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For a completed water-hammer analysis, explain how the plane would look. A hot-water line 50 ft long and ~ in. in diameter is made of cast iron. The water is at 150°F and is flowing at 5 ft/s when the valve is suddenly cut off. (a) At what speed will the resulting wave propagate? (b) […]

Give a physical interpretation of the characteristics C+ and C-. If a device with the velocity-head relationship is placed at the end of a pipe, explain how the boundary conditions could be imposed.

A valve is rapidly opened on a 6,000-ft segment of water line with ID = 18 in. The allowable head IOS8 is 40 ft-lbf/lbm, with minor losses estimated at lOV2 /2gc’ How long will it take the system to reach 99 percent of its steady-state value? 8/D = 0.0015.

Rework Example 7-4 with the valve-closure protocol given as

Find the complement  of the set C with respect to the space C if

Find the union  and the intersection   of the two sets  and , where

List all possible arrangements of the four letters , and y. Let  be the collection of the arrangements in which y is in the last position. Let C2 be the collection of the arrangements in which m is in the first position. Find the union and the intersection of and .

Concerning DE Morgan’s Laws (1.2.6) and (1.2.7): (a) Use Venn diagrams to verify the laws. (b) Show that the laws are true. (c) Generalize the laws to countable unions and intersections.

By the use of Venn diagrams, in which the space C is the set of points enclosed by a rectangle containing the circles , and , compare the following sets. These laws are called the distributive laws.

Show that the following sequences of sets,  are nondecreasing, (1.2.16), then find