Steam in a heating system flows through tubes whose outer diameter is 5 cm and whose walls are maintained at a temperature of 130 ◦c. circular aluminum alloy 2024-t6 fins (k = 186 w/m · k, ηf = 0.97) of outer diameter 6 cm and constant thickness 1 mm are attached to the tube. the space between the fins is 3 mm, and thus there are 250 fins per meter length of the tube. heat is trans- ferred to the surrounding air at t[infinity] = 25 ◦c, with a heat transfer coefficient of 40 w/m2 · k.
determine the increase in heat transfer from the tube per meter of its length as a result of adding fins.

Suppose water is leaking from a tank through a circular hole of area ah at its bottom. when water leaks through a hole, friction and contraction of the stream near the hole reduce the volume of water leaving the tank per second to cah 2gh , where c (0 < c < 1) is an empirical constant. a tank in the form of a right-circular cone standing on end, vertex down, is leaking water through a circular hole in its bottom. (assume the removed apex of the cone is of negligible height and volume.) (a) suppose the tank is 20 feet high and has radius 8 feet and the circular hole has radius 2 inches. the differential equation governing the height h in feet of water leaking from a tank after t seconds is dh dt = − 5 6h3/2 . if the height of the water is initially 8 feet, how long will it take the tank to empty? (round your answer to two decimal places.)

A5 foot by 5 foot box culvert is buried 6 feet beneath the surface of the ground. a crosssection of this very long culvert (into and out of the page) is illustrated below. assume that the soil in which the culvert is buried has the following properties: jt = 120 pcf, w = 12%, ko = 0.50, ka = 0.33, and kp = 3.00. calculate the total horizontal force per unit length of culvert (fh) felt on one of the vertical faces of the culvert.

If state law mandates that elevators cannot accelerate more than 2.40 m/s2 or travel faster than 14.8 m/s , what is the minimum time in which an elevator can travel the 373 m from the ground floor to the observatory floor? ?