Question

Consider the following temperature surroundings:

Ground level, 21oC; 500m, 20oC; 600m, 19oC; 1000m, 20oC.

1) If we release a parcel of air at 600m, will it rise, sink or remain at 600m?

2) If a 70-m stack releases a plume with a temperature of 30oC, how high does the plume rise?

Answer 1

1. There will be no rise nor sink if the parcel is released at 600m and 20* Celsius .
2. parcel will rise to 1200 m roughly.

• EXPLAINATION:
• The rate of Cooling ( Dry Adiabatic lapse rate ) of parcel is -1* for every 100m rise.
  Since the parcel is Warmer (30* celcius) then surrounding it will continue to rise until its temperature is cooled and gets equal to surrounding temperature (Enivornmental Lapse rate i.e given in question 1 ) .
• So when parcel rises say 1000 m above its initial position it's temperature decreases by 10* Celsius . Hence its temperature now becomes 20*c ( at height of 1000+70=1070 m) but surrounding temperature is still cooler (i.e 19 * Celsius as mentioned in question ) hence parcel will further rise and finally at height of (1200 m) it will stop disperse .
• Because in question it is mentioned at 600m temp is 20* Celsius and at 1000 m temp is 19* Celsius . So if we assume linear fall in temperature , it shows -0.25 * Celsius for 100 m . So at 1200 m surrounding temperature will be 18.5 * celcius , which would be same as if Parcel ( Adiabatic ) temperature .
• Hence parcel will stop at 1200 m roughly.