Thunderstorm Outflow Rain-cooled air near the core of a thunderstorm sinks and t

Question

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 1). 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. Suppose 1.0 m^3 of rain-cooled air has a density of 0.839 kg/m^3, while the warmer air surrounding it has a density of 0.818 kg/m^3. Taking into account the buoyant force on the parcel of air, find its downward acceleration. Express your answer to two significant figures and include appropriate units. If the parcel maintains the same acceleration from rest at an altitude of 4200 m, what is its speed when it arrives at the surface? Express your answer to two significant figures and include appropriate units.

Explanation / Answer

A)
net force acting on the parcel of air,

Fnet = m*g - Buoyant force

m*a = m*g - rho_hot*V*g

a = g - rho_hot*V*g/(m*g)

= g - rho_hot*V*g/(rho_cool*V*g)

= g - rho_hot/rho_cool

= 9.8 - 0.839/0.818

= 8.8 m/s^2 <<<<<<<<<<<----------Answer

B) speed of of parcel of air when it reaches ground,

v = sqrt(2*a*h)

= sqrt(2*8.8*4200)

= 2.7*10^2 m/s <<<<<<<<<<<----------Answer

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