How can you determine the net force of a bottle

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To determine the net force of a bottle under 2 atm of pressure with a 1 cm opening, Bernoulli's equation may be relevant, though its application is uncertain in this case. The pressure difference is crucial for calculating force, using the formula F = P * A, where P is the pressure and A is the area of the opening. If the bottle has two openings, their areas can be combined to calculate the total area for force calculations. The outside pressure does play a role in the overall dynamics of fluid flow. Understanding these principles is essential for accurately determining the net force exerted by the bottle's contents.
Gmaximus
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How can you determine the net force of a bottle who's contents are kept under 2 atm of pressure, and it has a 1 cm opening for example?

a1v1=a2v2 doesn't seem to apply, and the flowrate=dav doesn't seem to either. I suspect it is bernoulli's equation, but I am unsure.

I know P=F/A, but how do you find the pressure? is it simply the pressure difference?
 
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Also, if the bottle has two openings facing in the same direction, how does that work? Do you add the area of the two holes and use that for area, or is it two separate cases?
 
Pressure is defined as "force divided by area" or P= F/A so F= P*A. You are given that the pressure is 2 atmospheres and the fluid is coming out an area of pi cm2 (I am assuming that the "1 cm" hole has radius 1 cm. If it is diameter= 1 cm, then the area is pi/4 cm2).

Yes, if you have two holes of area A1 and A2, then that is the same as 1 hole of area A1+ A2.
 
Does the outside pressure matter?
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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