# Shower curtain

michelcolman
I am wondering why a shower curtain is pulled inward when you turn on the shower.

Yes, I have read the classic answer that this is due to Bernoulli's law: the water makes the air move, and moving air has a lower pressure. Only, this does not make any sense at all if you know anything about how Bernoulli's law works.

Bernoulli's law is about conservation of energy along the flow of a fluid or gas. Once you start adding energy to the system (through a pressurized spray of water, for example), it becomes completely invalid.

I'll enter into a bit more detail: Bernoulli's law basically says that, if air speeds up along a line of flow, something must have made it speed up, and this "something" can only be a pressure differential. Accelerating air parcels must have a lower pressure in front of them to make them speed up. Write this down mathematically, and "half rho v squared" pops out pretty easily. But in the shower, the air was not accelerated because of a lower pressure in a particular direction, but because of the water being sprayed under pressure into the shower! There is absolutely no way whatsoever you can still use Bernoulli's law in that case.

So, why is the shower curtain really being pulled inward?

Homework Helper
More likely it's being pushed inwards because the air flows down, under, then back up and against the shower curtain because the sides of the tub redirect the air upwards. In a shower room where it's a flat floor and no sides to redirect the flow of air upwards, it doesn't happen.

If you can believe it, someone performed a CFD model of this system:

The water flow sets up a recirculating air vortex which, in combination with the pressure imbalance, pulls in the curtain.

redargon
If you can believe it, someone performed a CFD model of this system:

The water flow sets up a recirculating air vortex which, in combination with the pressure imbalance, pulls in the curtain.

cool I love CFD

michelcolman
If you can believe it, someone performed a CFD model of this system:
The water flow sets up a recirculating air vortex which, in combination with the pressure imbalance, pulls in the curtain.
Looks like a nice simulation, but the explanation in the article is rubbish. Looks like someone knows how to use CFD software but does not have a clue what's really going on. Or the editor completely mangled the researcher's report (I hope the latter is the case).
the article said:
The Bernoulli effect is the principal behind flight and an airplane's wings producing lift. The Bernoulli effect is seen near the showerhead, as air moves faster on the shower side of the curtain and pressure drops to vacuum pressure.

Vacuum pressure?!?! :rofl:
But more importantly, the Bernoulli effect is NOT the "principal" behind flight and an airplane's wing producing lift.

Bernoulli can be used to calculate pressure from speed and vice versa along a streamline (or between different streamlines if they come from a comparable source), but from a cause and effect point of view the pressure differential is causing the speed change, not the other way around! The well-known story "air parcels agreed to meet each other at the trailing edge of the wing, so the ones going over the top have to speed up and therefore the pressure drops" is a myth that is completely wrong even though it is still being taught to pilots all over the world.

Something causes a low pressure (in the case of an airplane, the fact that the air has to curve over the top of the wing, among other factors) and this low pressure increases the speed of the airflow.

So, what's causing the low pressure in the shower?

The only thing that seems to make sense in the article is "driven cavity": if I understood correctly, air flowing over a cavity will cause a vortex and lower pressure inside the cavity. In this case the "cavity" would be the area around the flow of water. Basically the water is sort-of dragging surrounding air away with it, creating low pressure outside of the spray.

So, is that what's really happening? Or did I misunderstand completely?

Bob_for_short
In my observations it is not so if you take a cold shower. I take the cold shower each day and do not observe this effect. When I take a hot shower, the effect occurs indeed. So my explanation is the following: the hot air goes up and the cold air tries to replace it at the bottom. It pushes the curtain inwards.

Bob.

Roger44
Sorry to butt in, but would somebody be nice enough to look at my question on I posted yesterday about Bernoulli and temperature.

Simple question : is there a temperature drop when the fluid has to flow faster in a narrower part of the tube.

Homework Helper
The stream of water from the shower results in circulation of air due to visocity, and it's this circulation of air that is results in curtain movement. My curtain rod is adjustable, so I moved it inwards a bit and checked for air flow with the shower on. There is significant flow of air, outwards under the back of the curtain, and inwards under the front of the curtain, so the curtain was moved outwards at the back and inwards at the front (near the shower head). The direction and position of the shower head are also an issue. In my case, I direct the head outwards towards the curtain a bit to allow the stream to keep the curtain from being blown inwards.

Sorry to butt in, but would somebody be nice enough to look at my question on I posted yesterday about Bernoulli and temperature.

Simple question : is there a temperature drop when the fluid has to flow faster in a narrower part of the tube.
The short answer is yes. This is why liquids cool when taking a sudden expansion across a valve for example.

MathMatt
Synopses from my essay entitled:
The Forces at Play in:
THE ATTACK OF THE SHOWER CURTAIN

In my days as an undergrad, I did several experiments on this (both full scale in the morning and small scale in the lab). When taking a cold shower, the curtain encroaching effect is minimal (for reasons I will get to). Also, when the ratio of volume of the shower:volume of the room is lowered, the effect is amplified while keeping the same curtain size. When upping the temperature of the water, three things about the air are changed; the relative motion, the temperature of the air, and the amount of water vapor in the air. I will address these one at a time.

First, the relative motion of the air in the shower stall. The CFD model is correct in that the air does form a vortex while the water is on but what it seems to lack (at least from this write up) is the air outside the stall mixing with the air inside the stall when it is above the curtain rod. My interpretation of this is that when the air is that while the air is moving below the curtain rod, it is contained in the shower stall. Once it moves above the rod, it is allowed to mix with the rest of the air in the room and some air inevitably moves out of the shower stall with little moving back in above the rod.

