During cruise flight, a passenger airplane maintains the cabin air at an absolute pressure of 75kPa, while the ambient air outside the fuselage is at an absolute pressure of 25kPa. Each passenger window is circular with a diameter of 0.30m. On one leg of the flight, cabin pressure is programmed to rise linearly at a rate of 2.0kPamin−1 as the aircraft descends, whereas the external air pressure remains essentially constant for the first several minutes of descent.
(a) Calculate the gauge pressure acting on the interior surface of a window during steady cruise at the stated pressures.
(b) Determine the net force on a single window under the same steady-cruise conditions.
(c) Derive an expression for the net force on the window as a function of time during the first 5.0min of descent, and calculate the force exactly at t=5.0min.