I cannot comment on the science of the question, but I can comment on what happens with large quantities of spraying water. By trade I am a software engineer and that doesn’t do much to shed any light on the issue. But I am also a firefighter and we have been known to spray water on all sorts of things. One feature of our nozzles is that the stream pattern is variable, from straight stream to completely fanned out. Just like some of your garden hose nozzles. With the fanned out pattern on the fire hose, you immediately notice a nice little breeze coming in behind you. If you are standing in front, you also notice a nice little breeze coming in with the water. We can actually vent a room like this in a pinch.
I think the same thing happens in the shower. Whether or not this is the Bernoulli Effect or not makes no difference. It is the moving water pulling the air in behind it that creates the breeze.
Does it happen during cold and hot showers?
I am late to this question, so I may be repeating.
In a hot shower, the air inside would rise. Making negative pressure across many square feet of curtain.
I recommend reading the articles. One of my favorites.
According to Cecil and my own shower observations, the effect is invariant to temperature. I’ve noted that it does vary somewhat with water volume. For most showerhead positions, a running shower will create a circular flow of air inside the stall. In the center of the circular flow air pressure drops - just like a hurricane. That lower air pressure sucks in the shower curtain.
Solutions include lowering the water volume (maybe with an energy-efficient showerhead), positioning yourself and the spray so as to disrupt the spiral airflow, weighting down the curtain, or perhaps not closing the curtain fully, so as to leave some space for the air to rush in. Ok, I haven’t tried that last one.
It absolutely does apply to wing lift, it’s just that the common explanation involving Bernoulli is wrong. The common one is that since the air going over the top and bottom of the wing have to arrive at the trailing edge at the same time, therefore the air over the top goes faster, therefore lower pressure according to Bernoulli. The problem with this explanation is that the air streams do not arrive at the trailing edge at the same time. The one over the top actually arrives first.
I think we can all agree that (1) The air pressure is lower inside the curtain, and (2) The effect is not a thermal effect due to hot water.
Questions remain unclear:
(a) If the air is moving next to the inside of the curtain - for whatever reason - , isn’t it the force on the curtain described as “the Bernoulli Effect” ?
(b) When the curtain jumps that last inch towards you, is this the same cause & effect as the cause and effect that caused the curtain to blow in /swing in?
No, Bernoulli absolutely has to do with how airplanes fly, it’s just the common explanation of Bernoulli applied to airplanes is incorrect, as CurtC explained.
Sort of, but not exactly. Bernoulli is how you measure the pressure difference due to a moving airflow. However, the direction and pattern of airflow, and the cause of the airflow, are different because of the different explanations. The chimney effect posits that the thermal expansion causes the warmer air to rise, which drives it out the top. Cooler air gets pushed down and in at the bottom. Except it happens with cold water, too. The Coanda Effect explanation posits that it is not the air flowing past the curtain that causes the inflow of the curtain, but rather the water pulls the air along, and that air then pulls the curtain in. Coanda explains why the air is pulled along, but the fact that the curtain is then pushed in is due to the Bernoulli effect of the airflow.
The vortex explanation says that the air is pushed by the water, which then flows out of the way, pushing the “air packets” in the way up, pushing the “air packets” above those over, which leads to a rotation of airflow in the stall. That rotation of airflow creates a low pressure inside the vortex, which is what pulls the air in at the bottom. I don’t think that is actually the Bernoulli effect, but I need to refresh my understanding.
Yes, I know that’s the wrong explanation. But I don’t see what else Bernoulli might have to do with it either; is it not just that the air striking the bottom of the wing (as it’s tilted into the airstream) pushes it up, like holding your hand flat out a car window?
It seems to me, having stayed in a fair number of motels and hotels before and after that time, the was a very noticeable trend thereafter toward installing those bowed-out shower curtain rods in their bathrooms, which seemed to reduce or eliminate the problem. Probably just a coincidence, though.
Askance, deflected air is the cause of the airplane staying in the sky, but more air is actually deflected by the top surface of the wing than the bottom surface of the wing.
Once the airstream separates at the leading edge of the wing, there is nothing that demands that the air packets that separated at the front reach the rear of the wing together. In fact, the air is pulled over the top faster, and curved downward. That pushes it down, which causes lift.
Bernoulli’s principle is a small part of the big puzzle that is aerodynamics. It’s involved, but not in the way that the popular incorrect explanation describes it.
