Answer Happy

2. You are developing an experiment for DARPA to learn more about how insects fly. Specifically, you want to build a scale model of a house fly that is bigger so that it is easier to measure lift and visualize the flow around the fly. You are trying to model the lift force (FL) generated by wings with a width (i.e. chord length) of Le, a length of R, an angular amplitude of which has units of radians, the angular flapping frequency w, and the density p and dynamic viscosity . (a) Choosing w, R, and p as your repeating parameters, develop a non-dimensional relationship between lift force and the other parameters. Identify which Pi group is the Reynolds number and which is the Drag Coefficient (HINT: We don't have a velocity, so instead you will see a rotational velocity, i.e. w * R) (b) The Pi groups you just found turn out to not be the best for a flapping wing insect. Instead, the Reynolds number can be rewritten much more usefully as IIRe PRLow. If you want your scale model to have a wing length (R) H of 20 cm and and your wm can go no higher than 10 Hz because your camera is slow and faster wing beats will blur, choose the blank variables in the table such that you achieve similarity. HINT: you will need to choose a liquid that has a high viscosity. Parameter R لها μl P Le Ф Prototype 2.5 mm 200 Hz 1.5x105m²/s 1.23kg/m³ 0.7 mm 2.8 rad Experiment 0.2 m (c) Explain your working fluid choice. Use engineering arguments, i.e. cite rational design concerns (physical proper- ties, cost, corrosiveness, toxicity,...) (d) Finally, if your experiment measures a lift of 1.0x106N, what do you predict the lift force generated by a fly to be?