Q.1. One of the main problem in fluid mechanics is to determine the pressure variation in the fluid. Once known, pressure distribution can be integrated over the surface of a body subjected to the fluid, to determine the pressure forces. Pressure can vary in a fluid due to body forces (like gravity), inertial effects (acceleration or deceleration), and viscous effects. There are many cases where viscous effects are either absent (static fluids and fluids in rigid body motion) or assumed to be negligible. For such cases, Euler's equation is the general equation for pressure variation, which can be developed in different coordinate systems. By considering an element of continuum fluid in shear free situation, in spherical coordinate system, analyze the pressure variation in shear free fluid in spherical coordinates. Discuss the development of equations and interpret the equations. Simplify the derived equations for the case of static fluid. Consider the case of a spherical object of radius 'R' immersed in a static fluid. Integrate the pressure variation obtained from equations, over the surface of sphere to analyze the resultant pressure force and its point of application on the surface of spherical object. Compare your results with conclusions from buoyancy principle for the given object. [6+6] Q.2. A hydropneumatic elevator consists of a piston-cylinder assembly to lift the elevator cab. Hydraulic oil, stored in an accumulator tank pressurized by air, is valved to the piston as needed to lift the elevator. When the elevator descends, oil is returned to the accumulator. Design the least expensive accumulator that can satisfy the system requirements. Assume the lift is 3 floors, the maximum load is 10 passengers, and the maximum system pressure is 800 kPa(gage). For column bending strength, the piston diameter must be at least 150 mm. The elevator cab and piston have a combined mass of 3000 kg, and are to be purchased. Perform the analysis needed to define, as a function of system operating pressure, the piston diameter, the accumulator volume and diameter, and the wall thickness. [8]