Messrs. K and H. assure the public
Their production will be second to none
And of course Henry The Horse dances the waltz

("Being for the Benefit of Mr. Kite," the Beatles, 1967)

 

KEEP YOUR EYE ON THE PRIZE ...
UNDERSTANDING THE DEFINITION OF PRESSURE

PTOA Readers and Students should always remember and never forget that the most recent  PTOA Segments have been focusing on the concept and components that create the PV Pressure.

Admittedly, we've had to get a bit wonky about it.

Your Mentor is pretty sure half of the Process Technology instructors that are engaged reading the PTOA Introduction to PV Pressure Focus Study are thinking:

"Man, I just gloss over the part about defining Force ... even though it is one of the main components of Pressure!"

And most of the rest are thinking ...

"Wow! I always wondered why it was okay to be sloppy about calling a mass a force and vice versa!"

And that's because Process Operators don't ever really use what will be demonstrated in this PTOA Segment #144 ... it's like background muzak no one pays attention to.

However ...

PTOA Readers and Students are not your garden variety future Process Operator! They are self-motivated individuals who strive to understand how things really work!

 

So first let's quickly recap what PTOA Readers and Students who are reading the PTOA Segments in the intended sequential order have recently learned from PTOA Segment #142:

• Pressure is created by a Force which is distributed over an Area.
• The magnitude of the Force is determined by the amount of mass that is moving and the constantly increasing velocity of the mass, aka its acceleration.

It was Sir Isaac Newton that figured all this out for us.

Yep, there he was sitting under a tree and an apple hit his head and the goes and figures out:

• F= m * a which changes into
• F = m * g when the earth's gravity pulls the mass downward and creates a weight force.
• "g" is 32.2 ft/s².

 

Good for Isaac Newton!

But once back in his lab Newton realized the same thing Fred the Stickman realized at the end of PTOA Segment #143 ...

 

The units that are used to define a weight force don't equal the units of the two components that quantify the weight force ... and that's a big NO NO!

Otherwise stated:

F = m * g

but

1 lb_f    ≠    1 lb_m * 32.2 feet/sec²

How can we sleep at night knowing about this blatant inconsistency of units?

 

For the benefit of Fred and all the smart PTOA Readers and Students, Your Mentor will demonstrate in this PTOA Segment #144 how the problem is resolved.

Your Mentor doesn't think it's a waste of written nouns and verbs to perform the demonstration ... even though PTOA Readers and Students will not ever have to do it themselves.

Nor will the Control Room gossip ever be about differentiating lb_f from lb_m and other PV Pressure-related facts.

What will be accomplished is that Your Mentor will henceforth just assume without explaining that the magnitude of an accelerated mass can be declared to be a Force ... and vice versa.

 

INTRODUCING g_c

What do scientists do when they confirm a mathematical relationship exists but still needs a little tweaking?

 

They insert a "fudge factor" that makes the world right again.

g_c is the Earth's surface gravity fudge factor.

The sole purpose of g_c (pronounced "gee sub c") is to make the English units for a weight Force jive on both sides of the defining weight force equation, F= m*g.

The written form of the g_c fudge factor is:

g_c  = 32.2 (lb_m*ft)/(lb_f*s²)

To reiterate ...

The sole purpose of g_c is to make unit equivalency between the magnitude of a weight force and the mass that was accelerated to create that weight force.

And we are okay with this magical solution because we, too, want to interchangeably use the magnitude of an accelerated mass to automatically infer the magnitude of a force ... and vice versa.

So ... just accept this g_c thing and get on with life!

Modern text books get around introducing g_c by promoting the use of "a slug" as the English unit for mass.

Your Mentor will use "slug" as a unit of mass on the same day this bag of apples is sold on the basis of "slugs" instead of lb_m.

And don't stress out!

Especially you, Fred!

This is a one time only demonstration.

 

PTOA Readers and Students are not expected to be in the position to apply g_c ever!

So just suffer through this demonstration.

 

HOW g_c IS USED TO EQUALIZE UNITS

Okay we gotta get back under that dang tree one last time!

There's our boy, Isaac Newton.

The Earth's surface gravity (g = 32.2 ft/s²) pulls that 1 lb_m apple toward the earth and it hits Newton in the head.

