What is delta p equal to

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Examples about delta P the differential pressure
Darcy–Weisbach equation
Lung compliance
External links

Substitution: The change in momentum is equal to mass times the change in velocity, or delta p is equal to m times delta v.

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According to 2nd law in my Textbook, Rate of Change of Momentum is directly proportional to magnitude of net force and is in the direction of the Net Force.

This translates to: $F \propto Δp / Δt$

Where

F = Net force
Δp = Change in momentum
Δt = Change in time

My book states it slightly differently, as $F = Δp / Δt$

Is this wrong, or have I made a mistake of interpreting it instead?

ΔP stands for the difference between two measured pressure values. This can be measured either at different times/dates or at different positions in a system. The measurement at different times, can be a continuous measurement from day to day to see a trend as the ΔP develops over a longer period of time. Measurement at different positions in a system, i.e. you compare the pressure at the input with the pressure at the output of a machine. And get the pressure drop - Delta P.
The meassurement of a pressure, either an analog pressure gauge is used or an electrical sensor, which delivers its value to a central data system.

In a piping system or a heat exchanger with a moving fluid, the pressure usually drops due to friction. The friction happens in between the water and the contacting surfaces, e.g. the pipe wall. As higher the differnce, as more likely there is fouling in the system.
This pressure drop will increase as more incrustations are in the way of flow. The deposits in a water system are caused by limescale, suspended solids, biological growth or other kinds of fouling. The deposits build up in the pipe and interfere with the water flow. Therefore ΔP can be used to measure the flow resistance. One can calculate the amount of deposits in the pipe or heat exchanger. The unit for the pressure is given in millipascal / mPa. Which indicates the force acting on a surface.

The ΔP in the heat exchanger to the left can be calculated very simple. Subtract the inlet pressure (P1) at the point B, from the outlet pressure (P2) at the exit A and you will get Delta P.

The equation for the pressure difference is: ΔP = P2 – P1

It is obvious that a high concentration of deposits, in pipe or exchanger, lead to a high pressure drop, ΔP. If there are deposits the water can't flow free. Hence the outlet pressure is much lower than the inlet pressure.

Examples about delta P the differential pressure

If you are sitting in an airplane and drink from a plastic bottle, then the pressure in the bottle is the same as in the airplane. Once you have landed you will notice that the bottle is pushed inwards. That's because the pressure in the plane is much lower than the atmospheric pressure at the ground. This pressure difference can be seen on the bottle. The delta P would be the difference in between the lower pressure in the airplane and the normal pressure on the ground.

We at Merus use delta P for the performance monitoring. After the installation of Merus Rings the delta P decreases, if all works well to its design level.

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 hf expresses the pressure loss Δp as the height of a column of fluid,

Δ p = ρ ⋅ g ⋅ h f {\displaystyle \Delta p=\rho \cdot g\cdot h_{f}}

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

Δ p = f ⋅ L D ⋅ ρ V 2 2 {\displaystyle \Delta p=f\cdot {\frac {L}{D}}\cdot {\frac {\rho V^{2}}{2}}}

Lung compliance

In general, compliance is defined by the change in volume (ΔV) versus the associated change in pressure (ΔP), or ΔV/ΔP:

C o m p l i a n c e = Δ V Δ P {\displaystyle Compliance={\frac {\Delta V}{\Delta P}}}

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.[1]

Calculating compliance on minute volume (VE: ΔV is always defined by tidal volume (VT), but ΔP is different for the measurement of dynamic vs. static compliance.

Dynamic compliance (Cdyn)

C d y n = V T P I P − P E E P {\displaystyle C_{dyn}={\frac {V_{T}}{\mathrm {PIP-PEEP} }}}

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 Cdyn.

Static compliance (Cstat)

C s t a t = V T P p l a t − P E E P {\displaystyle C_{stat}={\frac {V_{T}}{P_{plat}-PEEP}}}

where Pplat = plateau pressure. Pplat 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. Pplat is never > PIP and is typically < 3-5 cmH2O lower than PIP when airway resistance is normal.

References

^ Dellamonica J, Lerolle N, Sargentini C, Beduneau G, Di Marco F, Mercat A, et al. (2011). "PEEP-induced changes in lung volume in acute respiratory distress syndrome. Two methods to estimate alveolar recruitment". Intensive Care Med. 37 (10): 1595–604. doi:10.1007/s00134-011-2333-y. PMID 21866369.