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ME 130L Pre-Lab_3 Fall 2010

ME 130L Pre-Lab_3 Fall 2010 - ME 130L 17810 17895 The...

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ME 130L 17810 – 17895 The University of Texas at Austin Mechanical Engineering Department Spring ’10 Dr. Hidrovo 1 ME 130L Experimental Fluid Mechanics Background and Pre-Lab #3 - Wind Tunnel Measurements and Dimensional Analysis of a Scaled Down Wind Turbine I. Background All of our measurements in this lab are based on an understanding of the Bernoulli equation. This equation and its application to velocity measurement are described below. 1. The Bernoulli Equation The Bernoulli equation is one of the most powerful, and most abused, in fluid mechanics. It states that the total energy of a fluid particle traveling along a streamline between any two points 1 and 2, shown on Figure 1, is conserved: () p + 1 / 2 · ρ V 2 + ρ gz 1 = p + 1 / 2 · ρ V 2 + ρ 2 = Constant p , V 11 p , V 22 z 1 z 2 reference line Figure 1: Streamline with reference potential energy line used in the Bernoulli eqn. This equation is really just a restatement of conservation of mechanical energy. In physics you learned that the potential energy ( mgh ) of a body is converted to kinetic energy ( 1 / 2 · mV 2 ) as it falls, but the total energy of the body (the sum of the two terms) is conserved and remains constant. The Bernoulli equation can be thought of as the same physical principle adapted to fluids in two important ways. The first is that it is converted to a per-unit-volume basis (hence the mass m is replaced by the density ρ ), and the second is that the static pressure term ( p ) is included. The Bernoulli equation is only valid when the following conditions are satisfied: 1. The equation is applied along a streamline. 2. The flow is steady. 3. The flow is incompressible; i.e., constant (true if the Mach number is less than about 0.3). 4. The flow is inviscid (frictionless).

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ME 130L 17810 – 17895 The University of Texas at Austin Mechanical Engineering Department Spring ’10 Dr. Hidrovo 2 2. Nomenclature p Static pressure, total pressure, or thermodynamic pressure is the pressure that is felt when moving with the flow.
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ME 130L Pre-Lab_3 Fall 2010 - ME 130L 17810 17895 The...

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