[经济学]化工原理课件CHAP5.ppt

Figure Fluid element in steady flow through pipe. rw Chap5flow of incompressible fluids in conduits and thin layers Shear-stress distribution in a cylindrical tube r dL Flow -(p+dp) p ? ? forces acting on the element: Force from the pressure on the upstream faces of the disk: Sbpb =餽2(p+dP) Force from the pressure on the downstream faces of the disk: Sapa=餽2p Shear force acting on the rim of the element: (2餽dL) ? So the total force acting on the element is Simplifying this equation and dividing by 餽2dL (5-1) In steady flow, the pressure at any given cross section of a stream tube is constant, so that dp/dL is independent of r,dp/dL=膒/腖, and r=rw,?魒, equation(5-1) then becomes (5-2) (5-3) and Relation between skin friction and wall shear For horizontal pipe and constant cross section, Zb-Za=0, and the two kinetic-energy terms cancels. The relationship between skin friction and pressure drop can be written . Then equation(4-30) becomes (4-30) Eliminating膒 from Eqs(5-2) and (5-4)gives (5-5) definition skin-friction factor by f (5-6) (5-4) Relations between skin-friction factor Eq(5-5)and(5-6) gives (5-7) The equation (5-7) is called the Fanning equation ,and the friction factor f is called the Fanning friction factor. thus (5-7a) ?=4f defining ?as a friction coefficient The equation(5-7) is the equation usually used to calculate skin friction loss in straight pipe. Laminar flow of Newtonian fluids The treatment is especially straightforward fluid, for which quantities such as the velocity distribution, the average velocity, and momentum and kinetic energy correction factors are readily calculated. The key step in derivation is that of relating local velocity ur to position in the stream. For Newtonian fluids (5-9) The negative sign in the equation accounts for the fact that in a pipe ur decreases as r increases. substitution of equation (5-9) into equation(5-3) provides the