I think that for your question it is more relevant to consider the rate of energy in time i.e. the power of shock wave front:

Pw=0,5dEW/dt=0,5dM/dt V2=0,5ρAdx/dt V2=0,5 ρAV3

A is the shock wave cross section area of the shock wave and

ρ is the mass density of the water

Regards

Ioan David , thank you for your participation. Would you introduce some relevant references? In the case I mentioned, the shock front is in the form of "condensed air", therefore the density of condensed air should be used. Do you have any suggestions for the "condensed air" density?

Hello Nima Khaledy : I hope my input as below is useful:

Instead of storing or saving energy, people sometimes want to enhance energy dissipation. Shock waves from bomb explosion is an example. When a bomb explodes, highly compressed air particles strike human body. Shock waves will then pass through in the body, causing damages to the tissues. Shock waves carry energy just like elastic waves. But they are faster and thus can transport more energy. We will show how the shock energy dissipates into matters and how the protective pads are designed to reduce destructive effects.

http://large.stanford.edu/courses/2013/ph240/shen1/

https://www.hindawi.com/journals/sv/2018/2721450/

https://core.ac.uk/download/pdf/33110795.pdf

Regards--

Ijaz Durrani ,

Thank you for your participation. My purpose is to study the energy dissipation through a given structure. However, I think comparing the dissipated energy with the input kinetic energy can be useful in this regard. I will look at the references you introduced.

Hello Nima Khaledy: The following inputs, extensively garnered should definitely help!!

Energy Dissipation in Collisionless Shocks. In the 1960s, scientists discovered a new kind of shock wave that traveled through space plasmas that did not rely upon collisions. ... As it travels through space, a complex system of charged particles from the sun and magnetic structures piles up in front of it.

https://science.nasa.gov/heliophysics/focus-areas/recent-research/energy-dissipation-collisionless-shocks

http://adsabs.harvard.edu/full/1969SoPh...10..348M

Article Interfacial Effects on the Dispersion and Dissipation of Sho...

https://iopscience.iop.org/chapter/978-0-7503-1254-7/bk978-0-7503-1254-7ch1.pdf

Article Shockwave Energy Dissipation in Metal-Organic Framework MOF-5

Article Quantified Energy Dissipation Rates in the Terrestrial Bow S...

Best regards--

Nima Khaledy

I think that, the details in the attached appendix can be useful.

Regards

Ioan David,

Thank you for your more detailed file. I will check it out.

Dear Nima,

I think you do not need to calculate kinetic energy. If you want to consider energy dissipation or ductility, you can focus on input and output impulse. In fact, you can extract transferred impulse from structural elements to main structure. I have been working on ductile behavior of steel structures under blast impulsive loading. I suggest you to take a look at my journal papers especially my paper published in the journal of "structural engineering and mechanics". Should you have any questions, please do not hesitate to contact me.

Yours sincerely,

Saeid Lotfi

Dear Saeid Lotfi ,

thank you for your suggestion. Considering input and output impulses seems a good idea. However, I have not obtained satisfactory results from it. Considering input energy, dissipated energy, and output energy may work better.

Hello Dr Nima Khaledy : Shock is the effect on an object caused by the energy delivered to it by a force, usually an impact force, over a short time period. The effect of shock occurs when the energy of the impact is transferred from one individual or object to another. A couple of reference as below have been gleaned in response to ur last post. Hope these should clinch the issue for you:

https://opentextbc.ca/physicstestbook2/chapter/kinetic-energy-and-the-work-energy-theorem/

https://people.eng.unimelb.edu.au/imarusic/proceedings/7/McKelvieEtAl.pdf

http://large.stanford.edu/courses/2013/ph240/shen1/

Best of luck & regards--