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.