Measurements of the flow velocity within rockets and gas-turbines prove to be a difficult problem due to the high temperature, high pressure, and high noise levels encountered. Velocity measurements in such environments are required to understand the physics of the flow field to improve the design and efficiency of these engine types. The design of a water-cooled jacket intended for use in conjunction with an existing novel, miniature fiber-optic LDV probe to make velocity measurements in these extreme engine environments is the topic of this research. The jacket design uses off-the-shelf materials and machining techniques in order to reduce cost and simplify manufacturing. The jacket was designed and drawn using the 3D parametric modeling software called SolidWorks. The SolidWorks CFD add-in, FloWorks, was used to numerically simulate the insertion of the water-cooled jacket into the afterburner or augmentor section of an air-breathing gas-turbine engine operating at 2000 K static temperature. The augmentor diameter was chosen to be 18 inches based on the existing General Electric J-85 jet engine augmentor. Different configurations in which the combinations of jacket insertion distance, augmentor flow velocity Mach number, and alternate jacket tip designs were examined and analyzed in order to determine the operating conditions that will permit velocity measurements representative of the undisturbed freestream velocity. Computational results indicate that while a cooling water flow rate of 3 GPM allows for the successful operation of the jacket within the augmenter at Mach 0.7 and 2000 K, Mach numbers of 0.5 and below exhibit flow field disturbances that will allow for LDV measurements representative of the freestream.