1. A major Midwestern university is redesigning its air conditioning system because both faculty and students complain that every spring, when the weather turns warm, it takes almost a week for the heating system to turn off and the cooling system to turn on. Ideally the designers would like to deliver chilled water to each building on campus at a rate of 0.1 kg/s through a pipe of radius 1 cm. At what speed will water need to flow through the pipe?
(a) 0.3 m/s
(b) 0.4 m/s
(c) 0.5 m/s
(d) 0.6 m/s
(e) 0.7 m/s
2. This and the following question concern the same physical situation.
Many small sailboats use a passive bailing system: there is a plug in the bottom of the boat that can be opened to drain water out of the boat. This works only when the boat is moving, because only then is the pressure under the boat less than air pressure, by Bernoulli's equation.
Consider a boat whose bailing plug is located 3 cm below the surface of the water. What is the minimum speed the boat must have so all the water drains out of the boat?
(a) 0.25 m/s
(b) 0.5 m/s
(c) 0.75 m/s
(d) 1.0 m/s
(e) 1.25 m/s
3. Now consider a boat with bailing plug located 6 cm below the surface of the water. If your answer to the previous question is v, then the minimum speed for this boat is
(a) v
(b) 1.4 v
(c) 2 v