Fluid Mechs: Find Min Mass for Barge Stability

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The discussion focuses on determining the minimum mass that can be added to a barge without compromising its stability, specifically in relation to metacentric height. The user encountered a non-real solution while setting the equations, raising questions about its commonality. It is noted that non-real solutions can indicate that the barge is already at maximum stability, or that there may be errors in the calculations or assumptions made. To resolve the issue, it is recommended to review the equations and assumptions or to test different parameters. Overall, careful verification of the calculations is essential for accurate results in fluid mechanics.
Kenny Lee
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Hi there!
If anyone out there knows fluid mechs... please help out. Simple question on the stability of a floating body; has to do with the meta-centric height etc.

I was supposed to find the minimum mass which could be placed on top of a barge without causing it to lose stability; so I just set the equations with metacentric height equal to zero.

All I need to know is if acquiring a non-real solution is something 'common'? Cause that's what I got. And if it is, then pls let me know what I shud do. If it is not something 'common', then ignore this thread. I probably did something wrong; I'll just look through it again.

I WOULD post the question and my answer, but its a lot to type. And me not knowing how to use latex... thanks for reading.
 
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Non-real solutions in this type of problem are not uncommon. It may mean that the barge is already at its maximum stability and no more weight can be added without becoming unstable. It could also mean that a mathematical error was made somewhere in the equations or that the assumptions used to set up the equations were incorrect. The best way to check if there is an error is to go through your equations and assumptions again and make sure everything is correct. You could also try running the equations with different parameters to see if you get a real solution.
 
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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