Benjamin S. Valle

email: calmansys@yahoo.com

The measurement of pressure is considered the basic process variable

in that it is utilized for measurement of flow (difference of two pressures),

in that it is utilized for measurement of flow (difference of two pressures),

level (head or back pressure), and even temperature

(fluid pressure in a filled thermal system)

###### Pressure definition

Pressure is the action of one force against another over, a surface.

The pressure P of a force F :distributed over an area A is defined as

P = F/A

Pressure and Area:

For practical purposes, Pressure can be varied considerably for

###### Static, dynamic, and impact pressure

**Static** pressure is the pressure of fluids or gases that are

stationary or not in motion.

**Dynamic** pressureis the pressure exerted by a fluid or gas when

it impacts on a surface or an object due to its motion or flow.

P = F/A

Pressure and Area:

For practical purposes, Pressure can be varied considerably for

any fixed available Force by changing the surface Area. This is

the underlying concept of Hydraulic Systems.

the underlying concept of Hydraulic Systems.

stationary or not in motion.

it impacts on a surface or an object due to its motion or flow.

In the diagram, dynamic pressure is (B-A).

**Impact pressure** (total pressure) is the sum of the static and

dynamic pressures on a surface or object.

dynamic pressures on a surface or object.

Point B in the diagram depict the impact pressure.

Reference or starting point of different Pressure Types

Absolute pressure

Reference or starting point of different Pressure Types

Absolute pressure

The pressure is referenced to zero absolute pressure and has

units of psia. Absolute pressure can only have a positive value

### Gauge pressure

units of psia. Absolute pressure can only have a positive value

The pressure is referenced to atmospheric pressure and by

convention is measured in the positive direction, i.e. 7 psig

###### Compound pressure

convention is measured in the positive direction, i.e. 7 psig

The pressure is referenced to atmospheric pressure and Has

both a positive and negative component, i.e. -0.5" H_{2}O To +0.5" H_{2}O

###### Vacuum pressure

The pressure is referenced to atmospheric pressure and by

convention is measured in the negative direction, i.e. -50 mm Hg

Standard Atmospheric Pressure

both a positive and negative component, i.e. -0.5" H

convention is measured in the negative direction, i.e. -50 mm Hg

Standard Atmospheric Pressure

Pa = Absolute Pressure

Pg = Gauge Pressure

Patm = Atmospheric Pressure

Pa = Pg + Patm (when Pg > Patm)

Pa = Pg - Patm (when Pg < Patm)

Example

Problem: If a pressure instrument has a reading of 30 psig,

find the absolute pressure if the local barometric reading is 14.6 psi

11.5 psig and the atmospheric pressure is 14.6 psia.

**Definition of Pressure Terms**

**Differential Pressure**

The difference in magnitude between two related pressures

**Hydrostatic Pressure**

The pressure below a liquid surface exerted by the liquid above

**Line Pressure **(Static Pressure)

Force per unit area exerted on a surface by a fluid

Solution: Since Pg > Patm

Pa = Pg + Patm

Pa = 30 psi + 14.6 psi

Pa = 44.6 psia

Pa = Pg + Patm

Pa = 30 psi + 14.6 psi

Pa = 44.6 psia

Problem: Find the absolute pressure if a vacuum gauge

reads

reads

11.5 psig and the atmospheric pressure is 14.6 psia.

Solution: When dealing with pressure below atmospheric pressure

Pa = Pg – Patm

Pa = 11.5 psi – 14.6 psi

Pa = 3.1 psia

Pa = Pg – Patm

Pa = 11.5 psi – 14.6 psi

Pa = 3.1 psia

The difference in magnitude between two related pressures

The pressure below a liquid surface exerted by the liquid above

Force per unit area exerted on a surface by a fluid

flowing parallel to a pipe wall

**Vacuum**

Pressure below atmospheric

###### Pressure Measurement Units

Pressure below atmospheric

A number of measurement units are used for pressure.

