Pressure

Written by Jerry Ratzlaff on . Posted in Thermodynamics

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Pressure ( \(p\) ) 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.

PressureVisual Representation of Pressure

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 FORMULA

Pressure is measured force per unit area:

\(p = \frac {F}{A} \)          \(pressure  \;=\;  \frac { force } { area } \)

Where:

\(A\) = area

\(F \) = force

\(p\) = pressure

Solve for:

\(F = p A \)

\(A = \frac {F}{p} \)

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 Foot2, KSF
 Pascals, Pa Kip per Inch2, KSI
  Pound per Foot2, PSF
  Pound per Inch2, PSI

Absolute PRESSURE

A pressure at absolute zero can only exist in a total vacuum and any pressure above this is called absolute pressure.

absolute PRESSURE FORMULA

\(p_a =  p_g \; + \; p_{atm}  \)          \(absolute \; pressure  \;=\;  gauge \; pressure \; + \; atmospheric \; pressure  \)

Where:

\(p_a\) = absolute pressure

\(p_g\) = gauge pressure

\(p_{atm}\) = atmospheric pressure

Solve for:

\(p_g =  p_a \; - \; p_{atm}  \)

\(p_{atm} =  p_a \; - \; p_g  \)

Atmospheric Pressure

Atmospheric pressure ( \(p_a\) ) 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.

Dynamic Pressure

Dynamic pressure ( \(q\) or \(Q\) ) (also known as velocity pressure) is the amount of total pressure resulting from the media velocity.

Dynamic Pressure formula

\(q = \frac {1} {2} \rho v^2  \)          \(dynamic \; pressure   \;=\;  \frac {1} {2} \;  \left( \; fluid \; pressure  \;\;x\;\; fluid \; velocity^2  \;  \right) \)

Where:

\(\rho\) = fluid pressure

\(q\) = dynamic pressure

\(v\) = fluid velocity

Solve for:

\(v = \sqrt {\frac {2 q} {\rho} } \)

Fluid PRESSURE

Fluid at rest, exerts a force perpendicular to any surface in comes in contact with.

Fluid PRESSURE FORMULA

\(p =  \frac { F } { A }  \)          \(pressure   \;=\;   \frac { force } { area }  \)

Where:

\(A\) = area

\(F\) = force

\(p\) = pressure

Solve for:

\(F =  pA  \)

\(A =  \frac { F } { p }  \)

Fluid PRESSURE at Depth

The pressure exerted on a fluid depends only on the depth of the fluid.

Fluid PRESSURE at Depth FORMULA

\(p =  \rho \; \dot \;  g \; \dot \; h  \)          \(pressure   \;=\;     density  \;\;x\;\;  gravitational \; acceleration \;\;x\;\; height  \)

Where:

\(g\) = gravitational acceleration

\(h\) = height

\(p\) = pressure

\(\rho\) = density

Negative Pressure

Pressure is normally positive, but negative pressure is when the enclosed pressure is lower than the area around it.

Pre-ignition Cylinder Pressure of an Engine

Pre-ignition cylinder pressure ( \(p\) ) is the compression pressure of an engine.

Pre-ignition Cylinder Pressure of an Engine FORMULA

\( p   \; = \;   p_o  \cdot  CR^{\gamma}  \)          \( pre-ignition \; cylinder \; pressure   \; = \;   cylinder \; pressure \; at \; bottom \; dead \; center    \;\;x\;\;    ompression \; ratio^{specific \; heat \; ratio}  \)

Where:

\(CR\) = compression ratio

\(p\) = pre-ignition cylinder pressure

\(p_o\) = cylinder pressure at bottom dead center

\(\gamma\) = specific heat ratio

Pressure Coefficient

Pressure coefficient ( \(C_p\) ) (dimensionless number) is about the relative pressures throughout a flow field in fluid mechanics.

