Velocity and mass relation by fluid jet propulsion of a squid

[mysnoopy]

Several species, including the squid, cuttlefish, dragonfly fish and many microscopic organisms, move themselves around by a kind of jet propulsion.

In each case the animal absorbs fluid in a body cavity and expels it through an orifice by contracting the cavity. If a squid has a mass Ms when its cavity is empty, and can store mass Mw of water in the cavity, write down an expression relating the velocity of the squid Vs to the two masses and the velocity of the expelled water, Vw.

 

[clamtrox]

I think the easiest way to approach this is to use conservation of momentum.

 

[siddharth23]

I don't think conservation of momentum applies here. The external force of water resistance acts on the squid as it propells forward. Has been mentioned to neglect the water resistance?

 

[HallsofIvy]

If you are NOT neglecting water resistance then there is no way to do this problem. Use conservation of momentum.

 

[haruspex]

I don't think conservation of momentum applies here. The external force of water resistance acts on the squid as it propells forward. Has been mentioned to neglect the water resistance?

The affect of a force such as water resistance on the momentum will be as ∫F.dt, where F is a function of velocity. If the time taken to expel the water is very short then this quantity will be quite small. The main affect of the water resistance is in the subsequent slowing down.

 

[jwelch]

This is a common problem known as the Rocket Ship problem in most physics textbooks.

What is important about this problem is the setup. If you consider the mass of both the squid and the water to be the system you are interested in, then in the COM frame, the momentum doesn't change. It is basically the opposite of an inelastic collision where one particle sticks onto another: the particles separate and the energy changes, but the momentum transfers just the same.

Given that the momentum doesn't change with time, you can use the following relationship

\dot{p} = 0 = m*\dot{v} + v*\dot{m}.

From this step, you need to carefully consider what each V and M are and how to perform the necessary integrals to find your solution. Just remember what everyone always forgets when you integrate and use the initial conditions.