How flow sensors work?

Flow sensors are used for wide range of fluids in multiple industries for various measurements. There are many types of flow sensors and they all measure “volume or area per unit time”. And depending of the sensor type there are multiple ways this volume per unit time can be measured, but they all use basic concept of fluid flow principles with concept such as the Bernoulli’s principle. Some of the basic flow sensors used today are orifice meter, venture meter, flow nozzle, and pitot tubes which us the principle of difference in pressure from the Bernoulli equation. Then there are sensors which use direct force to measure the flow which include rotameter, turbine meter, propeller flow meter, coriolis mass flow meter. Using pressure differences and direct force are the most common methods used to measure flow rate but there are other complicated methods such as ultrasonic flow meters, magnetic flow meter, calorimetric flow meter, gear flow meter, thermal flow meter, and couple more.

All the flow sensors which use pressure difference use Bernoulli equation which is 

Where the condition on both sides of the sensors are inversely related to each other, therefore the equation can be manipulated into the pressure drop across the flow sensor is equal to velocity of the flow squared. When calculating the flow using the different sensors the area of the opening on both sides of the sensor, density of the liquid, and pressure readings from the sensors are known an can be plugged into the Bernoulli equation to find the velocity because V₁ = V₂ = V. Below are few images portraying how some of this sensors operate and how the pressures differences (dp) can be measured.     

Orifice Plate Flow Sensor

Venturi Tube Flow Sensor

Flow Nozzles Flow Sensor

Sensors using direct force to measure velocity use methods of balancing forces with in systems where the force applied by the fluid flowing through the sensor is measured and manipulated with a proportion factor to get the flow of fluid in the system. Below are some images which portray how the forces applied by the fluid are with few different types of direct force flow sensors.

Rotameter: resistance of gravity force of the bolt is being measured here.

Turbine meter: work is being measured here where work equals force times distance, and the distance id known so the force can be calculated from the work measured by the sensor.

Sources:

http://www.princeton.edu/~asmits/Bicycle_web/Bernoulli.html

https://controls.engin.umich.edu/wiki/index.php/FlowSensors