WHO AM I? WHY I DID IT?

I'm a mechanical engineer and I developed this project for my degree thesis. Naturally, creating an Orifice Plate from zero is not so easy, because you need to study Technical Physics (in detail Fluid dynamics). But, don't worry, I'll try to explain you how it works and how you can compute the mass flow within a pipe.

All the information are provided by UNI ISO 5167 2003 1 - 2.

I hope this project could help some Engineer or Science lovers. For any questions, don't hesitate to contact me!

WHAT DO YOU NEED TO KNOW?

Physics, Fluid dynamics (Reynold's number, Bernoulli equation), Numerical Analysis.

WHAT DO YOU NEED?

An Orifice Plate (there are different types of it, the model "D and D/2 tappings" is the easiest to build, so I recommend it to you, but if you want to learn more about the other prototypes, check the UNI ISO 5167-1-2 2003)
Arduino UNO
MPX 5050dp
thermocouple MAX 6675

HOW DOES IT WORK?

An orifice plate is a device which allows the user to calculate the axial velocity (and so the mass flow) of a fluid, within a pipe. For example, it is used in power stations, labs or airplanes (Pitot Tubes)!

In this case, I've built the model: "D and D/2 tappings".

One of the most important physics law involved in this process is the "Bernoulli's law".

I'll try to explain how you can adopt it in this particular case:

V. Mitchell e K. Cheesman, «Gas, tubes and flow», Anaesthesia & Intensive Care Medicine.

In an horizontal pipe, we can identify two sides ( in this picture it is identified by 1 and 2). When the pipe section decreases, the axial velocity increases from the section 1 to 2 (so v1

Shown below, the equation:

from this we can obtain this formula:

where:

qm = massic flow
C and 𝜀 = corrective coefficient
A1 = the initial Area of the pipe, before the section reduction
A2 = the reduced Area
P1-P2 = the pressure drop
𝜌 = fluid density

The Pressure drop and density will be found with Arduino, C and qm with numerical analysis and 𝜀 with its formula.

CONSTRUCTION REQUIREMENT (D&D/2 tappings)

From my thesis ( Ref. UNI ISO 5167 2003) :

d = diameter of the orifice
D = diameter of the pipe
𝛽 = d/D
ReD = Reynold's number computed with D.

I chose the following dimension.

For the orifice, I took in consideration three different diameters:12.93 mm, 24 mm, 31 mm.

ALL THE MOST IMPORTANT FORMULAS USED

qm [kg/s] =

w (axial velocity) [m/s]= qm/A1

ReD [adim] =

where 𝜇 is dynamic viscosity

C [adim] =

(Where: L1~1, L'2~0.47, M'2 = 2*L'2/(1-𝛽), A = (19000*𝛽/ReD)^0.8)

and if D<71.12 mm

𝜀 [adim] =

where k is the coefficient of adiabatic expansion.

HOW DO YOU GET THE MEASUREMENT?

Unfortunately, cause to Covid-19, I could not enjoy the laboratories of UniMore, so I used a fan to create the flow.

Before taking the measurement, I built a "U pressure gauge", to calibrate the pressure sensor.

At the end, for different fan's velocity, I've detected different pression drops and I've made a numerical analysis for each one.

NUMERICAL ANALYSIS

The calculation was carried out with excel.

I took in consideratiom different pression values and then I made the numerical analysis for each value.

Repeat the last four steps as long as the values converge within a specific tolerance.

ex. P1-P2= 1000 Pa, d=12.93 mm.

(from left to right).

MY RESULTS

d=12.93 mm

d=24 mm

d=31 mm

UNCERTAINTIES OF THE MEASUREMENT OF THE FLOW RATE

If you want to know how to compute the error, I can advice you to read UNI ISO 5167-1 2003. This is the formula:

I'll show you my values of uncertainties.

d=12.93 mm

where "ro" is the density.

EXPANDED TECHNICAL DETAILS

Industrial Fluid Measurement

This project uses an Arduino to measure the flow rate of liquids or gases through a pipe using the principle of differential pressure.

Bernoulli's Principle Interface: Uses a specialized MPX5010DP differential pressure sensor connected across an orifice plate. The Arduino captures the pressure drop ($\Delta P$) and uses the Orifice equation to calculate real-time flow (L/min).
Excel Data Streamer: Connects to Microsoft Excel via the "Data Streamer" add-in, allowing for high-resolution logging and 3D charting of fluid dynamics in a lab environment.

High-Speed Sampling

Filter Algorithm: Implements a Moving Average Filter in the firmware to smooth out the turbulent pressure readings, providing a stable and accurate measurement of flow.

MY EXPERIENCE

Here there are some images of the project caught from my thesis : "Progettazione e realizzazione di un misuratore di portata massica su piattaforma hardware open source".