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1. Find the circulation around a circle around the origin for the difused vortex flow of question 4.2c by directly integrating the line integral. Also find it by integrating the vorticity in accordance with Stokes' theorem. Do you get the same result? If not, explain why not.

2. Find the circulation around a square around the origin for the line vortex flow of question 4.2b by directly integrating the line integral. Also find it by integrating the vorticity in accordance with Stokes' theorem. Do you get the same result? If not, explain why not. (Hint: Note that the flow of the previous question is the same as the one here if seen from a large distance. So, if you do the integrals of the previous question over a large circle and you look at them from far away, things would look the same.)

3. 5.1 (b). Also do and explain $\int_{\rm FR} \rho\;dV$. Note that this is incompressible inviscid flow. The viscous flow is much more complex.

4. If the jet leaves a rocket through an area of 0.5 m$^2$ at a velocity of 500 m/s relative to the rocket, and the exit density is 0.5 kg/m$^3$, what can you say about what happens to the total mass of the rocket?

5. 5.1 (a).

6. 5.1 (d).