They are as follows:

1. Pounds per square foot (psf) or pounds per square inch (psi)

2. Atmospheres (atm)

3. Pascals (N/m^{2}) or kilopascal (1000Pa)*

4. Torr = 1 mm mercury

5. Bar (1.013 atm) = 100 kPa

**Atmospheres (atm)**

**Pascals** (N/m^{2}) or kilopascal (1000Pa)

**Torr** = 1 mm mercury

**Bar** (1.013 atm) = 100 kPa

14.696lbf/in^{2} equals 33.9 feet of H_{2}O

14.696lbf/in^{2} equals 29.921 inches of of Hg

**Atmospheres**

In 1954 the 10th Conférence Générale des Poids et Mesures (CGPM)

6. 14.696 lbf/in^{2} equals 33.9 feet of H_{2}O

7. 14.696 lbf/in^{2} equals 29.921 inches of of Hg

14.696lbf/in

14.696lbf/in

In 1954 the 10th Conférence Générale des Poids et Mesures (CGPM)

adopted standard atmosphere for general use and affirmed its definition

of being precisely equal to 1,013,250 dynes per square centimeter (**101,325 Pa**).

This value was intended to represent the mean atmospheric pressure

at mean sea level at the latitude of Paris, France, and as a practical matter,

truly reflects the mean sea level pressure for many of the

industrialized nations (those with latitudes similar to Paris).

**Pascals**

The SI unit for pressure is the pascal (Pa),

The SI unit for pressure is the pascal (Pa),

equal to one newton per square meter.

A Newton (N), the SI unit of force,

A Newton (N), the SI unit of force,

is equal to the force required to accelerate 1 kilogram

of mass at a rate of 1 meter per second squared.

Thus a Pascal is equal to the pressure of 1 newton

over a surface area of 1 square meter

**Torr**

The torr (symbol: torr) is a non-SI unit of pressure defined

The torr (symbol: torr) is a non-SI unit of pressure defined

as 1/760 of an Atmosphere. It was named after

**Evangelista Torricelli**, an Italian physicist and mathematician

who discovered the principle of the barometer in 1644

Torricelli's mercury barometer

Torricelli's mercury barometer

The weight of the mercury in the tube is balanced by the

force of the air on the mercury in the dish

**Bar**

The word bar has its origin in the Greek word βÎ¬ρο (baros), meaning weight.

The word bar has its origin in the Greek word βÎ¬ρο (baros), meaning weight.

Its official symbol is "bar" the earlier "b" is now deprecated, but still often see

especially in "mb" rather than the proper "mbar" for millibars

The bar and millibar were introduced by Sir Napier Shaw in 1909

The bar and millibar were introduced by Sir Napier Shaw in 1909

and internationally adopted in 1929

Example

What pressure in pascals corresponds to 15 psi?

p = 15 psi (6.895 kPa/psi) = 102.9 kPa

Class Exercise

What pressure, in psi, would be indicated by an absolute pressure gauge

Example

What pressure in pascals corresponds to 15 psi?

p = 15 psi (6.895 kPa/psi) = 102.9 kPa

Class Exercise

What pressure, in psi, would be indicated by an absolute pressure gauge

that is lying on a workbench not connected to anything?

**Pressure Units**

As previously noted, pressure is force per unit area and historically

As previously noted, pressure is force per unit area and historically

a great variety of units have been used, depending on their

suitability for the application.

For example, blood pressure is usually measured in mmHg.

**Pressure Units**

The following conversion factors should help in dealing with the various units

1psi = 51.714 mmHg

= 2.0359 in.Hg

= 27.680 in.H2O

= 6.8946 kPa

1 bar = 14.504 psi

1 atm = 14.696 psi

Example

Convert 200 mmHg to psi

200mmHg x 1 psi/51.714 mmHg = 3.867 psi

For example, blood pressure is usually measured in mmHg.

because mercury manometers were used originally.

