Question

BIG UPVOTE FOR RIGHT ANSWER

Viscous fluid flow 2nd edition Frank White

I need answer of 2.17

I have attached 2.14 question and solution for reference.

2.17 As an extension of Prob. 2-14, consider the heat-transfer aspect by assuming a uniform entrance profile T = To and an exit profile approximated by T(r) = T0(1.5 + 0.5r2/ri). For flow with constant (p, F, cp, k) and negligible kinetic- and potential-energy changes, use the integral relations to compute the total heat transfer (dQ/dt) through the pipe walls between entrance and exit. How would one nondimensionalize this heat transfer rate? Hint: The continuity or mass-balance part of Prob. 2-14 must be solved first.

116 convection equations and define any parameters which arise. 2-14. For laminar flow in the entrance to a pipe, as shown in Fig. P2-14, the entrance flow is uniform, u = U., and the flow downstream is parabolic in profile, u(r) = C(r-r). Using the integral relations of Sec. 2-13, show that the viscous drag exerted on the pipe walls between 0 and x is given by Drag = arõ(po - Px – į pu) r=10 LUKUU uo ir po B Fully developed FIGURE P2-14 2-15. To illustrate “boundary-layer" behavior, i.e., the effect of the no-slip condition for laroe Revnolds numbers, Prandtl in a 1932 lecture proposed the following model (lin-

Answer 1

Internal relation of energy conservation- & is = 2 2 [ Sou lů + 2 + g Z) pdf] + Sulh + y² +92) p (J.ſlda Olsteady state assumption) 8 = s hplunda NO ove cap (42.c6s), sandy + J & Tapeterie 414) = 2001- ) Loiven in previous part) -- Aptopus, 1915 + G Topelo Toriya (653058)26-. 29 de Calculation of integral I: het 9 = t then a I= já listost?) 11-4², it at -41'-ost- +15+)dt = 4(40) = + 9 = -Gp To pu, tyle + $ 49 TO PUO A 3, ? 22 Co To P40 79 Cola
For Non-dimensionalization of heat transfer rate Q' one choice can be
do СрТориото

**Please Note that in the image I have written dQ/dt as Q'