In the end it boils down to credibility
I had none, so I will die with the secrets of the sea

("Submarine," by the Lumineers, 2013)

 

HOW PRESSURE IS CREATED AND EXERTED BY A CONTAINED LIQUID

By the time PTOA Readers and Students finish this PTOA Segment #146 they will have combined recently gained knowledge to become experts at determining the pressure created by any liquid that is held in a container of any shape.

PTOA Readers and Students who are reading the PTOA Segments in the intended sequential order learned in PTOA Segment #144 that the pressure created by a 1 foot tall "column" of water is 0.433 psi.

 

PTOA Readers and Students learned in PTOA Segment #145 that the pressure created by a contained liquid depends upon two things:

• The density of the liquid..
• The height (aka "h") of the liquid ... meaning "the length from the surface of the liquid to the submerged point where the pressure of interest is to be determined." Clarification of this wordy phrase is below.

 

WHAT LIQUID "COLUMN"  AKA "COLUMN HEIGHT" MEANS

There must be a jargon term to replace the wordy phrase "the length from the surface of the liquid to the submerged point where the pressure  of interest is to be determined"  ... and there is:

The word is "column."

For example, in the below graphic the "column height" differs for three different tanks.

• The left side tank filled with water has a column height of 100 feet.
• The middle tank filled with brine has a column height of 83 feet.
• The right side tank filled with gasoline has a column height of 133 feet.

Note that the pressure created by all three of the contained liquids is 43.0 psi for each tank.

Keep on reading, PTOA Readers and Students!

You will soon be able to expertly determine the pressure created by a liquid that is held in any kind of container ... and that includes the waters of the seas and oceans that are contained between the continents!

 

LIQUID PRESSURE DEPENDS ON THE HEIGHT ...
BUT NOT VOLUME ...
OF THE CONTAINED LIQUID! 

Who besides Your Mentor thinks it is interesting that the pressure created by a contained liquid is not dependent upon the volume of liquid in the container?

Only the height of the liquid column and the density of the liquid contribute to the pressure that is created and exerted on the interior walls and bottom of the container.

For example ...

Water is in each of the widely diverse containers shown below.

Thus, each of the diversely shaped containers is filled with a liquid that has the same density.

The pressure that is created by the water and exerted on the bottom of each container is also the same ...

4.3 psi in each case ...

because the height of the water column is the same for all three containers (and incidentally h=10 feet which is explained below*).

The PTOA Department of Redundancy Department posts the following bulletin:

THE PRESSURE CREATED BY CONTAINED LIQUIDS DEPENDS ONLY UPON THE LIQUID'S DENSITY AND COLUMN HEIGHT.

THE PRESSURE CREATED BY CONTAINED LIQUIDS DOES NOT DEPEND UPON THE VOLUME OF THE CONTAINED LIQUID.

THE PRESSURE PROFILE OF A CONTAINED LIQUID

The gradually darkening blue shading in the graphic to the left is supposed to illustrate that the pressure increases from zero at the surface of the water to a maximum of 4.3 psi exerted on the bottom of each container.

Gradually increasing pressure is also exerted on the dude shown cannonballing into a pool.

The arrow on the right hand side of the graphic indicates the height of the water column as the dude sinks below the top third of the pool.

The arrow on the left hand side indicates the height of the water column as the dude continues to sink to the bottom of the pool.

The dude would feel more and more pressure on his ears as his body sinks downward.

Here's another way to illustrate how pressure increases with the height of the water column (aka "depth of the liquid)."

Pretend the swimming pool is represented by the plastic bottle with holes punched at several levels A through D as shown below on the left hand side photo.

The weaker stream flowing from Point A gradually increases in strength through Points B, C, and D ...

visual proof that the pressure exerted on the interior walls of the plastic bottle increases with the height of the water column.

If it were possible to attached dinky PIs at each level:

• The PI at the surface of the water would read 0 psi(g).
• The PIs at points A, B, C, and D would indicate increasing magnitudes of pressure.
• If a PI were punched in at the bottom of the plastic bottle, the maximum pressure created and exerted by the contained water would be indicated.

In summary:

The "pressure profile" created by any contained liquid increases with increasing depth of the liquid.

 

HOW TO DETERMINE PRESSURES CREATED BY CONTAINED LIQUIDS

In PTOA Segment #144, PTOA Readers and Students learned that a pressure with the magnitude of 0.433 psi is created by a one foot high column of water.

Guess what?

 

Any multiple of feet will create a multiple order of water-created pressure.

For example, 10 feet of water will create 4.33 psi* because:

4.33 psi = 0.433 psi / foot * 10 feet

So that must mean the pressure created by any height of water column would be:

Pressure (psi) = 0.433 (psi/foot) * h (feet)

where h = height of the water column.

Right On!

The above mathematical expression is used to determine the pressure created and exerted by water that is held in any type of tank or container.

