Pressure
Pressure, abbreviated as p, is one of the most important concepts in piping design. Simply put, it is the force exerted perpendicular to the surface of an object and is expressed as force per unit area. Why is this important? The purpose of a pipe or pressure vessel is to keep pressure contained in a specific location. Differential pressure is also what causes fluids to move. It will always flow from high to low pressure. Pressure differences introduced by a pump or compressor will cause the fluid to flow.
Pressure is a scalar quantity having direction, some of these include area, density, energy, entropy, length, mass, power, speed, temperature, volume, and work.
There are several different types of pressure, each used for different things. For example:
Absolute Pressure  Absolute pressure is the pressure in the piping that takes into account the atmospheric pressure. No matter where you are on earth, the atmosphere exerts a pressure force on everything. Absolute Pressure is useful when calculating the net positive suction pressure for a pump.
Gauge Pressure  Gauge Pressure is the difference of pressure that is measured by the gauge.
Differential Pressure  Differential pressure is used to describe the amount of pressure created by a pump or compressor. It also is used for pressure drop in a pipe, piece of equipment or an orifice plate.
pressure Calculator

Pressure formulas
\(\large{ p = \frac{F}{A} }\)  
\(\large{ p = \rho \; g \; h }\)  (caused by liquid) 
\(\large{ p = K \; \frac{V_c}{V_i} }\)  (bulk modulus) 
\(\large{ p = \frac {Ca\; \rho\; U^2} {2} + p_v }\)  (Cavitation number) 
\(\large{ p = \frac{ n \; R* \; T }{ V } }\)  (ideal gas law) 
\(\large{ p = \rho \; R \; T }\)  (ideal gas law) 
\(\large{ p = \gamma \; \left( NPSH  \frac{ v^2 }{ 2 \; g } + \frac{ p_v }{ \gamma } \right) }\)  (net positive suction head) 
\(\large{ p_b = p_t + \rho \;g\; h }\)  (Pascal's law) 
\(\large{ p_t = \rho \; g\; h  p_b }\)  (Pascal's law) 
Where:
\(\large{ p }\) = pressure
\(\large{ A }\) = area
\(\large{ K }\) = bulk modulus
\(\large{ Ca }\) = Cavitation number
\(\large{ U }\) = characteristic velocity
\(\large{ \rho }\) (Greek symbol rho) = density
\(\large{ F }\) = force
\(\large{ g }\) = gravitational acceleration
\(\large{ h }\) = height of the liquid column
\(\large{ n }\) = mole
\(\large{ NPSH }\) = net positive suction head
\(\large{ p_b }\) = pressure at bottom of column
\(\large{ p_t }\) = pressure at top of column
\(\large{ R }\) = specific gas constant
\(\large{ \gamma }\) (Greek symbol gamma) = specific weight
\(\large{ T }\) = temperature
\(\large{ R* }\) = universal gas constant
\(\large{ p_v }\) = vapor pressure
\(\large{ v }\) = velocity
\(\large{ V }\) = volume
\(\large{ V_i }\) = initial volume
\(\large{ V_c }\) = change in volume (volume differential)
Typical Units
Some common units for pressure are as follows. For a more complete list, visit the pressure conversion page.
INTERNATIONAL SYSTEM OF UNITS, SI 
ENGLISH UNITS 

Bar  Inches of Mercury 
Centimeter of Mercury  Inches of Water 
Centimeter of Water  Kip per Foot^{2}, KSF 
Pascals, Pa  Kip per Inch^{2}, KSI 
Pound per Foot^{2}, PSF  
Pound per Inch^{2}, PSI 
Atmospheric Pressure
Atmospheric pressure, abbreviated as \(p_a\), is the pressure exerted upon the earth's surface by the air because of the gravitational attraction of the earth. Standard atmosphere pressure at sea level is 14.7 pounds per square inch (psi). Measured with a barometer.
Negative Pressure
Pressure is normally positive, but negative pressure is when the enclosed pressure is lower than the area around it.
Pressure Instruments
In piping design, pressure is measured several different ways. On a Piping & Instrumentation Diagram, the typical instruments are:
Pressure Indicator  A pressure indicator is a pressure gauge. It is a mechanical device, that is calibrated to display a pressure.
Pressure Transmitter or pressure indicating transmitter  This is used to display the pressure in the equipment and send an analog signal to a computer for futher processing. It might be used as an alarm in case the pressure gets outside normal operating conditions.
Pressure Switch  A pressure switch is used to send a digital signal (yes or no, 1 or 0) to a computer for an action to be performed. E.g. send an alarm, turn off a pump, etc.
Pressure Temperature