Science and Math of flowbenching

[gijoe985]

Hey all,

I have lurked this forum a little bit over the last few years. I knew I wanted to build one, but also knew it wasn't the time. Either way, I am a high school auto shop teacher and I have been wanting to make a flowbench for our school. One of the things that would help me sell the idea is by showing the math and science/physics that the kids could learn from a flow bench. I was just hoping that some people could give me some examples. While I know some myself, I'm sure the collection of knowledge on here could help create a list quickly.

What I am looking for is something like this-

They will learn "this" math skill by doing "this" or when they have to calculate "that".
Or, by understanding "this" law of physics they can get better flow results.

And if you don't know the name of the math skill or formula, I can get that part. I don't expect everyone to be teachers... But listing off some of the procedures you would do for testing and for analyzing results would be a start.

[blaktopr]

You can basically have a week about pressure differentials. It's how the bench works, a plane flies, makes engines run, makes wind blow, I can go on and on.
Beruilli principal.

If you need more, you will find it here. I will come up with some others also.

Chris

[blaktopr]

Hey all,

I have lurked this forum a little bit over the last few years. I knew I wanted to build one, but also knew it wasn't the time. Either way, I am a high school auto shop teacher and I have been wanting to make a flowbench for our school. One of the things that would help me sell the idea is by showing the math and science/physics that the kids could learn from a flow bench. I was just hoping that some people could give me some examples. While I know some myself, I'm sure the collection of knowledge on here could help create a list quickly.

What I am looking for is something like this-

They will learn "this" math skill by doing "this" or when they have to calculate "that".
Or, by understanding "this" law of physics they can get better flow results.

And if you don't know the name of the math skill or formula, I can get that part. I don't expect everyone to be teachers... But listing off some of the procedures you would do for testing and for analyzing results would be a start.

http://en.wikipedia.org/wiki/Venturi_tube#Venturi_tubes
http://en.wikipedia.org/wiki/De_Laval_nozzle
I like this one, animated
http://home.earthlink.net/~mmc1919/venturi.html
http://en.wikipedia.org/wiki/Fluid_dynamics

Here are some equasions care of Larry Meaux.

Estimated total engine Air Flow = (cid/2)*rpm*ve

Engine CFM demand at max piston speed = (cid * RPM * .000978474) / (number of cylinders)

Engine CFM demand Average = ((cid * RPM * .000978474) / (number of cylinders))*.6872



360 = ( 12 inches * 60 seconds ) / 2 Revolutions ...for 4 Cycle

282.7433388 constant = 360 * .785398163

.003536777 = 1 / 282.7433388

2.4 = ( 144 Sq.Inches / 60 Seconds )

.416666667 = 1 / 2.4

rearranging equations around

RPM = ( FPS * CA ) / ( Bore * Bore * Stroke * .00353 )

where;
RPM = point of desired Peak HP
FPS = Feet per Second
CA = Cross-Sectional Area in Square Inches (smallest measured)


FPS = ( Bore * Bore * Stroke * RPM * .00353 ) / CA


CA = ( Bore * Bore * Stroke * RPM * .00353 ) / FPS


Example=> ProStock 500 cid

4.115 Sq.Inch Area = ( 4.687 * 4.687 * 3.62 * 9000 * .00353 ) / 613.9758744

where 613.9758744 = .55 Mach



Speed_of_Sound_FPS = (( 459.67 + TempF) * 2402.625624 ) ^ .5

1116.319772 fps @ 59 F

.55 Mach = 613.9758744 fps

Speed_of_Sound = (( 459.67 + TempF) * 1.4 * 32.174 * 53.34 ) ^ .5

Speed_of_Sound = (( 459.67 + TempF) * 1.4 * 1716.567377 ) ^ .5

and the easiest equation is

Speed_of_Sound = (( 459.67 + TempF ) ^ .5 ) * 49.02

TempF = temperature in degrees Fahrenheit

459.67 = Rankine degrees

=============================================

In your calc. you use
"314.5 = Air velocity in Feet per Second " how is that measured, on the flow bench or engine?

its calculated or guesstimated
306.7 to 314.5 FPS range is about 1/2 the .55 Mach number (613.98)
its represents the average port velocity baseline starting point
..you could use a number of your own to correlate your data

on the FlowBench, you would never "calculate or guesstimate" this
you would instead measure Port Velocity with a 180 degree or "U" or "J" shaped Pitot Probe attached to a 48" inch or so Vertical Manometer

the Pitot Tube would accurately account for Port's corner radius effects
..you can use equations to account for that, but the Probe is better/quicker/accurate

if your Pitot Probe Pressure in Inches of water "exceed" or equal your Test Pressure..theres are good chance you are already in or close to being into Choke under live conditions

you can get into a Choked port "sooner" than your Test Pressure number
..just depends how far the Choke's smallest-area is away from the
valve , and what are differences in pressure between the Short Turn Pressure and the Choke pressure

on the Short Turn's Apex you can flip the Pitot Probe upside down and attempt to measure localized velocity there on the apex...but that area seems to be worth 5 to 25 HP Losses if too high...but if the Port's Velocity in the smallest cross-sectional area is "too-high" its worth 50 to 100+ HP Losses..just depends on how far this area is from the valve

just like the Valve's Curtain Area in the Lift Curve will be the final Choke,
the Short Turn's Apex speed/pressure will be the next choke point,
then further up the smallest cross-sectional area Choke point

if you have a CA Choke point..it will control or dominate the port,..it will cause greater HP Losses than the Short Turn apex localized velocity

the straighter the Port (like a straight piece of tube)
the higher the velocity fps can be without flow separation or choke
the higher the fps...the higher the Volumetric Efficiency attainable

heads like #292 Turbo, #034 Bowtie, #461, #462, etc
all had "potential" pushrod area choke problems


