When flow through a hypersonic blowdown tunnel is initiated by the bursting of a diaphragm, expansion of the process gas into the downstream vacuum of the facility creates a strong rarefaction wave. This rarefaction propagates upstream, generating significant pressure drops in upstream components, such as a heater. These pressure drops can be attenuated with the use of a metering orifice, which requires an accurate prediction of the pressure drop for proper sizing. So as to be generally applicable and to provide physical insight, a closed-form or simple numerical solution for determining this pressure drop is preferred over computational fluid dynamics. Three methods are investigated: acoustic reflection, flow pattern assumption, and the Method of Characteristics. By examining the three methods in conjunction, tradeoffs between complexity and physical accuracy can be analyzed. Ultimately, this study shall lead to the design of an experiment to verify the accuracy of the three methods.