By John J. Bertin
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Additional info for Aerodynamics for Engineers,
8 at a height of 10 km, what is the speed of aircraft in m/s, ft/s and knots? 2 to obtain the value of the speed of sound. 17. 22), calculate the temperature and pressure of the atmosphere at 9000 m. 2. 18. 7, develop metric-unit expressions for the pressure, the temperature, and the density of the atmosphere from 11,000 to 20,000 m. 650 K over this range of altitude. 19. 18, what are the pressure, the density, the viscosity, and the speed of sound for the ambient atmospheric air at 18 km? 2. 20.
If the airplane is flying at constant altitude and constant velocity, the terms of the flow-field equations that contain partial derivatives with respect to time are zero in the vehicle-fixed coordinate system. Thus, as shown in Fig. 2, the velocity and the flow properties of the air particles that pass through a specific location relative to the vehicle are independent of time. The flow field is steady relative to a set of axes fixed to the vehicle (or pilot). Therefore, the equations are usually easier to solve in the vehicle (or pilot)-fixed coordinate system rather than in the ground-observer-fixed coordinate system.
This flow is easier to solve if the coordinate system is moved to the bottom plate, as shown in Fig. 10, and the distance between the two plates is h. The governing equation for this flow is: m dp d2 u = constant = 2 dx dy which is the same as Poiseuille flow, but the boundary conditions are: at y = 0 u = 0 at y = h u = U After integrating in the same way as was done previously: u = 1 dp 2 y + C1 y + C2 2m dx Evaluating the boundary condition at y = 0 gives C2 = 0. Evaluating the boundary condition at y = h gives that C1 = U>h, and the velocity distribution, as well as the nondimensional velocity distribution, becomes (with some algebraic re-arrangement): y y y y y h2 dp y a 1 - b = U + UP a 1 - b h 2m dx h h h h h 2 y y y y y u h dp y = a1 - b = + P a1 - b U h 2mU dx h h h h h u = U h2 dp is a dimensionless 2mU dx pressure gradient.
Aerodynamics for Engineers, by John J. Bertin