A laparoscopic tool consists basically of a long, thin shaft with a gripper at the end. Its shaft is a hollow tube through which a wire is used to actuate the gripper. Derive a performance index for a light, stiff, thin-walled tube of this type under bending loads. Consider the diameter to be fixed and the tube thickness to be the free variable. [Hint: use the fact that this is a thin-walled tube to obtain a simplified moment of inertia expression for use in deriving the performance index.]

At steady state, air enters an insulated duct of varying cross-sectional area (similar to a nozzle or diffuser) at 200 kpa, 52°c with a mass flow rate of 0.5 kg/s. at the duct exit, the pressure of the air is 100 kpa, the velocity is 255 m/s, and the cross-sectional area is 2 x 10-3 m^2. assuming an ideal gas model, determine: a)-find the specific volume of the air at the exit, in m3/kg. b)- the temperature of the air at the exit, in k. c)-the velocity of the air at the inlet, in m/s. d)-the inlet cross-sectional area, in m^2.