ch06 - 6.1 PROBLEM DEFINITION Situation Identify the...

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6.1: PROBLEM DEFINITION Situation : Identify the surface and body forces acting on a glider in fl ight. Also, sketch a free body diagram and explain how Newton’s laws of motion apply. Find : Surface and body forces acting on a glider in fl ight. PLAN Make use of a sketch with a free-body diagram. SOLUTION The forces acting on glider in fl ight are: Surface forces: 1. Lift - a surface force because the wing must touch the air to generate lift. 2. Drag - both form drag and friction drag result from air touching the glider. 3. Thrust - the air and propellors must touch in order to generate thrust from the engine’s energy. Body force: 1. Weight - the pull of the earth on the glider through the action of a gravity fi eld. Earth and the glider do not need to touch in order for the force of gravity to act, so weight is a body force Sketch: An acceptable sketch would be Fig. 6.2 in §6.1 of EFM10e. Newton’s Laws: Newton’s fi rst law (i.e. force equilibrium) tells us that the sum of forces must balance. Therefore the glider stays at the same elevation when lift is equal to weight. The glider stays at the same speed when thrust balances drag. For the glider to accelerate, thrust must be greater than drag. 1
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6.2: PROBLEM DEFINITION Situation : Interpretation of Newton’s second law. F = d ( mv ) dt , F = m dv dt + v dm dt Find : Relationship between momentum and acceleration. SOLUTION Expressing Newton’s second law as F = d dt ( mv ) is correct. However, Newton’s second law is valid only for a system of constant mass so di ff erentiation yields F = m dv dt In the di ff erentiation by parts, the dm/dt term is zero. 2
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6.3: PROBLEM DEFINITION Situation : Which are the following are correct with respect to the derivation of the Momentum Equation? (Select all that apply.) a. Reynold’s Transport Theorem is applied to Fick’s Law. b. The extensive property is momentum. c. The intensive property is mass. d. The velocity is assumed to be uniformly distributed across each inlet and outlet. e. The net momentum fl ow is the “ins” minus the “outs”. f. The net force is the sum of forces acting on the matter inside the CV SOLUTION The correct statements are b, d and f. 3
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6.4: PROBLEM DEFINITION Situation : When making a force diagram (FD) and its partner momentum diagram (MD) in order to set up the equations for a momentum equation problem (see Fig. 6.10 in §6.3), which of the following elements should be in the FD, and which should be in the MD? (Classify all below as either FD or MD.) a. Each mass stream with product ˙ m o v o or product ˙ m i v i crossing a control surface boundary. b. Reaction forces required to hold walls, vanes, or pipes in place. c. Weight of a solid body that contains or contacts the fl uid. d. Weight of the fl uid. e. Pressure force caused by a fl uid fl owing across a control surface boundary.
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  • Winter '15
  • SteveTarrent
  • Force, y-direction, momentum equation

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