A clutch manufacturer has called you to consult on a new design being considered. The system essentially consists of two rotating disks as shown. The axial loading will be about 2000 N, and the manufacturer estimates that the pressure distribution between the disks will be such that the wear will be uniform. This means that the product of pressure P and radius r will be constant C (i.e., Pr = C). F= 2000 N Stainless steel disk Teflon disk F= 2000 N N=5000 RPM 100 mm = 0.35 Teflon is being considered for one of the disks since during some modes of operation the disks will be slipping relative to one another and it is hoped that the low coefficient of friction ( = 0.04) between the steel and the Teflon will reduce losses. During operation the stainless steel disk will be at 5000 RPM, but the Teflon disk may be less than this. The frictional heating will cause the interface temperature to rise. For safe operation of the Teflon its maximum temperature should not exceed 150 C. The manufacturer is now planning to build the clutch with the only cooling being the 35 C air surrounding the disks. Your task is to estimate the slippage RPM that could be allowed without overheating the Teflon. In addition, the manufacturer is wondering what the increase in allowable slippage might be if a water cooling system were designed that would maintain the outer edge of the stainless steel disk at a temperature closer to or below the ambient. Note: for disks rotating in air, the average heat transfer coefficient h is given by V To =35 C hR k Where k and v are the thermal conductivity and kinematic viscosity of air respectively. WR WR2 3 mm T 12 mm V > 250,000