# What is the inlet/outlet speed of air going in/out of our mouth during inhalation/exhalation

During inhalation, your alveoli expand, creating a pressure difference between the atmosphereic pressure and our lung sacks and therefore air will flow into the repspiratory airways.

I am trying to find what the (I guess average) speed of this flow is, and therefore estimate the pressure difference. I have spent some time online trying to find this, but I have not got a definite number yet. It should be an order of magnitude of 1 m/s ?

-

## migrated from physics.stackexchange.comDec 11 '12 at 12:46

This question came from our site for active researchers, academics and students of physics.

– RedGrittyBrick Dec 5 '12 at 17:48
I'm thinking this may be hard to answer due to: (1) Different people breathe differently and (2) breath seems to "accelerate" if you will (I start out breathing slowly than end quickly with each breath). So do you mean the average of breath span? Or the average per person? Or the average per person per breath span? – mjgpy3 Dec 5 '12 at 19:25
Just the average – l3win Dec 6 '12 at 17:58

Quick clarification firstly, the main change in thoracic volume that causes inspiration is not as a result of the alveoli expanding - they have no smooth muscle lining therefore are unable to spontaneously contract. They do have some elastic fascia however their expansion is passive. The change is mainly as a result of the diaphragm contracting to become flatter, increasing the space that the lungs can occupy. The external intercostal muscles also raise the ribs (in adults) which further allows for inspiration.

Figure One: Inspiration and Expiration(1). "Rib muscles" refers to the external intercostal muscles.

With that being said, the value I think you are looking for is peak expiratory flow. Peak flow is a common medical measurement that is often taken in the management of patients with respiratory conditions, either as part of their management plan or acute assessment. Peak flow is a measurement of the maximum speed that a person can exhale at.

As the comments on your question suggest, this varies dramatically between person to person. Ignoring any pathologies - such as asthma, chronic obstructive pulmonary diseases (COPD) or nerve damage to the diaphragm/intercostal muscles - peak expiratory flow varies primarily with age, gender and height. These variations are summarised in charts of expected peak flow that are used, amongst other things, to grade the severity of an asthma attack (and consequently how aggressively to manage it). Charts resemble the following:

Figure Two: Normal values for peak expiratory flow used in UK hospitals - The EU Scale (2)

So if you pick the height, gender and age that you feel is appropriate for your question, you can then read off peak flow in litres per minute. Then you would need, I think, to work out the area of the aperture (in your case the mouth) to get a speed in metres per second?

1. Medina B. Brenda's A&P eportfolio: objective 48 & 49: inhalation and exhalation [Online]. 2011 [accessed 2012 Dec 11]. Available from URL: http://blm1128.blogspot.co.uk/2011/04/objective-49-contrast-inspiration-and.html.
2. Häggström M. File: normal values for peak expiratory flow - EU scale.png [Online]. 2009 [accessed 2012 Dec 11]. Available from URL: http://en.wikipedia.org/wiki/File:Normal_values_for_peak_expiratory_flow_-_EU_scale.png.
-
Figures 4 and 5 of "Airflow Dynamics of Human Jets: Sneezing and Breathing - Potential Sources of Infectious Aerosols" appear to provide the requested information (Figure 4 is for nasal breathing); the paper also comments that "units of airflow rate (litres per second)" "are difficult to convert to comparable airflow velocities (in m/s)". – Paul A. Clayton Oct 2 '14 at 19:51

I'm not sure this is a great answer, but since no-one else has stepped up: it will vary a great deal depending on what you're doing.

According to Wikipedia the tidal volume for a breath is typically about 500 cm$^3$, so you can work out the velocity from the time taken for a breath and the cross sectional area of the mouth. The trouble is that the breath rate varies enormously e.g. from resting to running a marathon. Also would you take the cross sectional area of the lips, or the larynx, or some other point in the respiratory tract?

In any case under most circumstances I doubt the limiting factor during an inhalation is the pressure difference. I suspect it's more likely to be how fast the ribs can expand. It seems to me that if I take a sudden breath and try to stop halfway through, the inhalation stops immediately. If the limiting factor were the pressure difference I'd expect the air to keep flowing in after I'd stopped trying to inhale.

-
But as you expand your lungs, you create a pressure difference between the the ambient air and you lung sacs. . If you stop expanding you will stop creating a pressure difference, therefore stop the flow. The pressure difference reduces as the air flows into your lung sacs, this happens fast I presume, that´s why the flow stops if you stop expanding. – l3win Dec 6 '12 at 17:51
Yes. I guess the point is that the pressure difference is going to be very small. It also won't be the same everywhere in the lungs. I'd guess the main pressure drop in the small tubes to the alveoli rather than in the throat, trachea or bronchioles. So it's the velocity in the small tubes that matters, not the exhalation velocity. – John Rennie Dec 6 '12 at 18:02
btw... if it takes about 2 seconds to get 500 cm^3 of air into your lung sacs, then Q = 250 cm^/s * (1m/100cm)^3 = 0.00025 (m^3/s). Then the volume flow rate is Q = Velocity * Area and therefore Velocity = Q/Area = 0.00025/(pi*(9*10^-3)^2 = 1 m/s if the cavity of the mouth is approximated as a tube with radius equal to 9 mm. Seems like the velocity is approximately 1-2 m/s – l3win Dec 6 '12 at 23:48