Fluid Mechanics seventh edition by Frank M. White · Problem P3.53

Integral Relations for a Control Volume — Frank M. White

Physics — Fluid Mechanics · linear-momentum-equation

Problem

Consider incompressible flow in the entrance of a circular tube, as in Fig. P3.53. The inlet flow is uniform,

u_1 = U_0

. The flow at section 2 is developed pipe flow. Find the wall drag force

F

as a function of

(p_1, p_2, \rho, U_0, R)

if the flow at section 2 is (a) Laminar:

u_2 = u_{\max}\left(1 - \dfrac{r^2}{R^2}\right)

(b) Turbulent:

u_2 \approx u_{\max}\left(1 - \dfrac{r}{R}\right)^{1/7}