Yeah, sure ... we know the weight force created can be explained by the following mathematical expression:

F = m * g

But to make the units work out on both sides of the equation ... g must be divided by g_c.

F= m * g/g_c

Let's first deal with g/g_c:

g/g_c = 32.2 ft/s² / 32.2 [(lb_m *ft)/(lb_f *s²)]

Clearing out all the garbage from the above expression:

g/g_c = 1 * lb_f/lb_m

So ...

F= m * g/g_c

becomes:

F = (1 lb_m) * (1 * lb_f/lb_m)

Clearing out the trash again ...

F = 1 lb_f

Ta-dah!

Fred is happy again!

The 1 lb_m apple and gravity create a 1 lb_f and the world is right again because the units match up!

 

 

SHOW ME WHY I SHOULD CARE ABOUT THE ABOVE g_c DEMONSTRATION

Spoiler alert!

The following is a Sneak Preview about how the PV Pressure is created by any liquid level. 

Did you know that there's 8.34 lb_m of water in one gallon of water?

Remember that 1 foot long by 1 foot high by 1 foot wide container introduced in PTOA Segment #143 ?

Let's figure out the Pressure that is experienced on the bottom surface of a one cubic foot container that is filled with water. 

P = Force / Area

 

First we need to figure out how much water mass would fit in a 1 foot long by 1 foot wide by 1 foot high container ... (aka 1 ft³).

Here's a handy-dandy conversion factor:

There are 7.48 gallons of water in one cubic foot of water (1 ft³).

So it follows that:

8.34 lb_m/gal * 7.48 gal/cubic ft  = 62.4 lb_m water/ft³

Otherwise stated:

"The one cubic foot of water contains 62.4 lb_m of water."

Now there is sufficient information to determine the pressure at the bottom of the container caused by the presence of liquid! Remember:

P = Force / Area

The Area at the bottom of the container is one square foot ... 1 ft by 1 ft ... aka 1 ft²!

P is the pressure that the mass of water is putting on that cubic foot on the bottom of the container:

P = 62.4 lbf/ 1 ft²

However ... in the good ole USA ...

The unit of pressure measurement is "pounds per square inch" ... aka psi ...

So ... the ft² needs to be converted to square inches:

 

P = 62.4 lb_f/ft² * 1 ft²/144 in² = 0.433 psi

P = 0.433 psi

Voila!

The pressure exerted on the bottom of the 1 cubic foot container designed as shown in the picture is 0.433 psi!

That means if we stuck a PI gauge at the bottom of that container that's what it would read!

PTOA Readers and Students will soon learn how Process Operators and Instrumentation Technicians actually use this pressure that is caused by a single foot tall "column of water" to estimate the pressure of any container holding any fluid.

Now ...

Who amongst you PTOA Readers and Students realized that the mass of the water was determined and then we just decided to call it a weight force so that pressure could be calculated.

You don't need to worry about it evermore ... but g_c made that slick move possible by making units of force and mass equivalent!

And now ... forgettaboutit!

TAKE HOME MESSAGES: The PV Pressure is created when a Force is spread out over an Area.

Otherwise stated:

P=F/A

The English unit for Pressure (which is used in the USA process industries) is "psi" which stands for "pounds per square inch."

Any container holding liquid is experiencing pressure pushing on the sides and bottom of the container.  

One cubic foot of water stored in a 1 foot long by 1 foot wide by 1 foot tall container creates a pressure of 0.433 psi on the bottom surface of the container.

PTOA Readers and Students already know that the  Force that creates a Pressure has two components, mass and acceleration; Acceleration is sometimes the pull of gravity, g.

When the acceleration of the mass is due to gravity, a weight Force is created and a fudge factor has to be used to make the units of Force equal the units of mass * g.

g_c ("gee sub c") is the fudge factor that is used when Forces are caused by gravity acting on a mass.

The behind-the-scenes use of g_c explains why it is okay to equate mass to force when determining the Force component of the PV Pressure.

©2016 PTOA Segment 0144
PTOA Process Variable Pressure Focus Study Area
PTOA Introduction to PV Pressure Focus Study

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