Pressure derivation If possible, fast please.

AI Thread Summary
The discussion centers around the derivation of the pressure formula P=Po+(mg)/(π*r^2). The initial attempt at deriving the formula resulted in P'(r)=(2mg/π(r^3))*Δr, which was deemed incorrect by the teacher. The teacher pointed out that the derivation failed to account for changes in Po and m, denoted as ΔPo and Δm. The user seeks guidance on how to correctly perform the derivation for error calculation in laboratory work. Clarification on these variables is essential for accurate results.
kristiine_c
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Homework Statement



I' have formula P=Po+(mg)/(π*r^2)

I need to derive it.
I have derived it P'(r)=(2mg/π(r^3))*Δr

but it's incorrect. The teacher wrote me "You have forgotten about ΔPo and Δm!"
I don't know how I could derive it. It's for mistake calculation in laborotory work!
 
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kristiine_c said:

Homework Statement



I' have formula P=Po+(mg)/(π*r^2)

I need to derive it.
I have derived it P'(r)=(2mg/π(r^3))*Δr

but it's incorrect. The teacher wrote me "You have forgotten about ΔPo and Δm!"
I don't know how I could derive it. It's for mistake calculation in laborotory work!

Your question is without context.
 
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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