An advanced aerospace glider cruises near the edge of space

An advanced aerospace glider cruises near the edge of space at 51, 000 feet of elevation where p_atm = 11 kPa. Using a static cable, it drops a sensor down into the atmosphere. The sensor in the atmosphere reads 200 mm of mercury. How long is the sensor cable in meters? Assume p_Hg = 13, 600 kg/m^3, p_air = 1.1 kg/m^3 and 3.281 feet = 1 meter.

Solution

P = p0 + Pa*g*h

h = P -p0/(Pa*g)

P = pm*g*h = 13600*0. 2*9.81 = 26683.2

h = 26683.2 - 11000 / ( 10.78 )

h = 1454.84 meters

h = 4773.33 feet