Can you please explain L/D ratios

the L/D Ratio is just

Valve_Lift / Valve_Diameter

.3732 Ratio = .724 Lift / 1.940 OD Intake valve


.4215 Ratio = 1.060 Lift / 2.515 OD Intake Valve

if you look at any Flow Curve...the Flow rate increase is pretty good until you reach .25 L/D Ratio..then the Flow rate increase really drops off

the older style heads with poorer design/shaped Ports, can't handle the air velocity as well as modern shaped ports...so increasing L/D Ratio above .37 to .39 usually shows no Dyno gains, and most times HP Losses above .39 L/D ...whereas, ProStock style heads like .41 to .42+ L/D Ratios

all you'll do with older heads above .39 L/D Ratio is slow down the Curtain Area velocity and increase the pressure differential between a possible choke point further up the Port ..like at the pushrod area ...causing the Port to go into Choke sooner in the Lift Curve.Meaux Racing Heads
MaxRace Software
PipeMax and ET_Analyst for DragRacers
http://www.maxracesoftware.com
http://maxracesoftware.com/bulletinboar ... cesoftware
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[1960FL]

GiJoe,

I would start with a couple of basic points when it comes to this lesson and possible Class Projects.

First, I would look at some of the math it may be above the High School level or at least for those who are taking auto shop and not heading off to engineering school.

The first lesson would be fun and bring up our old friend the Pito tube bench, and this is a very simple concept to grasp when talking about measuring air flow. One, use a simple Pito tube to measure the speed of the air in a known diameter tube and you can tell how much air is flowing through the tube. I/E a 2” ID pvc pipe has Pito Tube in it, we use some basic geometry to calculate the area of the inside of the tube (pi * R squared).

Next we need to know the speed of the air flowing through the pipe this is done with the Pito-Static tube ( http://en.wikipedia.org/wiki/Pitot_tube ), for this basic lesson you can just use a Pito-Static tube centered in the pipe. For a flow element that were we want to be extremely sensitive and accurate across a wide range of air flow we use a device called an averaging Pito tube.

Once we have done the basic math and have calculated the speed of the air moving through the pipe we use basic algebra to calculate the volume of air flowing through the pipe. So lets say your Pito calculations tell you the air is moving at 100fps the area inside the 2” pvc pipe is 3.14159* (1 squared) or 3.14159 * 1 = 3.14149 sq/inches thus in 1 second of time the air would have moved a length of 100 feet or 1200 inches. How much area is this (think volume of a cylinder) Pi * R squared * Height or
(3.14159 * (1*1)) sqinchs * 1200inch = 3.14159*1200 or 3769.9 Cubic inches in a second of time
Well if one cubic foot is 12*12*12 or 1728 Cubic inch’s then we have 3769.9/1728 or
2.18 Cubic feet per second of air. Now we need to convert to CFM or Cubic Feet Per Minute, in this case it is very simple as there are 60 seconds in a minute we must multiply by 60 thus 2.18 CFS * 60 = 130.8 CFM

As a side note/lesson and could be some great fun for the students if you will have access to a digital monometer, would be to set up an experiment where in using the Pito Static probe they would perform the math to convert the measured air speed to Miles Per Hour then attach the device (Pito Static Probe they make) to a car and use it as a speedometer to test/calibrate there probe, just like on an airplane.

Once you have a complete understanding of the Pito tube style bench you will see its deficiencies as it is affected (Mathematically) bay so many variables that make up air density.

Now is the time to move on to the orifice bench and begin to discuss the principle of its design and the benefits there in (Ratiometric Design) un effected by altitude and air density etc. (http://en.wikipedia.org/wiki/Orifice_plate ) This discussion will take you on to Bernoulli’s Principle and this is where the math gets a little more complicated ( http://en.wikipedia.org/wiki/Bernoulli's_principle ). This is the basic principle of the PTS bench and the ideal way to go. The concept is if I have a known hole diameter with a known CD Coefficient of discharge and I know the pressure on each side of the plate then X amount of fluid is flowing through the hole.

I hope this gets you started on your project I will check back in to fill in any blanks along the way.

Rick

[DaveMcLain]

This is some very good information, thank you for sharing.

[kennedyrd]

I am just reading a great book "Engine Airflow" by Harold Bettes. It could also be named "Flow Bench Math(s) for Dummies". I think it could provide many good math/physics equations related to the flow bench, from very simple to advanced.