# Is this air/water thrust/drag comparison correct?

On another list, someone asked regarding a blimp animal (hot-air balloon type object) propelling itself by using basically a bellows - and comparison to a nautilus (which bellows water to move around).

So,

"but seeing as air density is very low compared to that of water, you would need huge amounts of air expulsion pressure, so much so that I doubt a biological organism would be able to generate unlike one that lives in water..."

but then ..

"Air density being much lower than water means that the air jet produces less thrust, but also the blimp has to overcome less drag. I'd assume any potential thrust/drag ratio is the same for air as it is for water, since in both cases the same fluids are producing the thrust and drag."

The second comment seems wrong to me.

Is it?

How do "submarines" compare to "aircraft" in this? They both use propellors to push the fluid around. And for that matter does it make any difference if you're "squirting" the fluid?

Intuitively it seems to me easy for a sea being to move around by squirting water; intuitively it would seem all-but impossible for the Goodyear Blimp to move around by squirting air? (There seems to be "less" of the air; the drag doesn't seem relevant?)

• I would imagine it has more to do with the relative densities. The acceleration comes from the force pair between the submarine expelling the water and the water pusing back on the submarine. Since water is much denser than air you would need to accelerate a much higher volume of air to create the same pushback force. – cal Mar 22 '19 at 16:52
• got you @cal . Are you essentially saying the drag doesn't matter much ? (Which makes sense to me.) – Fattie Mar 22 '19 at 17:08

I believe I misunderstood the problem, after some thought the second comment does make sense. Suppose these Blimp animals are spewing out air at $$s_{ms^{-1}}$$ continuously (although not necesaraly as a constant rate) - for this to happen the creature must be putting power into the air: $$P= \frac{1}{2}\rho s^{2} \frac{dV}{dt}$$ As I mentioned, since this is a pair of forces the creature experiences a driving force in return: $$F = \frac{1}{2}\rho s \frac{dV}{dt}$$ Since both the driving force also involves the density of the medium, the terminal velocity of the creaure will not: $$v_{t}^{2} = \frac{s}{C_{d}A}\left(\frac{dV}{dt}\right)$$ This "formulation" is admittedly making a lot of assumptions but I think it helps illustrate the point in the second comment that the maximum veolicty of this animal isnt dependent on the density of the fluid it is moving thorugh. It is however function of the shape of the animal and the way in which it spits out the fluid.