Atmospheric pressure is usually expressed in mmHg for the same reason.

Atmospheric pressure is usually expressed in mmHg for the same reason.

The following conversion factors should help in dealing with the various units

1psi = 51.714 mmHg

= 2.0359 in.Hg

= 27.680 in.H2O

= 6.8946 kPa

1 bar = 14.504 psi

1 atm = 14.696 psi

Example

Convert 200 mmHg to psi

200mmHg x 1 psi/51.714 mmHg = 3.867 psi

Class exercises

If a cubic foot of water weighs 62.4 pounds, it exerts a pressure

If a cubic foot of water weighs 62.4 pounds, it exerts a pressure

of how many pounds per square inch (psi)?

And what is approximately the pressure, in psi, at the bottom of

And what is approximately the pressure, in psi, at the bottom of

a 20-foot tank filled with a fluid that has a specific gravity of 1.5

Hint

Remember that pressure is force (weight) per unit area and that

Hint

Remember that pressure is force (weight) per unit area and that

Specific gravity (SG) is the density (mass/volume) of a substance

with reference to the density of water. Also remember that

a substance, which has an SG of 1.5, as in this problem,

has 1.5 times the mass of water

Solution:

Imagine a cubic foot of water. It's 12 inches wide,

Solution:

Imagine a cubic foot of water. It's 12 inches wide,

12 inches back, and 12 inches high.

Because the base of this cube of water is 12 by 12,

we know that the base is 144 square inches.

The question asks how many pounds per square inch does

the box exert. Put 62.4 pounds in the numerator and 144

square inches in the denominator, divide, and you get 0.433 psi

Multiply it by 20, we get the psi of the 20-foot-high column

Now we multiply that by 1.5 because the substance in this

problem has 1.5 times the mass of water (0.433 x 20 x 1.5 = 12.99)

Hydrostatic pressure is the pressure which rises above a

certain level in a liquid owing to the weight of the liquid mass

ps = h * ρ * g

ps = hydrostatic pressure (gravitational pressure) [Pa]

h = level of the column of liquid [m]

ρ = density of the liquid [kg/m^{3}]

g = acceleration due to gravity [m/s^{2}]

In accordance with the SI international system of units, hydrostatic pressure

certain level in a liquid owing to the weight of the liquid mass

ps = h * ρ * g

ps = hydrostatic pressure (gravitational pressure) [Pa]

h = level of the column of liquid [m]

ρ = density of the liquid [kg/m

g = acceleration due to gravity [m/s

In accordance with the SI international system of units, hydrostatic pressure

is given in both Pascal and bar. The level of the column of liquid

is given the unit “metre”, the density of the liquid “kilograms per cubic metre”

and the acceleration due to gravity “metres per second squared".

The hydrostatic pressure, or simply “pressure” as it is known for short,

The hydrostatic pressure, or simply “pressure” as it is known for short,

does not depend on the type of vessel used. It is purely dependent

on the height and density of the column of liquid

Column = 300m Reservoir = 15m Elevated Tank = 5m

Which of the three structures will give the highest pressure reading at the base?

Manometer basics

Characterized by its inherent accuracy and simplicity of operation. It’s the U-tube manometer, which is a U-shaped

Manometer basics

Characterized by its inherent accuracy and simplicity of operation. It’s the U-tube manometer, which is a U-shaped

glass tube partially filled with liquid.

This manometer has no moving parts and requires no calibration.

Manometer measurements are functions of gravity and the liquid’s density, both physical properties that make the U-tube manometer a NIST standard for accuracy.

With both legs of a U-tube manometer open

to the atmosphere or subjected to the same pressure,

the liquid maintains the same level in each leg,

establishing a zero reference.

With a greater pressure applied to the left side of a U-tube manometer, the liquid lowers in the left leg and rises in the right leg.

