Can someone help me understand Bernoulli's Equation?

AI Thread Summary
Bernoulli's Equation expresses the principle of conservation of energy in fluid dynamics, represented as C = v^2/2 + gz + P/p, where C is the total energy per unit volume. It combines kinetic energy per unit volume (v^2/2), potential energy per unit volume (gz), and pressure energy (P/p). The equation illustrates how these forms of energy are interrelated in a flowing fluid, indicating that an increase in one form results in a decrease in another, maintaining constant total energy. Understanding this relationship is crucial for analyzing fluid behavior in various applications. For a deeper explanation, resources like Wikipedia provide comprehensive insights into the equation and its implications.
06mangro
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C=v^2/2+gz+ P/p

This is it... there is pressure P... and then kinteic energy per unit volume and potential energy per unit volume... adding all of these gives = conservation of energy...

Why is this?
(Might need to explain the conservation of energy)
Preferably a more wordy reply :) thanks
 
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Wikipedia has an excellent article on it.
 
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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