Answer
0.96 atm.
Work Step by Step
Use Bernoulli’s equation to estimate the air pressure inside the hurricane. Assume the pressure outside the hurricane is 1.0 atm, the airspeed outside is 0, and that the two pressure measurements are made at the same height. 300 km/h = (300000m)/(3600s) = 83.33 m/s.
$$P_{in}+\frac{1}{2}\rho v_{in}^2+\rho g y_{in}= P_{out}+\frac{1}{2}\rho v_{out}^2+\rho g y_{out}$$
$$P_{in}= P_{out}-\frac{1}{2}\rho v_{in}^2$$
$$P_{in}= 1.013\times10^5\;Pa-\frac{1}{2}(1.29\;kg/m^3) (83.33\;m/s)^2$$
$$P_{in}= 9.7\times10^4\;Pa\approx 0.96\;atm$$
