1. The functional frequency n of a stretched string is a function of the string length L, its diameter D, the mass density r, and the applied tensile force T. Suggest a set of dimensionless parameters relating these variables.
2. The power P required to run a compressor varies with compressor diameter D, angular velocity ω, volume flow rate Q, fluid density ρ, and fluid viscosity μ. Develop a relation between these variables by dimensional analysis, where fluid viscosity and angular velocity appear in only one dimensionless parameter.