When the liquid in the tube is mercury, for example, the indicated pressure his usually expressed in inches of mercury. To convert to pounds per square inch, P2 = dh

Where P2 = pressure, psig

d= density, lb/in^{3}

h= height, inches

For mercury, the density is 0.490 lb/in^{3} at 60^{O}F (15.6^{O}C),

The liquid moves until the unit weight of the liquid, as indicated by h, exactly balances the pressure.

When the liquid in the tube is mercury, for example, the indicated pressure his usually expressed in inches of mercury. To convert to pounds per square inch, P2 = dh

Where P2 = pressure, psig

d= density, lb/in

h= height, inches

For mercury, the density is 0.490 lb/in

and the conversion of inches of mercury to

Variations on the U-Tube Manometer

pounds per square inch becomes

P2 = 0.490h

P2 = 0.490h

Gauge pressure is a measurement relative to atmospheric pressure and it varies with the barometric reading.

A gauge pressure measurement is positive when the unknown pressure exceeds atmospheric pressure (A), and is negative when the unknown pressure is less than atmospheric pressure (B).

A gauge pressure measurement is positive when the unknown pressure exceeds atmospheric pressure (A), and is negative when the unknown pressure is less than atmospheric pressure (B).

Variations on the U-Tube Manometer

The pressure reading is always the difference between fluid heights, regardless of the tube sizes.

With both manometer legs open to the atmosphere, the fluid levels are the same (A).

With both manometer legs open to the atmosphere, the fluid levels are the same (A).

With an equal positive pressure applied to one leg of each manometer, the fluid levels differ, but the distance between the fluid heights is the same (B).

Reservoir (Well) Manometer

In a well-type manometer,the cross-sectional area of one leg

(the well) is much larger than the other leg. When pressure is applied to the well, the fluid lowers only slightly compared to the fluid rise in the other leg.

(the well) is much larger than the other leg. When pressure is applied to the well, the fluid lowers only slightly compared to the fluid rise in the other leg.

One leg of the manometer is increased many times in area to

that of the other the volume of fluid displaced will represent very little change of height in the smaller area leg. This condition results in an ideal arrangement whereby it is necessary to read only one convenient scale adjacent to a single indicating tube rather than two in the U-type.

that of the other the volume of fluid displaced will represent very little change of height in the smaller area leg. This condition results in an ideal arrangement whereby it is necessary to read only one convenient scale adjacent to a single indicating tube rather than two in the U-type.

The larger area leg is called the well. The true pressure still follows

the principles previously outlined andis measured by the difference

the principles previously outlined andis measured by the difference

between the fluid surfaces.

It is apparent that there must be some drop in the well level.

This is readily compensated for by spacing the scale graduations in the exact amount required to reflect and correct for this "well drop".

This is readily compensated for by spacing the scale graduations in the exact amount required to reflect and correct for this "well drop".

Inclined-tube Manometer

With an inclined indicating tube, 1 in. of a vertical rise is stretched

over several inches of scale length. The inclined-tube manometer has better sensitivity and resolution for low pressures.

over several inches of scale length. The inclined-tube manometer has better sensitivity and resolution for low pressures.

Low pressure and low differentials are better handled with an inclined-tube manometer, where 1 in. of vertical liquid height can be stretched to 12 in. of scale length.

Exercise

When reading a mercury manometer, the center of the meniscus should be

A. Higher than the outer edge

B. Lower than the outer edge

C. Same as the outer edge

D. Level to the outer edge

Exercise Hint

The meniscus is the characteristic upward or downward curving shape

When reading a mercury manometer, the center of the meniscus should be

A. Higher than the outer edge

B. Lower than the outer edge

C. Same as the outer edge

D. Level to the outer edge

Exercise Hint

The meniscus is the characteristic upward or downward curving shape

of a liquid in a glass or tube such as a manometer.

A meniscus happens because there are characteristic surface tensions,

and adhesive and cohesive forces at work in liquids.

