HW_10_Soln - ME 309 Fall 2008 Section 2(Merkle Homework 10...

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ME 309 Fall 2008 Section 2 (Merkle) Homework # 10 Due Fri 10 September 2008 Problem 10-1 Find the mass and momentum flow across the right and left faces of a rigid, hexahedral control volume and express conservation of mass and conservation of momentum for the control volume as viewed from the specified observation frames for the following cases: a) The control volume moves to the right at a velocity of 10 m/s with respect to the ground. The air is motionless relative to the ground. The observer sits at a fixed position on the ground. b) The control volume moves to the right at a velocity of 10 m/s with respect to the ground. The air is motionless relative to the ground. The observer sits in the frame of the control volume and moves with it. c) The control volume moves to the right at a velocity of 10 m/s with respect to the ground. The air is moving to the right at a velocity of 15 m/s relative to the ground. The observer sits at a fixed position on the ground. d) The control volume moves to the right at a velocity of 10 m/s with respect to the ground. The air is moving to the right at a velocity of 15 m/s relative to the ground. The observer sits in the frame of the control volume and moves with it. The areas of the right and left faces are both 0.01 m 2 . The density is 1000 kg/s. Be careful to specify the velocity and relative velocity on each face in each case. As there is no velocity in the other two directions, consider only variations in the x direction and only the x- momentum component. Solution: Mass flow always depends on relative velocity: ( ) = - CV CS rel dVol dt d dA ρ ρ n V a) The relative velocity between the right face and the air is:-10 m/s . The normal is in the positive direction. The mass flowing out through this face is -10*1000*0.01=-100
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