πD²/4)v = (πDE)/(4kB)×10⁸
Where:
E – Induced electromotive force (V)
B – Magnetic induction intensity (T)
D – Inner diameter of the measuring pipe (m)
v – Average flow velocity (m/s)
k – Sensor constant
3. Ultrasonic Flow Meter (Time Difference Method)
The ultrasonic flow meter calculates flow velocity by measuring the time difference of ultrasonic waves propagating downstream and upstream in the fluid. This technology allows for non-contact measurement, suitable for large diameter pipelines, with a measurement accuracy of up to ±0.5% and no pressure loss.
Calculation Formula:
Time difference calculation:
Δt = t₂ – t₁ = (2Lvcosθ)/(c² – v²cos²θ)
Flow calculation:
Q = (πD²/4)·(c²/2Lcosθ)·Δt
Where:
Δt – Time difference (s)
L – Sound path length (m)
θ – Angle between the sound beam and the pipe axis (°)
c – Speed of sound (m/s)
4. Thermal Mass Flow Meter
The thermal flow meter is based on the principle of thermal diffusion, calculating mass flow by measuring the heat carried away by the fluid. This sensor directly measures gas mass flow without the need for temperature and pressure compensation, making it particularly suitable for small gas flow measurements, with an accuracy of up to ±1%.
Calculation Formula:
Constant power mode:
ΔT = P/(hA) = aQ_m^b
Mass flow:
Q_m = [P/(aA)]^(1/b)
Where:
ΔT – Temperature difference (K)
P – Heating power (W)
h – Heat transfer coefficient (W/m²K)
A – Heat transfer area (m²)
a,b – Empirical constants
5. Coriolis Mass Flow Meter
The Coriolis flow meter directly measures mass flow using the Coriolis effect generated by fluid in a vibrating tube. This technology can simultaneously measure density and is not affected by fluid properties, with a measurement accuracy of up to ±0.1%, but it is relatively expensive.
Calculation Formula:
Phase difference equation:
Δφ = (2ωL_m)/K_s·Q_m
Mass flow:
Q_m = (K_sΔφ)/(2ωL_m)
Where:
Δφ – Phase difference (rad)
ω – Drive frequency (rad/s)
L_m – Effective tube length (m)
K_s – Tube bundle stiffness (Nm/rad)
6. Differential Pressure Flow Meter
The differential pressure flow meter is based on Bernoulli’s equation, calculating flow by measuring the pressure difference before and after a throttling device. This technology is mature and reliable, but it has a larger pressure loss, with a measurement accuracy generally between ±1-2%.
Calculation Formula:
General flow equation:
Q = Cε(π/4)d²(2Δp/ρ)^0.5
Where:
C – Discharge coefficient
ε – Expandability coefficient
d – Throttling hole diameter (m)
Δp – Differential pressure (Pa)
ρ – Fluid density (kg/m³)
All constants in the above formulas need to be determined through actual flow calibration, and in practical applications, factors such as Reynolds number, temperature, and pressure must be considered. For special media (such as non-Newtonian fluids) or extreme conditions, specialized correction calculations are required.