An entrepreneurial new civil engineering graduate started a lab for testing endocrine disrupting compounds. The lab just broke even the first year, but in years 2 through 5, it made a profit of $97,000 each year. What is the present worth in year 0 of the profit at an interest rate of 10% per year?

Asolid cylinder is concentric with a straight pipe. the cylinder is 0.5 m long and has an outside diameter of 8 cm. the pipe has an inside diameter of 8.5 cm. the annulus between the cylinder ad the pipe contains stationary oil. the oil has a specific gravity of 0.92 and a kinematic viscosity of 5.57 x 10-4 m2/s. most nearly, what is the force needed to move the cylinder along the pipe at a constant velocity of 1 m/s?