Flow Rate

[mick88]

One for the technical minded or mathematical minded!
If a 12 mm restrictor was placed in a two inch (50.8mm) pipe what would be the reduction in flow rate/volume. Would 12 mm only allow 25% of 50.8 through or would it be even less?
Lets say at 15 psi if you need to have a pressure.


Thanks and cheers,
Mick.

[p38arover]

This sounds like one of those calculus questions we had at high school. I've forgotten pretty much all of any calculus that I may have known.

[Toxic_Avenger]

Wolfram alpha knows!

flow rate calculator - Wolfram|Alpha (http://www.wolframalpha.com/input/?i=flow+rate+calculator&lk=4)

If water is the fluid, 15psi upstream pressure and 0.058m upstream, 0.012m downstream, then I got 1.628L/s flow

If I recall correctly from some past studies, the change in flow rate is not linear in regards to diameter.

https://www.aulro.com/afvb/images/imported/2015/01/666.jpg
p1 : Primary Pressure (kPa abs)
p2 : Secondary Pressure (kPa abs)
do : Diameter of Orifice (mm)
C : Discharge Coefficient
Qw : Water Flow Rate (m3/h)
FL : Pressure recovery factor (=0.9)
FF : Critical pressure ratio factor
P : Absolute vapor pressure of the water at inlet temperature (kPa abs)
SG : Water gravity (kg/m3)

[Toxic_Avenger]

... and using this calculator Calculator: Water Flow Rate through an Orifice | TLV (http://www.tlv.com/global/TI/calculator/water-flow-rate-through-orifice.html)

I got 73.36cubic meters per hour at the 2" pipe,
and only 4.09cubic meters per hour with the 12mm pipe

so by increasing the orifice diameter by 4x the original diameter, you are getting ~17x the flow.

[Fluids]

I do this stuff at work numerous times every week .... So much so that I have a set of charts that I refer to as it's way quicker to just look it up instead of having to calculate it every time.

Charts are at work ....

If you need a second opinion :) let me know and I'll check on Monday.

Sent from my iPad using Braille

[Toxic_Avenger]

I do this stuff at work numerous times every week

^^^
Listen to this bloke!

[Blknight.aus]

Water or air?

The roughtimation I use when all else but diamter remains constant is the square of the ratio between the diameters.

It's not super accurate but it gets you in the ball park.

50:12 is near enough 4:1. Square it and you wind up with 16.

If all else remains unchanged you'll get about 16 times Moe flow out of the bigger pipe.

[mick88]

Thanks guys!
I suspected approx. 17 times more volume, however I just did the pi R squared thing to find the area of circle and went from there but I didn't know if it related to the volume of liquid that would pass through the orifice.


Fluids I would be very interested to see what your ready reckoner chart reads too please.


Thanks, Mick.

[Fluids]

Pretty much what the others have said ...

2" open flow with 15psi upstream pressure discharging to zero psi downstream pressure (atmosphere) - 1466l/min

1/2" orifice inserted in (assumed) the end of the pipe so we have 15psi upstream pressure and zero psi downstream pressure (again assuming discharging to atmosphere) - 92l/min.

Approx' 16x

This is a close approximation as the shape of the lead up to the orifice (tapered, parallel, etc), the shape of the orifice (square edged, rounded edge ... inlet/entry side AND outlet/exit side will affect the actual figure) ... then any backpressure on the discharge/exit side of the orifice plate will also affect the result (head & pipe friction on the discharge/exit side).

The relationship is an inverse proportion law. Doubling of the pipe diameter will give 4x the flow rate at the same upstream pressure.