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## Homework Statement

i)Derive the fact that hydrostatic pressure increases linearly with depth under the surface of a fluid (assumed to be of constant density). Comment on how your answer would change if density is also allowed to vary with depth.

ii) Show that the force per unit volume in a fluid is simply [tex] -\nabla p [/tex]

iii) A block of mass 'm' and density '[tex] \rho [/tex]' is suspended from a spring (with spring constant k) in a fluid of density [tex] \rho_f < \rho [/tex]. Drive an expression for the extension of the spring from its equilibrium length.

## Homework Equations

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## The Attempt at a Solution

Honestly I have been staring at this for a while not knowing how to start. I've only had one lecture on this in the class so far. It was pretty basic, archemide's principle, force is normal to object, pressure is a function of depth, yada yada yada...

Also I remember the del notation from Calculus III, but haven't used it yet in Physics. I remember its [tex] \nabla f = < \frac{\partial f}{\partial x} , \frac {\partial f}{\partial y} , \frac {\partial f}{\partial z} > [/tex] and I think this is the direction and slope of greatest rate of change? I can't think of how this applies to part ii.

Any tips on any of the parts would be GREATLY appreciated!