Question

For laminar flow through a circular pipe, the value of the kinetic energy correction factor for Bernoulli’s equation is α = 2. Show that this is true.

Answer 1

dA 2TYdr Consides an elementam area dA in the tesm with width ds at radinus aring .. Rate of fiuid flowing ds Nelocityx trea of rirg roughring ele meut u2 1TT. dY ..da

of fluid fio wirg through the Kinetic eneray e lementany ing will be, -mass low satex (relocin S.C4x .dv) u 1-7 Total actual kinetic eneng vers tube S- K.Eactual we kngwi velocity distn bution hsogh a cixcular at any adicus is, Pipe fos \aminar fu u- K.E ९ 6 =S (4-35).R d 3R+ 3eJ ३ () 3 R Soluirg K.E.ath 6443 NOw, K.E orof bascd on avesage reloc Eav Zmass f ew u S. A. X ---G-aug velority 11 2 l (R 2 TT R

. K.EauS ST \024 쓰3 K.E. actual K.Eavg (- 1024 사3 1024 64x8 2 IA 1l
summery:

KE = (1/2) Mass * velocity^2

Alpha = KE based on actual velocity/ KE based on average velocity