Think about it this way: when a fluid flows from a region of high pressure to a region of lower pressure there’s more pressure behind than in front. That exerts a net force on the fluid that causes it to speed up. Bernoulli’s equation quantifies this idea.
The only way that a plane can stay in the air with gravity pulling down on it is for there to be a pressure difference between the bottom and top of the wings, with lower pressure above. When the air flows through this region of lower pressure it speeds up.
Bernoulli’s principle doesn’t explain why there’s lower pressure on top of the wing, only that this lower pressure is accompanied by a higher speed.
Bernoulli’s principle concerns itself with pressure changes parallel to the air flow so it’s not a very good explanation of why there are pressure differences perpendicular to the airflow. Fortunately, there is a nice formula for that which was discovered by Euler around the time Bernoulli published Hydrodynamica:
dp/dz = rho x v^2 / R
dp/dz is the pressure difference in the vertical direction (or differential if you want to be more precise) , rho is the density of the air, v is the velocity, and R is the radius of curvature. This formula says that whenever a fluid follows a path that is curved there is a pressure difference with higher pressure on the outside of the curve and lower pressure on the inside. Faster flow or tighter curves make for bigger pressure differences, and for straight flow (R->infinity) there is no pressure difference.
Air flowing past an airplane wing is deflected downward and follows a curved path, this is associated with pressure differences according to the formula above. (you could also cut to the chase and use Newton’s laws to say that since the air is forced down by the wing the wing must be forced up by the air, skipping the discussion of pressure altogether - it depends on what you want to emphasize).
This downward deflection / curved path occurs both above and below the wing, so it’s not just the air striking the bottom of the wing. The curved airflow above the wing contributes strongly to the lift.
Returning to the shower curtain, the vortex in the stall means air is flowing in a curved path. That means there is lower pressure on the inside of the vortex and this lower pressure “sucks” the shower curtain inward. I think we all know that a vortex has lower pressure on the inside, the formula above just quantifies it.
Not only does the air smacking into the underside of the tilted wing push it up, but the shape of the wing throwing air downwards produces a Newtonian reaction force upwards.
So I’m right- Bernoulli has nothing whatsoever to do with the plane staying up. It purely describes the pressure-speed relationship of the airflow, which in and of itself has nothing to do with creating lift. The lower pressure on top of the wing creates some lift, AND Bernoulli describes why that air also speeds up - but that speeding up is irrelevant to the production of lift. So Cecil’s statement
is flat-out wrong. Bernoulli happens, but as a side-effect of phenomena that also cause lift, it is not the cause of lift itself.
Bernoulli has nothing whatsoever to do with the plane staying up.
While I think your explanation is basically right, there’s more than one way to (correctly) explain lift. You don’t need Bernoulli’s principle to explain how a plane flies, but saying it has nothing whatsoever to do with it is over-stating things.
As I said earlier, Bernoulli’s principle is a small part of a large puzzle. Here’s where it fits in:
The more or less standard treatment in aerodynamics texts is to start with conservation of momentum and conservation of energy at the infinitesimal level and model the airflow with differential equations. The result is the Navier-Stokes equations, which are unfortunately damn near impossible to solve. But if you make some simplifying assumptions and approximations they are.
The solution is a vector field that indicates the speed and direction of the air at each point in space. Once you have that, you can use Bernoulli’s equation to calculate the pressure at each point on the wing, and if you add up all the pressure you’ll get the lift.
That’s more or less how it’s taught to engineers, with Bernoulli’s equation being the next-to-last step in a long chain of mathematics. Once you know the velocity distribution of the air in the vicinity of the wing, Bernoulli’s equation tells you the pressure distribution. But determining the velocity distribution is no small task.
My view is that this is more of a convenient trick that facilitates the calculations and not all that important unless you are actually doing the calculations. All the important physics is modeled early in the process when you write the differential equations - the rest is mostly just a bunch of math.
“The wing pushes the air down, so the air pushes the wing up” is sufficient for most people. If you want to discuss pressure, noting that curved airflow implies pressure differences with lower pressure on the inside of the curve. Dragging Bernoulli into it without also discussing the massive amount of math needed to get to the point where his equation can be applied almost always results in a nonsensical explanation that defies the laws of physics.
But that doesn’t invalidate his equation, or mean that it can’t be part of a careful (if complicated) explanation.