Cavitation in the Wake of an Underwater Bullet

In this video, Destin was hoping to continue his investigation on guns underwater. He opted to use an AK-47 and a high-resolution, 27,450 frames-per-second camera in a swimming pool. At normal video speed, you cannot see the bullet exit the gun but you can see the disturbance in the fluid around it. The bullet travels about 5 to 6 feet before being completely slowed by the water.

In the slow motion of the video, we observe a more sophisticated fluid motion. As the bullet leaves the chamber, a cloud of disturbance traces the bullet’s trajectory in three regimes: gunpowder, water jet, and bow shock. We learn that each bubble undergoes volume oscillations due to momentum and pressure forces as well as the balancing of mechanical energy. After collapsing, the bubbles never become as large as they were in the first moment after the bullet passed because of energy dissipation.

Destin explains how this bubble phenomena is dictated by the Rayleigh-Plesset equation shown below

where P_B(t) is the pressure within the bubble, P_∞(t) is the pressure at a distance infinitely far from the bubble, L is the density of the liquid, R(t) is the radius of the bubble, v_L is the kinematic viscosity and S is the surface tension of the bubble. The phenomena characterized by the Rayleigh-Plesset equation is called cavitation.

In practice, the reason that the bubble forms in the first place is because the fluid around the bullet when gains kinetic energy from the velocity of the bullet and pushes the fluid to expand outwards. The bubble eventually stops expanding as the kinetic energy turns into potential energy and the pressure difference inside and outside of the bubble is great. The pressure gradient of low pressure inside the bubble and high pressure outside the bubble then forces it to compress.

Destin kindly annotated the fluid disturbance in the image above where each bubble is a result of a process of the firing mechanism. One explanation as for why the leftmost bubble looks smoother than the right bubbles is that the flow around the bullet in this region best resembles laminar flow due to a smaller velocity as dictated by the reynold’s number

Re=ρvd/μ

While I am from Texas, I’ve only shot a gun once in my life and it too was an AK-47. Guns don’t interest me terribly but gun safety does. Some of the appeal of this video is the strategy behind jumping in water when being shot at- this information could come in handy one day. This video also piqued my interest because it was related to a 2010 Mythbusters episode where they did a similar experiment in which they discovered that an even bigger gun--- a 50 caliber sniper lost all velocity at 3 feet into water.

References:

1. Leighton, T.G. (2007) Derivation of the Rayleigh-Plesset equation in terms of volume. Southampton, UK, Institute of Sound and Vibration Research, University of Southampton, 26pp. (ISVR Technical Reports, 308).