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v1 2.006F08 1 MASSACHUSETTS INSTITUTE OF TECHNOLOGY 2.006 Thermal Fluids II Problem Set 1 Issued: Tuesday, February 5, 2008 Due: Thursday, February 14, 2008 Problem 0 Please read the course notes Chapter 10. Part A: In an attempt to help you refresh your memory, we would like you to do the short questions from last term’s 2.005 final exam. Please support all your answers. Relevant properties appear on the last page of this problem set. 1) A 10 cm diameter pipe is a kilometer long. Oil is pumped through the pipe at 1 kg/s. What is the viscous pressure drop across the pipe? 2) A 5 cm diameter copper sphere is suspended in 10 C air. If the sphere is initially at temperature 30 C and the overall heat transfer coefficient to the air is 10 W/m 2 K, how long does it take for the sphere to cool to 20 C? 3) One kilogram of helium is initially at a temperature of 300 K and pressure of 10 5 Pa. The gas undergoes a heat transfer process by interacting with a 500 C temperature reservoir, followed by a work process where 10000 J of work are performed on the gas. This is followed by an irreversible heat transfer interaction with a -50 C temperature reservoir. The gas is then isolated and allowed to come to internal thermal equilibrium. The final temperature and pressure of the gas is 330 K and 2x10 5 Pa. What is the change of entropy of the gas for the complete process? 4) What is the energy change for the gas discussed in problem 3? 5) One kilogram of helium initially at pressure and temperature of 10 5 Pa and 300 K, undergoes a reversible and adiabatic process. If the final pressure is 10 6 Pa, what is the final temperature? 6) A massless rigid-corner gate shown above keeps water from flowing out of a vat. As the vat is filled, the water level slowly rises until the gate opens, pivoting around the hinge. What is the height h just before the gate opens? 7) A 0.3 m diameter hollow sphere is comprised of two hemispheres sealed with a gasket along its equator. The interior volume is evacuated. The sphere is then immersed in fresh water and brought to a depth of 100 m. What force is required to pull the two halves apart by pulling on cables connected to the poles of the sphere?
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v1 2.006F08 2 8) An ice cube is placed in a glass of water. A line is marked on the side of the glass to indicate the current level of the liquid water in the glass. The time passes and the level of the water is noted just after the ice cube melts. The final level of the water: a) is above the line, b) is below the line, c) is at the same level as the line, d) depends on the shape of the glass. 9) As shown above, a jet of mercury leaves a nozzle at velocity v 0 =10 m/s and cross sectional area of 10 -4 m 2 and falls onto a massless 30 cm diameter circular dish as shown in the figure above. Presuming the effects of gravity and viscosity can be neglected, what is the force W measured by the scale in the figure?
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