In reality, the boundary layer on the airfoil discussed in prob. 5.37 is neither fully laminar nor fully turbulent. the boundary layer starts out as laminar, and then transitions to turbulent at some point downstream of the leading edge (see the discussion in sec. 4.19). assume that the critical reynolds number for transition is 650,000. calculate the skin friction drag coeffi cient on the naca 2415 airfoil, and compare your result with the experimental section drag coeffi cient in app. d. note: you will fi nd from the answer to this problem that 86 percent of the airfoil section drag coeffi cient is due to skin friction and 14 percent due to pressure drag from fl ow separation. comparing this answer with the result of prob. 5.36 , which pertains to a thinner airfoil, we fi nd that the pressure drag is a higher percentage for the thicker airfoil. however, for airfoils in general, the pressure drag is still a small percentage of the total drag. this drag breakdown is somewhat typical for airfoils at small angles of attack. by intent, the streamlined shape of airfoils results in small pressure drag, typically on the order of 15 percent of the total drag.

bacteria that live on the ocean floor are sustained by phytoplankton. phytoplankton, microscopic marine photosynthetic organisms, have a vastly significant role to play not only in the marine food web of which they’re part of, but also on a more global scale. despite their infinitely small size in comparison to other marine organisms, these tiny creatures occupy an immensely important ecological niche: they are the foundation of the marine food web, and as primary producers, play key roles in supporting all other organisms in the marine environment, as well as in the regulation of the earth’s climate through the sequestration of carbon, oxygen production, and other related processes. phytoplankton account for roughly half of all global primary productivity; therefore, their significance extends far beyond the marine environment alone. there is an intriguing sense of irony in the realization that these tiny living beings that often live out their existence unnoticed and undetected by the rest of the world, have such a far-reaching impact on the lives of virtually all other living organisms on the planet, particularly on those in the marine environment. the world that we have become accustomed to has been and is continuously shaped by the workings of these miniscule yet vital “plants of the sea”.

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pythagoras' theorem

square root (-5^2+9^2)

square root (25+81)

square root (106)

angle is tan^-1(9/5)

neg x, pos y