Problem $3\mathrm{.}57$

The liquid level in a tank is determined by measuring the pressure at the bottom of the tank. A calibration curve is prepared by filling the tank to several known levels, reading the bottom pressure from a Bourdon gauge, and drawing a plot of level $($m$)$ vs$.$ pressure $($Pa$).$

Would you expect the calibration curve to be a straight line? Explain your answer.

The calibration experiment was done using a liquid with a specific gravity of $0\mathrm{.}900,$ but the tank is used to store a liquid with a specific gravity of $0\mathrm{.}800.$ Will the liquid level determined from the calibration curve be too high, too low, or correct? Explain.

If the actual liquid level is $8\mathrm{.}0$ meters, what value will be read from the calibration curve? If the tank has a height of $10\mathrm{.}0$ m$,$ what value will be read from the curve when the tank overflows?