Second, the temperature increase. We all know that if we heat a balloon it will expand since the molecules, effectively, are farther apart taking up more volume but there's still the same amount of stuff in the balloon. In the case of the shower stall, that heated air is allowed to move out of the shower stall, over the rod, and take up as much space as it wants to. Since the air inside is being continually heated by contact and the air outside is being heated by convection and since there are far fewer air flows outside of the stall than there are in, the cooler air is, essentially, compressed to the bottom of the room outside of the stall making your first dramatic pressure difference inside vs. outside of the shower stall.

Third, the issue of the water vapor. Any observant person with an unventilated, relatively small bathroom will attest to the fact that, when you're finished with your shower and you go to get out, the air near the ceiling is very hazy and the air near the floor is clear and dry. Occasionally you can also see this if you have a full length mirror in your bathroom, under good conditions you can find that the top of the mirror is fogged but the bottom is not. This has the same effect, in the same manor, as the temperature, increasing the pressure of the air at the bottom of the shower outside of the stall.

Another condition that amplifies the effect is how much air is allowed to escape out the bottom of the door (assuming that you shut the door while taking a shower). If little to no air is allowed to leak out, the effect is amplified.

When the Volume in to Volume out ratio is changed and the Volume out is increased, the warm, partially saturated air is allowed to spread over the ceiling. This, while still lowering the pressure inside the stall, does not increase the pressure outside the stall as much resulting in less deflection. Following this through and taking the Volume outside of the stall to become infinite (say, building your shower stall outside, assuming no wind) the effect is still present but it becomes far less pronounced.

Lastly, for the folks out there that like the idea that Bernoulli's principle is the most prominent of the forces that are acting on the shower curtain, in a small shower stall (approx. 125cm X 125cm) and a small room (approx. 2m X 1.75m), once the effect has started and the air in the stall is very warm and partially saturated, when the water is turned off, the curtain has a greater inward deflection due to the fact that the water itself is no longer hitting it pushing it outward.

I am still working on a mathematical model of this system to make my arguments more convincing (I have only mentioned a few of the things that can have a slight effect on the system) but until then, this is what I have found.

-Matthew P. Liscio

MathMatt
Synopses from my essay entitled:
The Forces at Play in:
THE ATTACK OF THE SHOWER CURTAIN

In my days as an undergrad, I did several experiments on this (both full scale in the morning and small scale in the lab). When taking a cold shower, the curtain encroaching effect is minimal (for reasons I will get to). Also, when the ratio of volume of the shower:volume of the room is lowered, the effect is amplified while keeping the same curtain size. When upping the temperature of the water, three things about the air are changed; the relative motion, the temperature of the air, and the amount of water vapor in the air. I will address these one at a time.

First, the relative motion of the air in the shower stall. The CFD model is correct in that the air does form a vortex while the water is on but what it seems to lack (at least from this write up) is the air outside the stall mixing with the air inside the stall when it is above the curtain rod. My interpretation of this is that when the air is that while the air is moving below the curtain rod, it is contained in the shower stall. Once it moves above the rod, it is allowed to mix with the rest of the air in the room and some air inevitably moves out of the shower stall with little moving back in above the rod.

Second, the temperature increase. We all know that if we heat a balloon it will expand since the molecules, effectively, are farther apart taking up more volume but there's still the same amount of stuff in the balloon. In the case of the shower stall, that heated air is allowed to move out of the shower stall, over the rod, and take up as much space as it wants to. Since the air inside is being continually heated by contact and the air outside is being heated by convection and since there are far fewer air flows outside of the stall than there are in, the cooler air is, essentially, compressed to the bottom of the room outside of the stall making your first dramatic pressure difference inside vs. outside of the shower stall.

Third, the issue of the water vapor. Any observant person with an unventilated, relatively small bathroom will attest to the fact that, when you're finished with your shower and you go to get out, the air near the ceiling is very hazy and the air near the floor is clear and dry. Occasionally you can also see this if you have a full length mirror in your bathroom, under good conditions you can find that the top of the mirror is fogged but the bottom is not. This has the same effect, in the same manor, as the temperature, increasing the pressure of the air at the bottom of the shower outside of the stall.

Another condition that amplifies the effect is how much air is allowed to escape out the bottom of the door (assuming that you shut the door while taking a shower). If little to no air is allowed to leak out, the effect is amplified.

When the Volume in to Volume out ratio is changed and the Volume out is increased, the warm, partially saturated air is allowed to spread over the ceiling. This, while still lowering the pressure inside the stall, does not increase the pressure outside the stall as much resulting in less deflection. Following this through and taking the Volume outside of the stall to become infinite (say, building your shower stall outside, assuming no wind) the effect is still present but it becomes far less pronounced.

Lastly, for the folks out there that like the idea that Bernoulli's principle is the most prominent of the forces that are acting on the shower curtain, in a small shower stall (approx. 125cm X 125cm) and a small room (approx. 2m X 1.75m), once the effect has started and the air in the stall is very warm and partially saturated, when the water is turned off, the curtain has a greater inward deflection due to the fact that the water itself is no longer hitting it pushing it outward.

I am still working on a mathematical model of this system to make my arguments more convincing (I have only mentioned a few of the things that can have a slight effect on the system) but until then, this is what I have found.

-Matthew P. Liscio

michelcolman
Synopses from my essay entitled:
The Forces at Play in:
THE ATTACK OF THE SHOWER CURTAIN
-Matthew P. Liscio
Wow, thanks, that's a pretty detailed explanation, I'm starting to understand now. Or at least, I understand it's a lot more complicated than I expected.

Thanks a lot,

Michel