Design for Manufacturing Assignment

Question 1: If the elastic and inertia forces within a structure have to scale proportionately, how would the angular acceleration associated with the system change with respect to physical size if the material remains the same?

Question 2: A new heat storage system has to be tested using a model where the ratio between the heat capacity and the conducted heat has to remain constant, how would the volume flow rate data collected scale with respect to the model size?

Question 3: If when building a larger weir the ratio between the inertia and gravity forces have to remain constant, how would the flow rate over the weir scale for the same fluid?

Question 4: If a system is characterized by requiring that the ratio between gravity and inertia forces remain constant, how would the drag associated with the system scale with respect to system size?

Question 5: The lowest power motor in a series of six motors is 40 kW and the highest in the series is 160 kW, with a fine range of powers at the low end a coarser range of powers at the high end. If the scaling is based on a constant Cauchy number, what would be the associated range of shaft diameters, if the largest motor had a shaft diameter of 25 mm? In addition, what would be the associated torque values associated with each motor, if the torque for the weakest motor is 300 Nm?