Air in a pipe with a diameter of 10 cm starts out at a temperature of 700 K and pressure of 4 × 105 Pa. The initial flow velocity is 10 meters per second. If the pipe diameter contracts to 5 cm with the air speeding up to 115 m/s and the temperature decreases to 500 K, what is the pressure after the contraction? You can assume the molecular weight of air is 28.97 kg/kmol and a steady state. Start from the integral form of the continuity equation.