The critical Reynolds Number in this thesis is determined by the method of pipe function. This method is based on the Poiseuille's law of laminar flow. The film coefficients of the SAE 20 oil are obtained from the equation, h = Q/AΔT Where h = film coefficient of oil, in BTU/(sq ft) (hr) (°F) Q = rate of heat flow, in BTU/hr A = total cooling surface, in sq ft ΔT = mean temperature difference between the oil and the pipe wall, in °F The rate of heat flow is calculated from the temperature drop and the rate of flow of oil. The cooling surface is obtained by multiplying the actual inside periphery of 3/8 pipe by the total length of the heat exchanger. The mean temperature difference is solved by the method of balance of energy. The critical Reynolds Numbers obtained lie between 1700 and 2360. The pump pressure causes the vibration of the pipes and the initial turbulence of flow, and consequently has the most dominating effect on the critical Reynolds Number. The temperature and size of pipe effect the pump pressure required for testing reaching the transition region but have little direct effect on the critical value. The pressure drop for laminar flow is approximately proportional to the Reynolds number. The film coefficients of laminar flow are very low and approximately proportional to Re⁰⋅⁴. However, when the transition region is reached the film coefficients increase suddenly and rapidly, and more and more slowly as the Reynolds Number is further increased. For the same Reynolds Number, the hotter oil has the lower film coefficient. / M.S.