#$5.(20)$ A cylindrical rod of cross section A is pushed at constant velocity V with force F into a cylinder with cross section Aw$.$ Fluid in the cylinder is squeezed out of the cylinder into the ambient atmosphere. Assume that i$)$ the fluid is inviscid; and ii$)$ the gravity can be neglected.

a$)$ Is there a reference frame in which the flow from the cylinder to the annulus appears steady?

b$)$ Draw your control volume in that frame.

c$)$ Derive an expression for F in terms of Pw$,$Pa$,$Aw$,$V$,$A$,$ and rho.