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If you draw the following diagram: you can see that the volume of the crater is the volume of the "truncated inverted cone" plus the volume of the bit of sphere. Since the volume of a cone is $V=\frac13 A h$ where $A$ is the area of the base and $h$ is the height, the volume of the truncated cone is given by $$V_{cone} = ...


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You could use two approaches. Sounds like now you're trying to carefully characterize and measure the shape of the crater, and then calculate the displayed volume. It sounds like the shape isn't completely regular, though, so you may have a tough time doing this accurately. Another approach would be to empirically measure the displaced volume of sand. Let's ...


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When the pressure increases, the flow decreases thereby providing the same "power". You can have larger flow if you naturally decrease the pressure, or larger pressure if you restrict the flow.


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Your answer lies in the ideal gas law: $$PV = nRT$$ where $P$ is pressure, $V$ is volume, $n$ is the amount of substance (usually in moles), $R$ is the "ideal gas" constant, and $T$ is temperature. You can see from the equation that if you're adding substance (i.e. increasing $n$), $V$ must increase proportionally (i.e. the piston must be displaced) to ...



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