Can someone explain this fluids formula to me?

AI Thread Summary
The discussion centers on understanding the hydrostatic pressure formula in the context of hydrostatic lifts. The equation P0 + P1 = P0 + P2 + (rho)gh illustrates that the term (rho)gh represents the hydrostatic pressure due to the weight of the fluid column. This pressure is derived from the relationship between mass, density, and volume, where mass is expressed as density multiplied by volume. The force exerted by the fluid is determined by the height of the fluid column, not the area, confirming that hydrostatic pressure is dependent on the fluid's density and height. The explanation clarifies the connection between gravitational force and fluid pressure in this context.
fernancb
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Homework Statement


The question pertains to hydrostatic lifts. So, assuming you have a lift and you're applying pressure to one side and the other side is rising:

P0 + P1 = P0 + P2 + (rho)gh

Now, when we look at the equation, why is it (rho)gh? I'm thinking it's something like mgh, so to convert it to fluids it would be (rho)Vgh why is this?
 
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rho*g*h is the hydrostatic pressure due to the gravity force on a fluid. Basically, the force a column of fluid will exert on a region beneath it is equal to the mass of the fluid times the acceleration of gravity, or m*g. Mass can also be written as density multiplied by volume, so m*g = rho*v*g. Now, per unit area, the volume of fluid is simply the height of the fluid column, so the force per unit area is equal to rho*g*h.
 
Okay, so the force exerted depends just on the the mass/volume/height of the fluid above it. Not the area. Did I get that right?
 
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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