Water at a gauge pressure of 3.8 atm at street level flows into an office building at a speed of 0.65 m/s through a pipe 5.6 cm in diameter. the pipe tapers down to 2.6 cm in diameter by the top floor, 20 m above (fig. 10-53), where the faucet has been left open. calculate the flow velocity and the gauge pressure in such a pipe on the top floor. assume no branch pipes and ignore viscosity.

The second largest public utility in the nation is the sole provider of electricity in 32 counties of southern florida. to meet the monthly demand for electricity in these counties, which is given by the inverse demand function p = 1,200 – 4q, the utility company has set up two electric generating facilities: q1 kilowatts are produced at facility 1, and q2 kilowatts are produced at facility 2 (so q = q1 + q2). the costs of producing electricity at each facility are given by c1(q1) = 8,000 + 6q12 and c2(q2) = 6,000 + 3q22, respectively. determine the profit-maximizing amounts of electricity to produce at the two facilities, the optimal price, and the utility company’s profit