LE 08 - Flow rate measurement with an orifice plate

Objective

Measure the flow rate of water by means of an orifice plate

Material

• Tubes with quick connectors
• Bourdon manometers
• An orifice plate
• Pipe test bench 

What to do

This experiment is based on the Dwyer orifice plate OP series. 

Please, follow the link: OP-C-3, to download the instruction manual of the instrument.

Fig. 01 Dwyer orifice plate OP - C- 3.

For flow measurements, you will need to measure the pressure at the two points specified in the orifice plate instrument and then follow the design equation to give the flow rate. For check on your measurements you can compare your results with that provided by the two rotameters down stream of the orifice plate.

The following data were extracted from the instruction manual,

Weight (lbs)	2.00
Line size (in)	2
Bore (in)	0.72
Beta (in)	0.69
Water flow capacity (GPM)	36.15
Orifice plate thickness (in)	0.125
Temperature (F)	70

How to do it

Step 1

Set up the bench.

• First, fill the water reservoir of the pipe test bench. 
• Next, prime the centrifugal pump (do not forget to set the pump drain screw).
• Once, enough water is in the equipment, check that valves to all pipes are closed except that for the orifice plate. Exit valve should be fully open as well.
• Start the pump and check that water flows and that no air is in the system. If there is air in the pipe, try adding more water into the reservoir.

Step 2

Set up the manometers

Use the analog Bourdon manometers

• The pump should be off.
• Use the tubes with quick connectors to connect the high/low ports of the orifice plate to the manometers.

Fig. 02 Dimensions and parts of the orifice plate.

• Start the pump and check that water flows through the tubes into the manometers.
• Use another tube to purge the manometers line. Use the small purge ball valves to release the air trapped in the system. You should see that all bubbles disappear from the tubes.
• Check your pressure readings in the units of your choice. These should be steady. You should see a pressure difference.

Step 3

Calculations

For water at $70\, F$ the following formula hods with this instrument,

$Q=44.748\, d^2\, K\, Y\, F_a\,\sqrt{\dfrac{\Delta\,P}{\rho_L}}$        Eq. (01)

where

$Q$ is the flow rate in $GPM$

$d$ is the orifice bore diameter in $in$

$K$ is a flow coefficiente (to be estimated)

$Y$ is a expansion factor (Water and most liquids normally=1)

$F_a$ is the thermal expansion factor (Water and most liquids normally=1)

$\Delta\, P$ is the differential pressure in $in\, of\, water$

$\rho_L$ is the density of the liquid at line conditions in $lb_m/ft^3$

The flow coefficient $K$ is estimated from the following equation,

$K=\dfrac{C}{\sqrt{1-\beta^4}}$        Eq. (02)

where $C$ and $\beta$ are defined as,

$C=0.5959+0.0312\beta^{2.1}-0.1840\beta^8+91.71\beta^{2.5}N_{Re}^{-0.75}$

$\beta=\dfrac{d}{D}$

being $D$ the internal diameter of the pipe.

If the Reynolds number $N_{Re}$ is not known $C$ can be estimated as $0.6015$.

Step 4

Checks on calibration curve

A calibration line of $Q$ vs $\Delta\,P$ can also be built following the below dimensionless realtionship,

$\dfrac{Q_2}{Q_1}=\sqrt{\dfrac{\left(\Delta\,P\right)_2}{\left( \Delta\, P \right)_1}}$        Eq. (03)

Several measurements of $Q$ and $\Delta\,P$ shall be needed for plotting the line. Will this line be curve or straight?

This is the end of the post. I hope you find it useful.

Any question? Write in the comments and I shall try to help.

Other stuff of interest

• LE01 - AC and DC voltage measurement and continuity test
• LE 02 - Start and stop push button installation 24V DC
• LE 03 - Turn on/off an 24V DC pilot light with a push button
• LE 04 - Latch contact with encapsulated relay for turning on/off an AC bulb light
• LE 05 - Emergency stop button installation
• About PID controllers
• Ways to control a process
• About pilot lights
• Solving the Colebrook equation

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Ildebrando.