Drag coefficients various shapes

For relatively flat leaves that can align with the wind direction, cd is usually 0.02 to 0.2, but it can be 0.5 to 0.9 for bluff bodies such as branches and tree trunks that block and hence substantially change the airflow. For flexible objects the drag coefficient defined by Equation 7.9 can decrease as the wind speed increases. In particular, the areas of leaves and small branches perpendicular to the wind direction can decrease threefold as the wind speed increases (Fig. 7-5), leading to a more streamlined shape, as occurs for many trees. Indeed, changes in shape to minimize drag have evolved many times, as is especially apparent for the fusiform shape of various marine animals. 

The hydrodynamic drag for the laminar flow of a fluid in tubes of various shape is considered in [80], The drag coefficient A between the pressure drop and the characteristic pressure head is introduced by the relation... 

Values of the drag coefficients for laminar flow in tubes of various shape... 

Table 1.2 presents values of the drag coefficients for tubes with various shapes of the cross-section (according to [80]). The Reynolds number Remean flow rate velocity and the equivalent diameter. 

In the book [117], some data are given on the hydrodynamic characteristics of bodies of various shapes these data mainly pertain to the region of precrisis self-similarity. The influence of roughness of the cylinder surface and the turbulence level of the incoming flow on the drag coefficient is discussed in [522]. In [211], the relationship between hydrodynamic flow characteristics in turbulent boundary layers and the longitudinal pressure gradient is studied. Analysis of the transition to turbulence in the wake of circular cylinders is presented in [333]. 

FIGURE 3.1-1 Drag coefficient versus Reynolds number for various particle shapes. Reprinted with permissino from Lapple and Shepherd, Ind. Eng. Chem., 32, 60S (1940), American Chemical Society. 

However, the curve of the sphere drag coefficient has some marked differences from the friction factor plot. It does not continue smoothly to higher and higher Reynolds numbers, as does the / curve instead, it takes a sharp drop at an of about 300,000. Also it does not show the upward jump that characterizes the laminar-turbulent transition in pipe flow. Both differences are due to the different shapes of the two systems. In a pipe all the fluid is in a confined area, and the change from laminar to turbulent flow affects all the fluid (except for a very thin film at the wall). Around a sphere the fluid extends in all directions to infinity (actually the fluid is not infinite, but if the distance to the nearest obstruction is 100 sphere diameters, we may consider it so), and no matter how fast the sphere is moving relative to the fluid, the entire fluid cannot be set in turbulent flow by the sphere. Thus, there cannot be the sudden laminar-turbulent transition for the entire flow, which causes the jump in Fig. 6.10. The flow very near the sphere, however, can make the sudden switch, and the switch is the cause of the sudden drop in Q at =300,(300. This sudden drop in drag coefficient is discussed in Sec. 11.6. Leaving until Chaps. 10 and 11 the reasons why the curves in Fig. 6.22 have the shapes they do, for now we simply accept the curves as correct representations of experimental facts and show how to use them to solve various problems. 

Most seed kernels are irregular in shape. Their drag coefficients depend not only on the shape but also on the orientation of the kernels in the airstream. Thus, an equivalent diameter is used in the determination of the Reynolds number. Drag coefficients for various crops are given in Table 27.15. 

The resistance (drag) coefficient Cx is a function of the Reynolds number, i.e., Cx = /(Re). In order to compare values of Cx for spherical and irregular particles, we introduce the sphericity factor k to account for the particle shape (see p. 168). For particles of various shapes with diameters from 1 to 100 fxm in water, with Reynolds numbers below 0.2, the sphericity factor has the following values ... 

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