Head games, and I can't take it anymore
Head games, I don't want to play the head games

("Head Games," by Foreigner, 1981)

 

FINAL POINTS ABOUT STATIC LIQUID PRESSURES

PTOA Readers and Students who are reading the PTOA Segments in the intended sequential order recently learned how a "column of liquid" creates a pressure on the interior walls and bottom surface of a container ...

even the exposed surface of a sunken submarine like the Kursk!

PTOA Readers and Students thoroughly understand that the pressure created by a liquid depends only upon the liquid's:

• height and
• density

PTOA Readers and Students learned how the below expression for  Pressure ...

P = F/A

... can be rearranged to determine the Force that created the pressure like this:

F = P * A

Furthermore, smart PTOA Readers and Students learned in PTOA Segment # 144 that the magnitude of the Force that creates a Pressure is equal to the Mass that creates the Force as shown in the below expression:

F = m * (g/g_c)

So there's just a few more connect-the-dot points to cover and one important jargon term before moving on to other PV Pressure fundamentals.

 

NEW JARGON WORD: HYDROSTATIC HEAD

PTOA Readers and Students recently learned in PTOA Segment #145 that the height of a "column of liquid" is directly related to the pressure that the contained water creates and is measured in units of length ... like feet or meters.

In industrial processing, the term "hydrostatic head" ...

and actually the more abbreviated term "head" ...

is used instead of "column of liquid."

Head is also measured in feet or other units of length.

Head can be quite a long distance.  Note the term head illustrating the very long column of liquid in the below graphic:

The PTOA will also use the terms "hydrostatic head" and/or "head" from now on.

In the below mathematical expression that defines pressure, the "h" now stands for "head":

Pressure (lb_f) = SG * 0.433 lb_f/foot * h (ft)

 

A COUPLE MORE FACTS TO APPRECIATE ABOUT CONTAINED-LIQUID PRESSURE

A Contained Liquid Exerts Equal Pressure in All Directions 

PTOA Readers and Students already know that the pressure profile of a contained liquid increases with:

• height of the liquid column ... which is also called the
• depth of the liquid ... which has just recently been renamed to ...
• hydrostatic head of the liquid.

A plastic bottle is shown punctured at successively lower points A,B,C,D in the below photo on the left-most side.

The head at point A is shorter than the head at point B which is shorter than the head at point C and point D has the longest hydrostatic head.

The left side photo illustrates that the pressure profile is directly related to hydrostatic head:

The greater the hydrostatic head (h) the greater the pressure exerted on the walls and bottom surface of the container.

Now it's time to focus on what the picture to the right is telling us:

The right side picture shows water flowing at equal intensity from a plastic bottle that has been punctured at 5 places ... each with the same hydrostatic head.

This happenstance may seem like a small potato ...

however ...

The natural conclusion to draw from this observation of equally exerted pressure from a uniform head infers ...

every little drop of liquid in a container is exerting an equal pressure in all directions.

Hey, you've already felt this contained-liquid phenomenon when swimming in a pool!

The water beneath you is exerting pressure in all directions and is pushing you up with a buoyant force.

The water above you is pushing down in all directions.

Ergo ...

Next-door-neighbor horizontal drops of water in a container are exerting equal pressure on each other.

But two stacked drops of water do not exert the same pressure on each other because ...

a drop that lies directly below another drop is exerting more upward pressure because it is at a slightly greater depth (aka head).

Now that might seem like no big deal but it's actually the basis of using hydraulic pressure in many commercial and industrial applications ... like lifting up a vehicle for service.

The dude that figured out how contained liquids create pressure was named Blaise Pascal.

Fun fact:

The SI unit for pressure is named after Pascal.

 

P = F / A

 1 Pascal = 1 Newton/M² =  0.000145 psi

If you don't remember what the SI unit of force is ... here's the definition of Newton again:

 

Gas "Blankets" Above Liquid Levels

When Your Mentor was a newbie Process Operator many years ago ...

On my first day of work more senior shift mates got a big yuk instructing me to go to the warehouse to requisition a "nitrogen blanket."

One type of head game.  Yuk.Yuk.Yuk.

A gas blanket has nothing to do with keeping a body warm.

