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hw2 - 2.016 Hydrodynamics Prof Alex Techet Fall 2005 HW#2...

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2.016 Hydrodynamics Prof. Alex Techet Fall 2005 HW #2 Out: September 20, 2005 Due: September 27, 2005 Problem 1: Buoyancy (3 pts.) An AUV is designed as shown below. It has three, hollow, cylindrical canisters arranged in an upside down triangle. The cylindrical canisters are constructed out of aluminum, specific gravity of 2.7, and have a wall thickness of 1 cm, length 2 meters, and an inner diameter 14 cm. What is the maximum load (kg) this vehicle can carry without sinking, ignoring the additional weight and buoyancy of the struts? (Think neutrally buoyant!) Assume the vehicle will be operating in SALT water ( 3 1025 / kg m ! = ). AUV Design. Problem 2: Basic Fluids & Math (3 pts.) a) Although fluids, such as water, are really made up of discreet molecules, we can describe their behavior by differential equations by virtue of the ________ hypothesis. b) Discuss the difference between a pathline and a streamline. Under what conditions are they the same? c) ( r V r " ) r V = 1 2 r " r V r V ( ) ( r " # r V = $ w $ y % $ v $ z & ( ) * + ˆ i + $ u $ z % $ w $ x & ( ) * + ˆ j + $ v $ x % $ u $ y & ( ) * + ˆ k = 0 ˆ i + 0 ˆ j + 0 ˆ k
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