An above-ground storage tank contains a large volume of industrial oil (density 850kgm−3). The tank is open to the atmosphere whose pressure is 1.01×105Pa. A pressure sensor is installed at a point h meters below the free surface of the oil.
The sensor will later be relocated to a refinery on Titan, Saturn’s moon, where the local gravitational field is gTitan=1.35ms−2. To guarantee that the sensor reading at the new site matches the gauge pressure it recorded on Earth, engineers propose changing only the sensor’s immersion depth.
(a) Derive a symbolic expression for the Earth depth hE that yields a gauge pressure of Pg in terms of the given quantities.
(b) If engineers wish the sensor to register a gauge pressure of 7.5×104Pa on Earth, calculate the required depth hE.
(c) Determine the depth hT that would produce the same gauge pressure on Titan.
(d) Qualitatively discuss how a decrease in gravitational field strength affects the required immersion depth and comment on whether the assumption of an incompressible fluid could influence your results at great depths.