If water is in a tube, for example, the adhesive forces between

If water is in a tube, for example, the adhesive forces between

the glass and the water is stronger than the cohesive forces among

the water molecules themselves

Thus,one sees a concave or downward curving meniscus

With mercury, the cohesive forces are much greater

Thus,one sees a concave or downward curving meniscus

With mercury, the cohesive forces are much greater

than the adhesive forces toward the glass wall,

and it has an upward curving or convex meniscus.

The correct answer is A

Pressure Sensing

Pressure is sensed by mechanical elements that are designed and constructed

The correct answer is A

Pressure Sensing

Pressure is sensed by mechanical elements that are designed and constructed

to deflect when pressure is applied.

This is the basic mechanism converting pressure to physical movement.

Next, this movement is converted to an electrical signal for remote indication

Finally, signal conditioning may be needed,

depending on the type of sensor and the application.

The basic pressure sensing element can be configured as

a C-shaped Bourdon tube (F); a helical Bourdon tube (H); flat

diaphragm (A); a convoluted diaphragm (B); a capsule (C); or bellows (D).

diaphragm (A); a convoluted diaphragm (B); a capsule (C); or bellows (D).

C type Bourdon Tube Pressure Gauge

In “C” type Bourdon tube, a section of tubing that is closed

at one end is partially flattened and coiled.

When a pressure is applied to the open end, the tube uncoils. This movement provides a displacement that is proportional to the applied pressure.

The tube is mechanically linked to a pointer on a pressure dial to give a calibrated reading.

When a pressure is applied to the open end, the tube uncoils. This movement provides a displacement that is proportional to the applied pressure.

The tube is mechanically linked to a pointer on a pressure dial to give a calibrated reading.

Helical and Spiral Bourdon Tubes Spiral Bourdon Tube Gauge

Bourdon Helix type are characterized by the following:

High over range (100%)

High pressure approximately 20 coils withstand up to 80,000 psi

Low pressure approximately 3 coils withstand up to 30 psi

Accuracy from 0.25% to 5% of span

Quite often used in filled thermal systems

Low pressure approximately 3 coils withstand up to 30 psi

Accuracy from 0.25% to 5% of span

Quite often used in filled thermal systems

Helical BourdonTube Gauge

Low Range Diaphragm Type Pressure Gauge

Differential Pressure Transmitter setup to measure flowrate.

A d/P transmitter measures differential pressure. In the pipe,

the pressure drop across the restriction will be sensed and

not the 100psi static pressure.

In the tank the transmitter senses pressure equivalent of the liquid height.

The 30psi static pressure is not sensed since it is applied to both sides.

To calibrate a pressure instrument we need a very accurate reference pressure Dead-weight pressure calibrator

To calibrate a pressure instrument we need a very accurate reference pressure Dead-weight pressure calibrator

—Deadweight Testers

The principle of a deadweight tester is very simple. A deadweight tester consists of a piston/cylinder combination and a set of weights. The area of the piston and the mass of the weights have been accurately determined. The calibration fluid **5** is pressurized by means of a ram screw **6** to the point where the piston **1**, including the weights **3**, starts to float, whereby the forces are balanced. Since From Newton’s law force (F) is equal to mass (m) times acceleration (g). Pressure (P) is equal to force divided by area (A). Example: The area of the piston is one square inch, the set of weights is 10 pounds, therefore the pressure generated is

P = __F = 10 lbs__ = 10 psi

A = 1"

The pressure gauge should also read 10 pounds per square inch.

**Advantages of using a deadweight tester:**

High stability

High repeatability

Simple operation. **Disadvantages of using a deadweight tester:**

Not a portable device

Suitable for use in laboratory only

Time consuming

style="margin-top: 0pt; margin-bottom: 0pt; direction: ltr; unicode-bidi: embed; vertical-align: baseline;">Generated pressure cannot be read from a display but has to be calculated from the applied weightsCorrections for gravity and temperature are required

email: calmansys@yahoo.com