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(b) is correct. Your equation applies only if all the fluid is the same fluid. Suppose that, as in your problem, E = gz, where z is the elevation above the base. So, the component of your equation in the z direction becomes $$\frac{dp}{dz}=-\rho g$$ Because points 3 and 4 involve the same fluid, the pressure at these two points is the same, say ...


Adiabatic bulk modulus of air $=1.4\times 10^5$ Pa and Young's modulus of steel $=1.8 \times 10^{11}$ Pa. Density of air $= 1.2 $ kg m$^{-3}$ and of steel $8050$ kg m$^{-3}$. The interaction between the atoms within steel is via the bonds whereas the interaction in air are by molecules colliding with one another and limited by the speed at which the ...


Please study Ned Wright's Cosmology FAQ: How do Astronomer's Measure the Density of the Universe? There it is pointed out that the local density varies from region to region; the scale of the region surveyed determines the granularity. The answer is clear and obvious: the density of the universe is NOT uniform at all distance and time scales.

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