solution-midterm-2-Fall-09

solution-midterm-2-Fall-09 - In class, Monday, November 2,...

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Unformatted text preview: In class, Monday, November 2, 2009 Professor Philip S. Marcus ME 106 Mid-term Exam II – Solutions The figure shows a jet of fluid with density ρ exiting a tube (heavy lines) into the air and pouring into a tank (heavy lines). At z = 0 the water exits the tank straight-downward into the air through a leak in the bottom. Four locations are shown: Point 1 at height z = H is in the jet as it exits into the air; Point 2 at height z = h is inside the jet and at the surface of the tank’s water; Point 3 at height z = 0 is just below the tank where the water leaks into the air; and Point 4 at height z = h is at the surface of the tank’s water and is far from the jet. At Points 1 to 3 , the fluid velocity vector is written as V i , with magnitude V i ≡ | V i | ; the cross sectional areas of the jet and leak are A i (where the plane of the cross-section is perpendicular to V i ), where i = 1 , 2 , 3. The tube and exiting jet at Point 1 is at angle θ 1 with respect to the horizontal. The jet enters the tank at Point 2 at an angle θ 2 . When the water from the tube strikes the surface of the water at Point 2 , it loses most of its energy and quickly spreads out along the upper part of the tank. At Point 4 on the water’s surface, the velocity V 4 = 0 . The cross-sectional area of the tank in the x- y plane is A . All control volumes in this problem have boundaries outside the tank and are either in the air, in the jet between Points 1 and 2 , or in the water exiting the leak. Thus, all parts of all control volumes’ boundaries have atmospheric pressure P atm ....
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This note was uploaded on 04/19/2010 for the course ME 106 taught by Professor Morris during the Fall '08 term at Berkeley.

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solution-midterm-2-Fall-09 - In class, Monday, November 2,...

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