The power P required for operating a pump depends on the diameter of the pump D, the pressure rise Ap across the pump, the fluid density p, the fluid viscosity and the volume flow rate Q through the pump. Using Buckingham's 7 Theorem, and D, Q and p as the repeating variables, the dimensionless TT group associated with is given by DaQbp. Determine the values of a, b and c. 1. [0.99, 1.01 2. [-1.01, 0.99 3. [-1.01, -0.99 a= b= C=

An elastic foundation is often used to support heavy machinery that vibrates in such a way to cause problems for the rest of the structure. An elastic foundation with two equal springs each of stiffness k = 600 lbs/in is used to support the equipment of weight W = 1000 lbs shown. The equipment vibrates in such a way that it causes a vertical forcing function P(t) = 100 sin(20t) [lbs]. %3D (a) Draw the degree of freedom for the motion of the machinery. (b) Determine the equation of motion. What type of motion is this? (c) Determine the natural frequency and the displacement of the machinery. (d) What is the maximum amount of force that will be felt by the rest of the structure? (Think about what causes force to the rest of the structure) Rest of structure Hww