Hydro Man calculations

[LukesMom]

My 4th grade son wants to do a science fair project on the science behind Spider Man--specifically on the villain Hydro Man who turns himself into water to knock down Spider Man. He has figured out how to measure the mass of water that could fill a volume the size of Hydro Man's body. He has estimated the area of his shoulder (which is the "hose" through which the water squirts out. Now he's stuck--despite some google searches. We've talked about how momentum is conserved... which I assume is part of the solution. But I am not sure what else to tell him. The online searches he has done produced complicated equations that are beyond his math skills. And a rough estimate seems more appropriate with such a crazy topic, in any case. I love the fact that he wants to investigate what's in his comics instead of picking a more traditional topic, but I'm not sure how best to help him. Thank you in advance for any suggestions!

[kgudger]

Hello and welcome to the forums!

I'm not sure what question you are asking, could you please add a little more background information? You have the volume / mass of the water, and I think you're saying you have the cross-sectional area of the "output pipe", but I don't know what you're trying to figure out. It's true that calculating the emptying rate of the container (body?) will involve calculus to be exact, but there should be approximations that would work. I'm not sure what you're asking about the conservation of momentum - all I can think of is Newton's third law.. If "Hydro Man" squirts water out from his body, there will be an equal and opposite reaction - in other words, a recoil.

Please reply with more information so we can help!

Keith

[LukesMom]

Sorry, I didn't explain properly: my son is trying to figure out how fast Hydro Man would have to turn himself into water (i.e., squirt out the water), given the cross-sectional area of the "output pipe," to knock over Spider Man, who weighs 165 lbs from a distance of about 20 ft.

Many thanks!

[kgudger]

Hi:

I first did a search on these terms: "force of water through a nozzle". Here are some relevant equations from this search:

The thrust force is proportional to the exhaust mass flow through the nozzle times the velocity of the exhaust relative to the nozzle.
F(thrust) = m uex = pw An uex^2
where:
m is the rate of mass flow of the expelled water [kg/s]
uex is the exhaust velocity of the expelled water through the nozzle [m/s]
pw is the density of water [1000 kg/m3]
An is the area of the nozzle [m2]

NEWTON'S 2nd LAW OF MOTION
This states that the change in momentum of a mass is equal to the impulse given to it.
Impulse = Force x time
Momentum = mass x velocity
Change in momentum = ∆mv
Newton’s second law may be written as ∆mv = Ft
Rearrange to make F the subject. ∆mv/t = F
Since ∆v/t = acceleration ‘a’ we get the usual form of the law F = ma
The mass flow rate is m/t and at any given moment this is dm/dt or m' and for a constant flow
rate, only the velocity changes.
In fluids we usually express the second law in the following form. F = (m/t) ∆v = m'∆v
m'∆v is the rate of change of momentum so the second law may be restated as
F = Rate of change of momentum

From the above, I think you can very easily calculate the Force coming from Hydro Man. The next question is what force would be needed to dislodge Spider Man. I don't know what that force is (and didn't find any answers on the Internet), but the acceleration needed is clearly more than gravity (9.8 m/s^2) because Spider Man is able to stick to buildings and climb up them.
One way to approach this is to compare the amount of water (in kg?) coming from Hydro Man to impart a certain acceleration to Spider Man. Is this realistic? How much time would it take Hydro Man to use up all of his mass trying to accelerate Spider Man to 20 m/s^2 ? As I mentioned before, Hyrdo Man will have a recoil of the same Force on him, so it would probably knock him off his feet, too.

Keith

[LukesMom]

This is great--thanks so much, Keith!

... my son has told me he wants to investigate Electro next time--who shoots 100,000V bolts of electricity... hmmm... hopefully we will have grown out of Spider Man by then!