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HW3 - AE311 Fall 2008 Problem Set 3 Due Oct 15th 2008...

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Unformatted text preview: AE311 Fall 2008 Problem Set 3 Due: Oct 15th 2008, before class 1. (10 pts) Anderson (4th ed.) Problem 3.3 2. (5 pts) Anderson (4th ed.) Problem 3.6 3. (5 pts) Anderson (4th ed.) Problem 3.7 4. (20 pts) Anderson (4th ed.) Problem 3.12 5. (30pts) In class we derived Bernoulli’s equation with the assumption that body forces are negligible. This is often a reasonable assumption for airplane flight as the density of air is about 1.2 kg/m3. For liquid flows, however, the density is greater (ρwater = 1000 kg/m3 at STP) and body forces due to gravity are not always negligible. a) Rederive Bernoulli’s equation to include gravitational forces. Begin with a form of Euler’s equation for momentum shown below in (1). Assume the flow is inviscid, steady, and incompressible. A form of Euler’s equation for steady, inviscid flow along a streamline is dp = − ρVdV − ρg o dz (1) where z is the vertical displacement relative to some datum and go is the acceleration due to gravity. Assume go is a constant, go = 9.81 m/s2. b) Use the version of Bernoulli’s equation derived in a) in the drainage through a rising tube problem shown below. The top of the tank and the tube exit are both open to the atmosphere and atmospheric pressure is 101.3 kPa. The entrance and exit diameters of the tube are the same. Assume the diameter at the top of the tank is sufficiently large to neglect any kinetic energy there. Solve for the pressure at the tube entrance and the velocity of the flow exiting the tube. ...
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