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{{About|the mathematical term used in fluid dynamics|the concept of delta-P in diving safety|Diving_hazards#Localised_pressure_differentials{{!}}Diving hazards}}

'''ΔP''' ('''Delta P''') is a mathematical term symbolizing a change (Δ) in pressure (P).

==Uses==
*[[Young–Laplace equation]]

===Darcy–Weisbach equation===
Given that the [[head loss]] ''h<sub>f</sub>'' expresses the [[pressure]] loss ''&Delta;p'' as the height of a column of fluid,

:<math>\Delta p = \rho \cdot g \cdot h_f</math>

where ρ is the density of the fluid. The [[Darcy–Weisbach equation]] can also be written in terms of pressure loss:

:<math>\Delta p = f \cdot \frac{L}{D} \cdot \frac{\rho V^2}{2}</math>

===Lung compliance===
In general, compliance is defined by the change in volume (Δ''V'') versus the associated change in pressure (Δ''P''), or [[Lung compliance#Calculation|Δ''V''/Δ''P'']]:
:<math>Compliance =  \frac{ \Delta V}{ \Delta P} </math>

During [[mechanical ventilation]], compliance is influenced by three main physiologic factors:
#[[Lung compliance]]
#[[Chest wall compliance]]
#[[Airway resistance]]

Lung compliance is influenced by a variety of primary abnormalities of [[lung parenchyma]], both chronic and acute. [[Airway resistance]] is typically increased by [[bronchospasm]] and airway secretions. Chest wall compliance can be decreased by fixed abnormalities (e.g. [[kyphoscoliosis]], [[morbid obesity]]) or more variable problems driven by patient agitation while intubated.<ref name="pmid21866369">{{cite journal |vauthors=Dellamonica J, Lerolle N, Sargentini C, Beduneau G, Di Marco F, Mercat A, etal | title=PEEP-induced changes in lung volume in acute respiratory distress syndrome. Two methods to estimate alveolar recruitment. | journal=Intensive Care Med | year= 2011 | volume=  37| issue=  10| pages=  1595–604| pmid=21866369 | doi=10.1007/s00134-011-2333-y | s2cid=36231036 | doi-access=free }}</ref>

Calculating compliance on [[minute volume]] (V<sub>E</sub>: Δ''V'' is always defined by [[tidal volume]] (V<sub>T</sub>), but Δ''P'' is different for the measurement of dynamic vs. static compliance.

====Dynamic compliance (C<sub>dyn</sub>)====
:<math>C_{dyn} = \frac{V_T}\mathrm{PIP-PEEP}</math>

where PIP = [[peak inspiratory pressure]] (the maximum pressure during inspiration), and PEEP = [[positive end expiratory pressure]]. Alterations in airway resistance, [[lung compliance]] and chest wall compliance influence C<sub>dyn</sub>.

====Static compliance (C<sub>stat</sub>)====
:<math>C_{stat} = \frac{{V_T}}{{P_{plat}-PEEP}}</math>
where P<sub>plat</sub> = plateau pressure. P<sub>plat</sub> is measured at the end of inhalation and prior to exhalation using an inspiratory hold maneuver. During this maneuver, airflow is transiently (~0.5 sec) discontinued, which eliminates the effects of airway resistance. P<sub>plat</sub> is never > PIP and is typically < 3-5 cmH<sub>2</sub>O lower than PIP when airway resistance is normal.

== See also ==
*[[Pressure measurement]]
*[[Pressure drop]]
*[[Head loss]]

==References==
{{Reflist}}

== External links ==
* [https://www.youtube.com/watch?v=AEtbFm_CjE0 Delta P, Diving Pressure Hazard]

[[Category:Mathematical notation]]
[[Category:Pressure]]
[[Category:Respiratory therapy]]
[[Category:Mathematics in medicine]]