What is the formula for pressure difference

Physical size
Surname print
Size type mechanical tension
Formula symbol of size p (1)
Derived from engl. pressure
Size and
System of units
unit dimension
(1) numerous other symbols for special pressures
(2) further units: N / mm², not SI-conform:Torr, at (ata, atü, atu), atm, psi, mm Hg (inHg)
See also: absolute pressure, air pressure, gauge pressure, atmospheric pressure difference

The print is an intensive physical state variable of thermodynamic systems and also a linear field variable.

In general:

 – Pressure is force per area, provided that the force is normal to the surface
... force force)
A. ... area area)

Formula symbol is p (from Engl. pressure) and its derived SI unit is the Pascal Pa. The formula symbol must not be associated with the service P. (from Engl. power) or with the impulse p be confused.

The concept is a simplification of the general stress tensor. The compressive stress is in contrast to the pressure no scalar state variable. The mechanical tension has the same physical dimension as the pressure, namely force / area. The pressure represents a special case of mechanical tension.

Pressure in flowing media


The pressure in flowing media consists of a static and a dynamic component. While both parts depend on the density, they differ in that the (hydro) static pressure, for fluids with constant density, increases linearly with the height of the fluid column. In addition, it is dependent on the acceleration of gravity, i.e. gravity. The dynamic component, on the other hand, increases quadratically with the flow velocity of the fluid. The picture on the right shows the constancy of the sum of the dynamic and static components in a frictionless flow. This is the consequence of the conservation of energy in the flow and, for this special case, known as Bernoulli's law.

Hydrostatic pressure

The hydrostatic pressure exerts a force on every surface that is in contact with the fluid, which is proportional to the size of the surface - the larger the surface, the greater the force acting on it. This form of pressure is therefore a special form of elastic tension that is inherent in ideal liquids and gases: in the ideal (frictionless) liquid there are only normal stresses, precisely that hydrostatic pressure. It is different in a real (friction-prone, viscous) liquid, because here tangential or shear stresses can also occur as a result of the frictional forces. In Mohr's stress circle, the hydrostatic pressure is therefore represented as a simple point. Examples of hydrostatic pressure are water pressure and air pressure.

The hydrostatic pressure in a column of fluid at a height H (on a y-axis) and the density ρ under the effect of the acceleration of gravity G, where p (y = 0) means the pressure on the surface of the fluid column, results from the basic hydrostatic equation as a special case

Hydrodynamic pressure

The hydrodynamic Pressure, or even shorter the dynamic pressure, results from the kinetic energy of a mass-afflicted body moving at a speed, the so-called fluid speed. According to Daniel Bernoulli, it is therefore the name for the reduction in hydrostatic pressure that occurs due to the movement of a liquid.

The speed can only increase from larger to smaller cross-sections if the pressure in the smaller cross-sections is lower and vice versa. The flow thus creates a hydrodynamic reduction in pressure in smaller cross-sections, and an increase in larger cross-sections, as a result of which the pressure conditions at rest - the hydrostatic pressure - are changed. The hydrodynamic pressure cannot be measured directly, but is used to measure the speed of the fluid. The following applies:

Gas pressure

The Gas pressure arises as the sum of all forces acting on a vessel wall by a gas or gas mixture. If a gas particle hits a wall, they exchange an impulse. The warmer the gas, the faster the particles and the greater the pressure. The momentum transfer depends on the kinetic energy of the gas particle. It also depends on the direction in which the particle hits the wall. For many particles these momentum transfers add up to a total force. This mainly depends on the number of particles that hit the wall per unit of time. The gas pressure is also obtained by adding all the partial pressures of the components of the gas mixture. Vapor pressure and saturation vapor pressure also represent special forms of gas pressure. Air pressure is an example of a gas pressure.

The kinetic gas theory delivers the equation of state from the mechanical and statistical considerations mentioned:

which can also be used as a definition of pressure as an intensive quantity for thermodynamics (see also fundamental equation). For an ideal gas this leads to the thermal equation of state:

Various formulas for the gas pressure can be derived from it:

From the kinetic gas theory it follows:

The individual symbols stand for the following quantities:

The averaged momentum transfer is contained in the product of the gas constant and temperature of the equation of state. Both terms can be converted into one another by means of piston sample experiments. Equivalent to the definition above, the gas pressure can also be understood as a hydrostatic stress tensor, as it is known from mechanics.


The SI unit of pressure is the pascal with the unit symbol Pa. One pascal corresponds to a pressure of one newton per square meter:

The SI-compliant unit is also used for higher pressures bar used, 1 bar corresponds to 100,000 Pa = 1,000 hPa or 100 kPa.

In engineering, the unit N / mm² is used for both pressure and mechanical tension:

Other pressure units that can still be found, but are no longer permitted, are:

  • 1 Torr = 1 mm Hg = 1 mm mercury column = approx. 133.3 Pa
  • 1 inch of mercury (inch of mercury, inHg) = 3386.389 Pa at 0 ° C
  • 1 meter water column (mWS) = 0.1 at = 9.80665 kPa
  • 1 Technical atmosphere (at) = 1 kp / cm2. = approx. 98066.5 Pa
  • 1 Physical atmosphere (atm) = 760 Torr = 101325 Pa = 1013.25 hPa = 101.325 kPa.
  • 1 psi = 1 lb.p.sq.in. = 144 lb.p.sq.ft = 1/200 tn.sh.p.sq.in = 1/2240 tn.p.sq.in = 0.07030695796 kp / cm² = 6894.757293168 Pa
  Pascalbar technical atmosphere physical atmosphereTorrPounds per square inch
(Pa) (bar) (at) (atm) (torr) (psi)
≡ 1 N / m² ≡ 1 Mdyn / cm² ≡ 1 kp / cm² ≡ pSTP ≡ 1 mmEd ≡ 1 lbf / in.²
1 Pa 1 1,0000 · 10−5 1,0197 · 10−5 9,8692 · 10−6 7,5006 · 10−3 1,4504 · 10−4
1 bar 1,0000 · 105 1 1,0197 · 100 9,8692 · 10−1 7,5006 · 102 1,4504 · 101
1 at 9,8067 · 104 9,8067 · 10−1 1 9,6784 · 10−1 7,3556 · 102 1,4223 · 101
1 atm 1,0133 · 105 1,0133 · 100 1,0332 · 100 1 7,6000 · 102 1,4696 · 101
1 torr 1,3332 · 102 1,3332 · 10−3 1,3595 · 10−3 1,3158 · 10−3 1 1,9328 · 10−2
1 psi 6,8948 · 103 6,8948 · 10−2 7,0307 · 10−2 6,8046 · 10−2 5,1715 · 101 1

Exponential representation rounded to four places.

Pressure gauges

Main items: pressure gauge, differential pressure sensor, barometer, manometer, venturi nozzle, pitot tube, blood pressure monitor

Special pressures

  • Air pressure / atmospheric pressure (flow resistance)
  • Water pressure
  • Turgor
  • Sound pressure
  • Back pressure
  • Radiation pressure
  • Nominal pressure
  • Gas operating pressure
  • Test pressure
  • Burst pressure
  • Osmotic pressure
  • Blood pressure
  • vacuum
  • Gravitational pressure
  • Solar pressure (solar wind)
  • Vapor pressure

Category: Thermodynamics