5. A biomedical device utilizes a stirrer to mix the specimen in a container. To design the device, we need to know the power required to operate this machine. It is known that the power is a function of 1) diameter of stirring impeller, 2) number of rotations of the impeller per unit time, 3) specimen viscosity, and 4) specimen density. Using Buckingham Pi theorem to obtain the relationship between power and other variables. In the experimental testing, the power consumption was found to be proportional to the square of rotation speed. By what factor would the power be expected to increase if the device needs to scale up and the diameter of stirring impeller was doubled?

Lake Ontario has a volume of approximately V =1600 km3. It is heavily polluted by a certain pollutant with a concentration of co = 0.1%.As a part pollution control, the pollutant concentration of the inflow is reduced to cin = 0.02%. The inflow and outflow rates Qin = Qout = Q = 500 km3 per year. Suppose that pollutant from the inflow is well mixed with the lake water before leaving the lake. How long will it take for the pollutant concentration in the lake to reduce to 0.05%?

Mist (airborne droplets or aerosols) is generated when metal-removing fluids are used in machining operations to cool and lubricate the tool and workpiece. Mist generation is a concern to OSHA, which has recently lowered substantially the workplace standard. An article gave the accompanying data on x = fluid-flow velocity for a 5% soluble oil (cm/sec) and y = the extent of mist droplets having diameters smaller than 10 µm (mg/m³): 90 177 180 354 365 442 964 y 0.38 0.60 0.47 0.66 0.62 0.69 0.91 (a) The investigators performed a simple linear regression analysis to relate the two variables. Does a scatter plot of the data support this strategy? shows a reasonable linear relationship. O No, a scatter plot does not show a reasonable linear relationship. (b) What proportion of observed variation in mist can be attributed to the simple linear regression relationship between velocity and mist? (Round your answer to three decimal places.) (c) The investigators were particularly interested in…

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An engineer wants to compare the tensile strengths of steel bars that are produced using a conventional method and an experimental method. (The tensile strength of a metal is a measure of its ability to resist tearing when pulled lengthwise.) To do so, the engineer randomly selecto

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