The Kraken-IV is an autonomous space probe designed to explore deep reservoirs of liquid hydrocarbons on Saturn's moon Titan.
The average density of the liquid hydrocarbon mixture in Titan's seas is 650 kg/m3650\text{ kg/m}^3650 kg/m3.
State the equation linking pressure difference, depth, density and ggg.
Calculate the increase in pressure as the Kraken-IV descends from the surface to a depth of 450 m450\text{ m}450 m. (Take g=1.4 m/s2g = 1.4\text{ m/s}^2g=1.4 m/s2 on Titan)
The atmospheric pressure at the surface of Titan is 1.5×105 Pa1.5 \times 10^5\text{ Pa}1.5×105 Pa.
Calculate the total pressure on the Kraken-IV when it is at a depth of 450 m450\text{ m}450 m.
On another mission, the Kraken-IV experiences a total pressure of 8.2×105 Pa8.2 \times 10^5\text{ Pa}8.2×105 Pa. The circular viewing port on the probe has an area of 0.35 m20.35\text{ m}^20.35 m2.
State the equation linking pressure, force and area.
Calculate the force on the outside of the viewing port.
The Kraken-IV is also tested in a calibration facility containing pure liquid ethane, which has a density of 540 kg/m3540\text{ kg/m}^3540 kg/m3. Explain why the pressure on the probe in the pure liquid ethane is less than the pressure in the liquid hydrocarbon mixture at the same depth.
A student is given a sample of liquid hydrocarbon labelled "Titan-simulant". Describe an experiment that the student could carry out to find the density of the sample.