Smart PTOA Readers and Students will not be so deceived.

The vast majority of tanks in a processing facility are not going to be open to the atmosphere.

A gas blanket fills up the vapor space above the contained liquid surface and thus keeps other bad actors from reacting with the tank contents.

Nitrogen gas (N₂) might be the gas blanket for a tank that contains highly volatile liquids because nitrogen does not react with chemical compounds and is readily available (it can be separated from air).

If safety allows, a gas blanket might be supplied by piping in natural gas (mostly methane, CH₄) because in many locations natural gas is cheaper than making nitrogen.

The gas blanket is held at a set pressure by a pressure regulator.

When the level in the tank decreases, more gas enters the tank to maintain the set point pressure of the gas blanket.

When the tank is being filled with more liquid, the entering liquid displaces some of the blanket gas and it exits via a vent or might be discharge into a vapor recovery system  (required in the modern USA processing facility).

Here's the important point about gas blankets:

The total pressure exerted by the contained liquid includes the pressure created by the gas blanket in the vapor space above the liquid level.

To account for gas blanketing, the mathematical expression for head plus blanket pressure is:

Pressure = (S.G. * 0.433 lb_f/ft * h (ft)) + Blanket Pressure (psi)

Let's assume the below tank is dedicated to gasoline service (SG = 0.75).

The current level in the tank is 20 feet.

The nitrogen gas blanket is held at 10 psi by the pressure regulator.

The total  pressure at the bottom of the tank is thus partially from head pressure and partially from the gas blanket:

Pressure = S.G. * 0.433 psi/ft * 20 feet + 10 psi

= 0.75 * 0.433 * 20 + 10

= 6.5 psi + 10 psi = 16.5 psi

NOTE: In this particular case the majority of the pressure exerted on the tank bottom comes from the gas blanket.

That may not always be the case.

Just remember to always add the pressure of the vapor space to the head pressure when determining the total pressure exerted on the interior walls and bottom surface of a container.

 

USES OF LIQUID PRESSURE

There are many uses of head pressure in the process industries.

PTOA Readers and Students will learn in a future PTOA PV Level Focus Study that head pressure can be used to measure the PV Level in process services that are too yucky to use other forms of level measurement (e.g., sewage slurry storage).

One of the most important and common uses of head pressure is electricity production via hydropower.

Hydropower is power that is produced when the force of water created by head turns the blades of a turbine that is coupled to an electricity generator.

The below schematic shows the head that extends from the "Forebay" to the "Powerhouse."

Although the water flows downward at a slant to the powerhouse, the head is the vertical distance between the Forebay and the Powerhouse through the Penstock (not labelled in the schematic).

The water supply may come from a dam as shown in this illustration of hydropower generation of electricity …

 

... or any source of pooled liquid that is at rest and is well mixed so that the specific gravity is constant throughout.

Here's the DIY Question for this PTOA Segment #147:

Why is the dam shown in the above schematic wider at the base than at the top?

 

TAKE HOME MESSAGES: This PTOA Segment #147 featured some final points about pressure that is created by a contained liquid.

"Hydrostatic Head"  or just "Head" will henceforth replace the term "column of liquid" in the PTOA.

Any contained liquid that has a constant specific gravity throughout and is at rest exerts a pressure and force that is easy to determine. 

The pressure of the gas blanket that is intentionally piped in above the vapor space of a contained liquid contributes to the overall pressure exerted by the liquid on the interior walls and bottom surface of the container.

The mathematical expression that explains the above paragraph is:

Pressure = (S.G. * 0.433 lb_f/ft * h) + Blanket Pressure

A drop of contained liquid exerts equal pressure in all directions. (That's Pascal's Law).

Pascal's Law explains buoyancy of water and why hydraulics can be used to create huge pressures and then have their forces do hard work.

There are a multitude of commercial and industrial uses of head pressure, for example:

Since hydrostatic head is directly proportional to the pressure exerted ... a linear relationship can be used to infer the PV Level.

Electricity produced by a hydropower plant is one common industrial application of head pressure.

©2016 PTOA Segment 0147
PTOA Process Variable Pressure Focus Study Area
PTOA Introduction to PV Pressure Focus Study

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