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1. Why is valve closing in a time greater than 2L/ a often referred to as slow closing, while valve closing in less than 2L/a is often called rapid closing? 2. What is the method of characteristics?

1. For rigid theory, why is it convenient to base all times on the time required for a flow to accelerate to 99 percent of its steady-state value? 2. All other factors being the same, what is the effect on a, the water-hammer wave velocity, of increasing wall thickness of a thin-walled elastic conduit?

Why is rigid theory a reasonable model for events (such as a valve closing) that happen slowly, while water-hammer analysis is needed for events that happen rapidly?

1. A pipeline (V = 6ft/s,D= 1 ft,H = 100ft-Ibfllbm,L= 8,000 ft) has its head increased to 300 ft-lbf/lbrn. How long willit take for the flow to accelerate from zero to the steady-state velocity for the initial H (100 ft-lbf/lbm)? How long for the new steady-state velocity to be attained? 2. A hydraulic turbine requires

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