Question

An aircraft comes into contact with supercooled water (supercooled water droplets exist in a range down to -20C) while flying through a cloud. Assuming that the cross-sectional area of the airplane is 10 m², the cruising speed is 200 mph, a horizontal traverse through the cloud core takes about 2 minutes, and that in the cloud there are 250 droplets per cubic centimeter, all of the same size and distributed uniformly with a radius of 20μm. Compute the cloud liquid water content (LWC) in the unit of g m^-3and the weight added on the aircraft after flying out of the cloud due to icing, assuming that all the water droplets the aircraft intercepted was by the cross-sectional area of the aircraft.

Answer 1

Liquid Water Content :

There are 250 droplets per cubic centimeter. Because 1 meter=100 centimeter,

So, the number of droplets in 1 cubic meter is  

Volume of a spherical droplet of radius    is :

Therefore, total volume of all the droplets in 1 cubic-meter of cloud is

  

Taking the density of supercooled water to be approximately 1000 kg/cubic-meter , not very different from density of water at 0 degree Centigrade and atmospheric pressure, the LWC is about 8.4 grams per cubic-meter.

Mass of ice added to the airplane :

The horizontal distance traversed by the aircraft, moving at speed of 200 mph , in a time interval of 2 minutes is

Given that the cross-sectional area of the airplane is 10 meter-square, we find that the plane covers a volume of

approximately .

Since LWC is 8.4 grams per cubic-meter, we find that the mass of ice picked up by airplane is about 900 kg .