Final answer:
The student wishes to know the reservoir pressure needed for a converging-diverging nozzle to achieve a Mach 2.0 flow at the exit without shock waves. The engineering problem involves applying fluid dynamics principles and isentropic flow relations. A numerical solution requires information about atmospheric pressure and reservoir temperature, which was not provided.
Step-by-step explanation:
The student is asking about the required reservoir pressure in a converging-diverging nozzle to achieve supersonic flow at the exit without the presence of a shock wave. Specifically, the Mach number at the nozzle exit should be 2.0. To answer this question, one needs to apply the principles of fluid dynamics and gas dynamics, particularly those relating to nozzle flow dynamics, the conservation of mass, momentum, and energy, and the equations governing the flow of compressible fluids such as the Bernoulli equation for compressible flow and the isentropic flow relations.
To determine the reservoir pressure, the nozzle must be designed to allow the gas to expand isentropically (without heat transfer or entropy change) from the reservoir to the exhaust where the flow achieves Mach 2.0. The design of the nozzle ensures that at any point within the diverging section, the flow remains supersonic and expansion occurs continuously until it reaches the desired exit Mach number. The pressure ratio between the reservoir and the atmospheric pressure (back pressure) should exceed the critical pressure ratio for the given Mach number according to isentropic flow relations.
Unfortunately, without providing the specific atmospheric back pressure and the temperature of the reservoir air, it's not possible to provide a numerical solution. However, the process generally involves using the isentropic flow equations to relate the exit Mach number with the conditions at the reservoir and the known atmospheric pressure conditions.