And it does not matter what the shape of the container is or the volume of water in the container.

Only the height of the water column impacts the amount of pressure created and exerted by the water on the interior walls and bottom surface of the container.

 

WHAT IF THE LIQUID ISN'T WATER?

Of course, water is not the only liquid that is contained in tanks.

Gee ...

if only there were a way to relate what we know about the pressure created by water ... and extend the knowledge to other liquids!

Wait, there is!

PTOA Readers and Students just learned in PTOA Segment #145 that specific gravity relates the density of any liquid to the density of water.

Ergo ...

The mathematical expression for determining the pressure created by any contained liquid ... even water ... is:

Pressure (psi) =  SG *  0.433 psi/1 foot   *  h (feet)

where SG = specific gravity.

 

REAL-WORLD APPLICATION:
DETERMINE THE PRESSURE AND FORCE ON THE KURSK

In 2000 the Russian nuclear submarine Kursk suffered an on-board explosion and sank 354 feet (108 meters) taking 118 souls with it to the bottom of the Barents Sea.

The first step of raising the Kursk required the determination of the pressure created by the column of sea water that was above the submarine.

Once this pressure was known, the force borne by the Kursk could be determined ... and this crucial information made it possible to figure out the counterforce required for a successful lift.

This extraordinary graphic drawn by Time Magazine artist Joe Lertola illustrated the challenge of raising the Kursk:

Let's determine the pressure created and exerted by the column of sea water above the Kursk:

P = F/A

P = SG *  0.433 psi/1 foot   *  h (feet)

• The SG of sea water is 1.2  ... so all smart PTOA Readers and Students instantly recognize that salty, cold sea water is more dense than typical surface water.
• The height of the water column above the sunken Kursk was 354 feet.

Therefore the water pressure on the sunken hull of the Kursk was:

Pressure (psi) = 1.2 * 0.433 psi/foot * 354 feet = 184 psi

Wow!

184 psi kind of sounds like a manageable number.

No big deal to raise the Kursk, right?

Well, let's determine how much force was bearing down on the hull of the Kursk.

If

P= F / A

then ... a little rearranging means Force = Pressure * Area or:

F = P * A

To determine the force bearing down on the sunken Kursk, the Area exposed to the hull needs to be known:

The length of the Kursk was = 505 feet

The beam (aka width) of the Kursk was = 60 feet

Therefore the area exposed to the downward force that created the pressure can be calculated:

A = 505 ft * 60 ft  = 30,300 ft² * 144 in² / ft² = 4,363,200 in²

Now there's sufficient information to determine the force bearing down on the hull of the sunken Kursk:

F = P *A =184 lb_f/in² * 4363200 in²=  802,828,800 lb_f !

OMG!

The force bearing down on the sunken Kursk is a whopping 803 million pounds of force!

The take-home message from the above exercise is:

The total magnitude of the force that is impacting a surface and creating a pressure can get lost in translation and thus become underappreciated. The key is the area over which the force is distributed.

 

LET'S GO TO THE MOVIES: DAS BOOT

Who wants to hear the the sound of increasing pressure as a submarine sinks?

Netflix and chill!

Your Mentor's all time favorite movie is the 1981 classic Das Boot ... English translation "The Boat."

 

 

In this case a German U-boat (U-96) sinks until it comes to rest on the bottom of the Strait of Gibraltar.

The depth of 280 meters (919 feet) exceeds the design parameters of U-96.

PTOA Readers and Students can hear the life-like sound of the pressure created on the hull of U-96 until it lands on "a shovel full of sand."

Here's a couple Do-It-Yourself (DIY) Exercises:

What is the pressure that is exerted on U-96 as it sat on the bottom of the Strait of Gibraltar?

What is the maximum pressure exerted by the water at the shallow and deep ends of the swimming pool shown below?

The answers to these DIY questions  will appear at the end of the PTOA Introduction to PV Pressure Focus Study.

TAKE HOME MESSAGES: The pressure created and exerted by a contained liquid does not depend upon the volume of the liquid but just the density and height of the liquid "column."

The jargon word "column" means "the distance between the surface of the water and the depth to which the exerted pressure is being determined."

The following mathematical expression is used to determine the pressure created and exerted by any contained liquid on the interior surfaces and bottom of the container:

P = SG *  0.433 psi/1 foot   *  h (feet)

Where:

• SG = the Specific Gravity of the contained liquid
• h = the height of the liquid column in feet.

The pressure profile for the pressure exerted by a liquid is 0 psig at the liquid's surface and increases to a maximum pressure which is exerted on the bottom of the container.

PTOA Readers and Students need to be vigilantly aware that the amount of pressure exerted often infers a very large force. The key between the two is the Area over which the force is distributed to create the Pressure.

©2016 PTOA Segment 0146
PTOA Process Variable Pressure Focus Study Area
PTOA Introduction to PV Pressure Focus Study

You need to login or register to bookmark/favorite this content.