How Do You Calculate the Expulsion Force in a Bellow Simulation?

[Orochi663]

TL;DR Summary

How does a bellow work especially
a. if it is not filled with air
b. If the outer atmosphere is not air but another fluid.

I am developing simulation of bellow, but as i am not a physics grad so far i have come to this formulation:
The thrust force from which it escapes when bellow handles are pushed are proportional to:

1. Rate of change of distance between the handles. that is the rate at which the volume of container decreases.
2. Angle from g. (From Downward)
3. diameter of escape nozzle.
4. viscosity of atmospheric fluid resistance. (for resistance that will be developed when the fluid is expelled out in the containing atmosphere)
5. viscosity of containing fluid.

But I know for sure that results are not accurate. Can someone please point me to the correct solution of formulation of Force by which the fluid will be expelled out of the bellow.

I will be thankful.

 

[gmax137]

If you have information to calculate the rate at which the volume is decreasing, then you can calculate the velocity through the nozzle (by knowing its area). That is, if you assume the fluid is incompressible, you can use continuity (rate of change in stored fluid = rate of fluid leaving via nozzle).

Alternate, if you know the force on the bellows handles you could calculate the pressure exerted on the fluid (via the area of the 'paddles'); then use Bernoulli to relate this pressure to the discharge nozzle velocity.

 

[Orochi663]

hmm, thanks. So how does the force will be affected by the escape nozzle size ?

 

[sophiecentaur]

Force applied to the fluid by the piston will equal the rate of change of momentum of the escaping fluid. Assume it starts off stationary and you have all you need to know for an estimate.

 

[Orochi663]

hmm Thanks. I am just confused now on direction of bellow, i.e. if nozzle is bigger the fluid escaping will have less momentum than when the nozzle is smaller. Also if the nozzle is pointing downwards the gravity will also contribute to escaping fluid force.

So how to add direction of nozzle and force of gravity into the formulation
So far i got: Fs = ((p-P) /D ) dV/dt

where D = diameter of escaping nozzle
dV/dt = rate of change of volume. // Force applied will change volume of Bellow
p = density of fluid in bellow. // Constant
P = density of fluid in the atmosphere. // Constant

Regards

 

[jbriggs444]

Thanks. I am just confused now on direction of bellow, i.e. if nozzle is bigger the fluid escaping will have less momentum than when the nozzle is smaller

You have not carefully specified what is being held constant as you vary the nozzle size.

If you are squeezing the bellows with a known force (creating a fixed pressure difference), the exhaust velocity will be independent of nozzle size.

If you are squeezing the bellows at a known rate (creating a fixed volumetric flow rate), the exhaust velocity will depend on nozzle size.

From the original post, it seems that a known force is applied. The nozzle size does not affect exhaust velocity but does affect volumetric flow rate.

 

[gmax137]

@Orochi663 , do you know how to calculate liquid flow through a hole in the side of a tank? perhaps you should work through that simpler problem first.

 

[Orochi663]

@gmax137 i am using a navier stokes solver (Joe Stam's) for fluid flow in the container, I am using the thrust as Force the pressure of squeezing the bellow that is exerted on each particle with respect to distance from nozzle.

 

[Orochi663]

@jbriggs444 Thanks
Well during the simulation every thing can be varied to see the affect. The constant force when applied over an actual bellow the distance the water travel varies with the diameter of nozzle and the direction of bellow and follow something like a projectile motion. Hence i am quite sure i am missing something in here. I guess if i can find out the velocity of liquid particle escaping from a container then i will be done. So i am not sure how direction will come into play i.e. i know it must be a something like a Cos(theta) between Fg and nozzle direction. But not sure.

 

[vasim rangrej]

Can you please tell me how thrust force can affect the bellow...?
i.e. if thrust force is in large quantity so then what should we do...?

 

[jbriggs444]

Can you please tell me how thrust force can affect the bellow...?
i.e. if thrust force is in large quantity so then what should we do...?

You are asking this question in a two year old thread. It would be better in its own thread.

As I understand it, you ask what happens if we push harder on a bellows. Answer: the air comes out faster.

 

[sophiecentaur]

You got that one out of a Christmas cracker, I bet.