A mountain climber determines his altitude using atmospheric pressure and temperature measurement data. He uses a mercury barometer to measure the atmospheric pressure at his position and information about the atmospheric pressure and temperature at sea level is transmitted to him.
At a certain time the climber's barometer reading is 583 mm Hg while the atmospheric pressure and temperature at sea level are given to him as 1013 mbar and 20 °C, respectively. The relative density of mercury is 13.6 and the acceleration due to gravity is 9.81 m/s2.
(a) If a mercury barometer is used to measure the atmospheric pressure at sea level, what height does the liquid in the barometer rise to(b) Assuming that the density of air is 1.2 kg/m3 and remains constant with altitude, determine the altitude at the position of the climber.
(c) In order to improve the accuracy of his altitude determination method, the climber decides to consider the variations of the atmospheric air density with height. In this case, he determines his altitude using the hydrostatic pressure equation for the general case of varying fluid density (as derived in the Lecture Notes, Section 2.1).
For the atmospheric air density ρ, the climber uses the equation:
ρ=p/RT
where: p = air pressure, T = air temperature (both pressure and temperature vary with height), and R = air gas constant = 287 J/(kg K). The atmospheric temperature lapse rate is 0.007 K/m (the temperature lapse rate is the temperature drop in degrees Kelvin per metre of altitude).
What is the altitude of the climber as determined using this more accurate method?
(d) In view of your results, is it reasonable to ignore the air density variation with height when determining the altitude?