4aerodynamics - Introduction to Aerospace Engineering 4....

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1 Introduction to Aerospace Engineering 4. Basic Fluid (Aero) Dynamics Here, we will try and look at a few basic ideas from the complicated field of fluid dynamics. The general area includes studies of incompressible, and compressible, inviscid (frictionless) and viscous, subsonic and supersonic flow. The exact type of flow fields we study depends upon what assumptions can be made and how accurate we want the results. There are two assumptions that we will make that will limit the application of the results that we obtain. Assumptions: 1) We will deal only with subsonic flow M a < 1 and that the Mach numbers of interest will be less than M a < 0.4. Under these circumstances the air can be considered incompressible . (That right, low speed air is just like water, D = constant! ). 2) We will assume the fluid is inviscid. We have discussed the fact the viscosity of air only affects the flow field near the surface of an object immersed in the flow (called the boundary layer). If we move away from that boundary layer, then the flow can be treated as inviscid. It turns out that for certain calculations, the above assumptions are very good. On the other hand, there are certain calculations that will yield poor results using these assumptions. Experience and experimentation helps discern when our calculations are suitable. 4.1 The hydro static equation We encountered this equation previously when we dealt with the atmosphere. He we will apply it to an incompressible fluid that could be a short column of air, or a tank full of water. The equation of interest is obtained by summing the vertical forces on a chunk of air: or (1) Under the assumption of incompressible fluid, everything in Eq. (1) is constant except dP and dh . Hence we can integrate to get:
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2 Fluid Static Equation (2) We can use this equation to make a device to measure pressures in fluid flows. The device is called a manometer and consists of a U tube with the ends open, one attached to a known pressure, and the other to the unknown pressure, or if we are interested in the difference of two pressures, just connected to each of the unknown pressures. The tube is partially filled with a fluid of known density (typically water, alcohol, or mercury). The figure at the right represents a U tube manometer that is open to two pressures, P 1 and P 2 . Typically one of these pressures would be a known atmospheric pressure and the other would be the pressure to be measured, say a static pressure in a wind tunnel. For example P 1 could be atmospheric pressure, and P 2 would be the wind tunnel pressure to be measured. Here we can apply the hydrostatic to the column of manometer fluid between P 1 and P 2. Just applying the equation strictly as it is written, we have: where is the density of the fluid in the manometer Hence if we know the properties of the fluid in the manometer, and can measure the height difference, we can determine the pressure difference, and if we know one of the pressures, we can determine the other.
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This note was uploaded on 08/17/2011 for the course AOE 2104 taught by Professor Staff during the Fall '08 term at Virginia Tech.

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4aerodynamics - Introduction to Aerospace Engineering 4....

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