Pressure Coefficient FORMULA

\(C_p = \frac { p \;-\; p_{\infty} }  {  \frac {1}{2} \rho_{\infty} v_{\infty}^2 } \;\)          \(pressure \; coefficient  \;=\;  \frac { free \; steam \; pressure   \;-\;  free \; steam \; density _{\infty} }  { \frac {1}{2} \;  free \; steam \; density _{\infty}  \;\;x\;\;  free \; steam \; velocity_{\infty}^2 } \;\)

Where:

\(C_p\) = pressure coefficient

\(p\) = pressure

\(p_{\infty}\) = free stream pressure

\(\rho _{\infty} \) = free stream density

\(v_{\infty}\) = free stream velocity

PRESSURE DIFFERENTIAL

Pressure differential is the pressure difference between two points of a system.

PRESSURE DIFFERENTIAL FORMULA

\(\Delta p = \frac {   1.59923 p_c d4   \rho   }{ m^2 } \)          \(pressure \; differential   \;=\;    \frac {   1.59923 \; change \; in \; pressure \;\;x\;\;  \left( \; pipe \; diameter  \;\;x\;\; 4  \; \right)   \;\;x\;\;  fluid \; density  }  { mass \; flow \; rate^2 } \)

Where:

\(d \) = pipe diameter

\(m\) = mass flow rate

\(\Delta p\) or \(p_d\) = pressure differential

\(p_c\) = change in pressure

\(\rho\) (Greek symbol rho) = fluid density

Pressure Drop

The difference in pressure between two points, usually caused by friction resistance in the pipe, but moisture can also affect it.

Pressure Drop Formula

A relationship for turbulent flow in commercial steel pipes is:

\(\Delta P = \frac{Q^{1.8} \mu^{0.2}}{C \cdot d^{4.8} \cdot \rho}\)          \(pressure \; loss  \;=\;   \frac{\; flow \; rate^{1.8}  \;\;x\;\;  viscosity^{0.2} }   { carbon \; steel \; pipe  \;\;x\;\;  diameter^{4.8}  \;\;x\;\;   density    }\)

Where:

\(\mathrm {C}\) = 20,000 for rough carbon steel pipe and 23,000 for smooth tubes.

\(d\) = the internal pipe diameter

\(\Delta P\) = pressure loss due to friction

\(\rho\) (Greek symbol rho) = density of the fluid

\(Q\) = flow rate

\(\mu\) (Greek symbol mu) = viscosity

Pressure Gradient

Pressure gradient ( \(p_g\) ) (dimensionless number) describes which direction and at what rate the pressure changes the most at a specific location.

Pressure Gradient FORMULA

\( \frac { d p  } { d x}   \; = \;   \frac { \Delta p  } { \Delta x }  \)

Where:

\(d\) = differential

\(p\) = pressure

\(\Delta p\) = pressure differential, high - low pressure

\(x\) = distance

\(\Delta x\) = distance differential, distance between pressures

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 of an Ideal Gas

 In an ideal gas, molecules have no volume and do not interact.

Pressure of an Ideal Gas Formula

\( p = \frac {n   R   T_a}{V} \)          \( pressure \;=\; \frac {amount \; of \; substance  \;\;x\;\;  specific \; gas \; constant  \;\;x\;\;  absolute \; temperature  }{  volume } \)

Where:

\(p\) = pressure

\(n\) = amount of substance

\(R\) = specific gas constant (ideal gas constant)

\(T_a\) = absolute temperature

\(V\) = volume

Stagnation Pressure

 Stagnation pressure is the pressure a fluid exerts when the velocity of the fluid is zero.

Stagnation Pressure Formula

\( p_s =  \frac { 1 } { 2 }  \rho v^2 \; +\; SP  \)          \( stagnation \; pressure \;=\;  \frac { 1 } { 2 } \; density \;\;x\;\;   velocity^2 \; +\; static \; pressure  \)

Where:

\(p_s\) = stagnation pressure

\(\rho\) (Greek symbol rho) = density

\(SP\) = static pressure

\(v\) = velocity

Surface Pressure

 Surface pressure is a two-dimension analog pressure - the lateral force per unit length applied on a line perperdicular to the force.

Surface Pressure Formula

\( \pi =  \frac { F } { l }  \)          \( Pi \;=\;  \frac { force } { length }  \)

Where:

\(F\) = force

\(l\) = length

\(\pi\) = surface pressure

Working Pressure

Working pressure (WPR) is the normal pressure that a system operates at. Also known as design pressure.

 

Tags: Equations for Pressure