Methane, approximated as a perfect gas, is compressedadiabatically from 101 kPa and 20°C to 300 kPa. Estimate(a) the fi nal temperature, and (b) the fi nal density.

For a hotshot wind tunnel with T=50o0k and P=100 MPa. Calculate and plot Mach number as a function of ratio A/At for the choked nozzle of the tunnel for 1) air in thermochemical equilibrium and 2) air with chemical composition and all internal energies except for translational.

A cylindrical tank shown below has a radius ? and a circular orifice at the bottom of radius ?. At time ? = 0 the liquid level in the tank is ho. (a) Use the Bernoulli equation to determine the relations between the orifice velocity ?o and the free surface velocity ?s (assume the surface velocity is not zero). (b) Use conservation of mass to determine the orifice velocity in terms of the free surface velocity. (c) Use the results in (a) and (b) to derive a differential equation for h(?). Note that ?s = − dh/dt. d) Separate variables and solve the equation for h(?) with the initial condition h(0) = ho (e) Determine how long it will take to empty the tank.

Does the Castgilanio's theorem consider a body of arbitrary shape only?