An industrial pressure sensor is submerged in two different fluids until it registers…

PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Fluids · Fluids

Problem

An industrial pressure sensor is submerged in two different fluids until it registers the same gauge pressure of

2.50\times10^{5}\,\text{Pa}

. In Trial 1 the sensor is placed in seawater of density

1.025\times10^{3}\,\text{kg}\,\text{m}^{-3}

, and in Trial 2 it is placed in liquid mercury of density

1.36\times10^{4}\,\text{kg}\,\text{m}^{-3}

. Assume the local gravitational field magnitude is

g = 9.81\,\text{m}\,\text{s}^{-2}

and that the surface atmospheric pressure for both trials is

1.01\times10^{5}\,\text{Pa}

. (a) Calculate the depth of the sensor below the mercury surface in Trial 2. (b) Calculate the depth of the sensor below the seawater surface in Trial 1. (c) Determine the ratio

\dfrac{h_{\text{seawater}}}{h_{\text{mercury}}}

and interpret physically why the two depths differ by this factor. (d) Suppose the sensor were instead submerged in an unknown oil and positioned until it again registers the same gauge pressure of

2.50\times10^{5}\,\text{Pa}

at a depth of

34\,\text{m}

. Using your results, estimate the density of the oil and comment on whether it is likely to float on seawater.

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