Chapter 15, Problem 98GP

Thunderstorm Outflow Rain-cooled air near the core of a thunderstorm sinks and then spreads out in front of the storm in a forward flank downdraft gust front (Figure 15-51). These gusts can vary from a cool breeze to a violent and damaging wind. Thunderstorms are extremely complex, but modeling air as an incompressible fluid can offer some insight. (a) Suppose 1.0 m³ of rain-cooled air has a density of 0.835 kg/m³, while the warmer air surrounding it has a density of 0.819 kg/m³. Taking into account the buoyant force on the parcel of air, find its downward acceleration. (b) If the parcel maintains the same acceleration from rest at an altitude of 4000 m, what is its speed when it arrives at the surface? (c) Now model the air as an incompressible fluid of constant density 1.02 kg/m³ that is at rest and has a pressure of 61.6 kPa at h = 4000 m altitude, but is moving and has a pressure of 101.3 kPa at h = 0 m. What is the speed of the air at the surface?

Figure 15-51 Problem 98