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I came across this Cool Science video and his description of it as an example of Bernoulli's Principle. I am looking for an explanation using equations and math and physics. The question has been raised in other forums, but I can't find any answers.

[EDIT]

Since this question was closed, needing details or clarity, guidelines advise to be more specific about what you're looking for, so here goes:

The experiment in the example presents a really surprising phenomenon, that the bag appears only partially filled with three lungfuls of air when his assistant blows directly into it, but goes from empty to full with a single lungful of air when it is delivered from a small distance from the opening of the bag.

The host, Steve Spangler, is not a charlatan. He has run an entertaining and authoritative channel for over ten years, presenting and explaining all manner of interesting physics phenomena, many involving pressure, balloons, and always basing his explanations on valid, classical physics principles. On this occasion he states that by "combining weather and science we use Bernoulli's Principle" and "using fast moving air" they fill the bag with a single breath.

I understand that Bernoulli's Principle states when an incompressible, inviscid fluid, flows through a tube, when the tube constricts, the fluid moves faster and the pressure reduces, and when it opens up again, the flow speed reduces and the pressure increases.

I know that mathematicians after Bernoulli formalised the principle int what is now referred to as Euler's equation, that goes along the lines p + ½ ρV^2 = constant (p = pressure, ρ=density and V = flow velocity)

The experimental data was presented: Tube 8' long, 10" around and holds 45 L of air . We can assume NTP conditions.

My question is how does that principle or that equation explain why a single breath delivered a little distance from the opening fills the tube that couldn't even be slightly filled with three full breaths?

[EDIT 2] He seems to have got the maths wrong: We have a cylindrical tube. Length = 8 feet, Diameter = 10 inches

Calculations:

Convert units:

1 foot = 12 inches

1 inch = 2.54 centimetres

1 litre = 1000 cubic centimetres

Calculate the radius:

Radius = Diameter / 2 = 10 inches / 2 = 5 inches

Calculate the volume of the cylinder:

Volume = π * radius^2 * height

Volume = 3.14159 * (5 inches * 2.54 cm/inch)^2 * (8 feet * 12 inches/foot * 2.54 cm/inch)

Volume ≈ 123,555.5 cubic centimetres

Convert to litres:

Volume = 123,555.5 cubic centimetres / 1000 = 123.56 litres (approximately)

Therefore, a tube that is 8 feet long and 10 inches in diameter can hold approximately 123.56 litres, not his estimate of 45 litres.

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  • $\begingroup$ Similar: physics.stackexchange.com/questions/759498/… $\endgroup$
    – BowlOfRed
    Commented Jul 25 at 0:36
  • $\begingroup$ HMMM, perhaps, but there are at least two theories duking it out. With no real answer. The Cool Science is an actual experiment rather than a thought experiment. We can make measurements and test the answers. $\endgroup$
    – rationalDiscourse
    Commented Jul 25 at 0:55
  • $\begingroup$ Not sure Bernoulli is all that helpful. I would simply argue with momentum conservation directly. $\endgroup$
    – FlatterMann
    Commented Jul 25 at 5:08
  • $\begingroup$ Good edits, thank you! $\endgroup$
    – Dale
    Commented Jul 26 at 3:25
  • $\begingroup$ That's interesting: The question has been up for three weeks with no answers. Is it that hard? $\endgroup$
    – rationalDiscourse
    Commented Aug 13 at 3:14

1 Answer 1

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It's simple.

Because air is viscous, when you blow air into a bag from a distance, due to its viscosity, the air you blow out will carry more air movement, filling the bag with one blow.

Bernoulli's law is a theory about ideal fluids without viscosity, so it cannot be used here.

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  • $\begingroup$ I think this answer could more clearly state the point for the OP: the moving air drags surrounding air with it, pulling it into the bag. When blown directly into the object, it does not pass by adjacent air and does not have a chance to do this $\endgroup$
    – RC_23
    Commented Sep 30 at 5:20
  • $\begingroup$ But also, the person in the video invokes Bernoulli's principle claiming that the central jet of air from his mouth has a lower pressure due to its motion, which causes surrounding air to rush inward, filling the bag. This would happen even with inviscid flow. $\endgroup$
    – RC_23
    Commented Sep 30 at 5:24
  • $\begingroup$ @RC_23 The analogy of blowing air with the mouth is not strict. For example, the surface of the lips is curved, and so on. You can use a garden hose analogy. Water flows out from a garden hose, and after leaving the outlet of the garden hose, the pressure of the water is generally atmospheric pressure. $\endgroup$
    – enbin
    Commented Sep 30 at 9:05
  • $\begingroup$ @RC_23 I'm interested in the idea that air "drags surrounding air". Do you have any literature on that (not Wiki!) $\endgroup$
    – rationalDiscourse
    Commented Oct 1 at 23:12

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