How Can I Calculate Spray Force Using Math?

[mistry]

Hi everyone

I'm doing a project which looks at the measurement of astha inhaler spray force. The idea is that a spray will be propelled from an inhaller onto a flat plate and the force will be measured using a load cell for example. To get an intial idea of the size of forces, I am trying to find a mathematic way of determine the force and wondering if you could help. People have suggested calculating spray force by looking at the kinetic energy of a particle or the momentum, but I'm confused on how to do this. How can you mathemtical calculate the force of a plume made up of thousands of particles which atmomise in a matter of seconds.

Thanks
Amit

 

[Topher925]

Like you stated, the simplest way would be just to determine the change in momentum. If you use a Eulerian description of the mist, you can make the assumption that the fluid has a uniform and homogeneous density including the fluid itself and the air it is passing through. To actually calculate the force, you can just use Newtons second law;

F = dp/dt = M_mist x (V_initial-V_final)

Obviously your V_final should be zero. The difficult part is determining that initial velocity and what affects does the air have on the fluid that is moving through it.

 

[mistry]

Hi

Thanks for that! I see what you mean abut using Newtons law. Saying that however, is there a differnce in calculating the force of a spray by considering it as individual particles and then considering it as a cloud of gas? Also are there alternative, more precise means of calculatig force or can you poitn me in a area where i can find out more

Also understanding the affects that air has on the fluid is straight forward, however in terms of force, can i say that the impact decrease due to friction between air and spray particles

 

[Topher925]

You consider each particle individually, but I believe you would require differential analysis eventually which can get quite complicated. See here: http://en.wikipedia.org/wiki/Navier-Stokes_equations

If you spray something into open air that is easily visible you can usually see vorticies and reverse flow in the fluid. Before you go to far in one path you should consider what your system will consist of and if affects such as these types of turbulence will be present. The air will definitely have an affect on the fluid and will need to be considered if you desire any kind of accuracy. The air will definitely decrease the force of the fluid on the surface due to its velocity decreasing like you said.