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What is the mass percentage of Earth's atmosphere that escapes to the outer space each year? Assume the atmosphere reaches 10 km above the ground, the pressure is everywhere the same (equal to the pressure at sea level) and it consists of ideal gas at tepmperature 300K whose molecular speeds obey the Maxwell-Boltzmann distribution. Also assume that the gravitational field is homogeneous.

• How would you draw (using only drawing-compass and a ruler) the Zhukovsky profil?
• Draw the streamlines around the Zhukovsky profile. Choose the parameters $d/l$ and $m/l$ so that they have real world justification.
• What is the lifting force acting on a square board? On a semicircular board?
• Draw the profile of a wing that corresponds to the Kármán–Trefftz transform.

Consider the double doors of a building, between which is in the middle even in closed position small gap, where air can flow. Each wing has a spring that returns it to the starting (closed) position. Wing is displaced and then released. What will happen be the other wing?

If you are not quite sure, try it first (e.g. Ke Karlovu 5, Faculty of Science, Prague, …).

Titan (satellite of Saturn) is very cold (surface temperature is 94 K) with nitrogen atmosphere, with icy surface and hydrocarbon lakes on the surface. Radium of Titan is 5150 km, mass is 1 ⁄ 45 mass of the Earth, thickness if its atmosphere is 200 km and pressure on the surface is 1,5 bar.

Based on previous facts calculate acceleration due to gravity on the surface and estimate density of atmosphere. Comparing with parameters of birds at earth conditions decide, if feathered person could fly on Titan.

Get a inflatable ball, blow it up, make a knot on the orifice and measure how its volume is changing in time. Try to find out, how many percent of the surface is taken by pores, through which the air is escaping.

In this set of questions we will visit the world of science fiction. Space is filled with many space ships – one of them is Rama (A. C. Clarke: Rendezvous with Rama, Rama II, The Garden of Rama, Rama Revealed). Rama is large intergalactic ship constructed by extra-terrestrial civilisation and came to Solar system. Lets discuss some challenges, which are facing us.

Rama has a shape of cylinder of length 54 km and internal diameter 16 km. It is filled inside by air. Rama has its own gravity, which comes from rotating around its axis once per every four minutes. On inside surface the pressure of air is 1 bar.

The entrance to Rama is an orifice in the centre of one of its basis. Before removing the space suit, lets think, if on axis is breathable air, what is its density comparing to density on cylinder surface. Assume the temperature is the same everywhere.

Finally you got onto the surface of Rama. Suddenly it started to shake and you think the rotation speed has changed. How you can measure the rotation speed? Can you find more than one experiment?

You travel in fast train and are looking outside of the open window. Three windows in front of you someone spits a chewing-gum. How long do you have to get back to coupe to avoid contact with chewing-gum? The chewing-gum is spherical shape and was not thrown out, but just laid in air flow.

Calculate a slope of front glass of a car, so that water drops at speed 80 km ⁄ h do not run off, but to the sides. Verify that you results is compatible with reality. What else influence the slope of front window?

A submarine has dived into deep ocean in Marian ditch and released a bubble of air. It started to go to surface. However, when you calculate, using gas equation, density of the air, you will see that it is bigger than density of water. Is it possible?

If you agree, explain your answer. If you do not agree, calculate what will be parameters of the bubble (mainly density).