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spl1 - Fluids Lab 1 Lecture Notes 1 Bernoulli Equation 2...

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Fluids Lab 1 – Lecture Notes 1. Bernoulli Equation 2. Pitot-Static Tube 3. Airspeed Measurement 4. Pressure Nondimensionalization Reading: Anderson 3.2, 1.5 Bernoulli Equation Definition For every point s along a streamline in constant-density frictionless flow, the local speed V ( s ) = | V | and local pressure p ( s ) are related by the Bernoulli Equation 1 p + ρ V 2 = p o (1) 2 This p o is a constant for all points along the streamline, even though p and V may vary. This is illustrated in the plot of p ( s ) and p o ( s ) along a streamline near a wing, for instance. s p p o 2 V ρ 1 2 s Standard terminology is as follows. p = static pressure 1 2 ρV 2 = dynamic pressure p o = stagnation pressure, or total pressure Also, a commonly-used shorthand for the dynamic pressure is 1 q ρV 2 2 so we can also write the Bernoulli equation in the following compact form. p + q = p o 1
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Uniform Upstream Flow Case V ( x, y, z ) = V Many practical flow situations have uniform flow somewhere upstream, with and p ( x, y, z ) = p at every upstream point. This uniform flow can be either at rest with V V 0 (as in a reservoir), or be moving with uniform velocity = 0 (as in a upstream wind tunnel section), as shown in the figure. V = 0 Reservoir/Jet Wind Tunnel V = const. const. p = const. p = V(x,y,z) p(x,y,z) V(x,y,z) p(x,y,z) In these situations, p o is the same for all streamlines, and can be evaluated using the upstream conditions in equation (1).
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