Unformatted text preview: r in the Moody chart (Fig. 6.13). The fact that f drops off with increasing Red should not mislead us into thinking that shear decreases with velocity:
Eq. (6.45) clearly shows that w is proportional to umax; it is interesting to note that w
is independent of density because the fluid acceleration is zero.
The laminar head loss follows from Eq. (6.30)
hf,lam 64 L V2
Vd d 2g 32 LV
gd 2 128 LQ
gd 4 (6.47) We see that laminar head loss is proportional to V.
EXAMPLE 6.4
An oil with
900 kg/m3 and
0.0002 m2/s flows upward through an inclined pipe as shown
in Fig. E6.4. The pressure and elevation are known at sections 1 and 2, 10 m apart. Assuming
d = 6 cm
2 10 m p2 = 250,000 Pa Q,V
1
40˚ p1 = 350,000 Pa, z1 = 0 E6.4 steady laminar flow, (a) verify that the flow is up, (b) compute hf between 1 and 2, and compute
(c) Q, (d) V, and (e) Red. Is the flow really laminar?  v v 342  eText Main Menu  Textbook Table of Contents  Study Guide 6.4 Flow in a Circular Pipe 343 Solution
Part (a) For later use, calculate
(900 kg/m3)(0.0002 m2/s)
z2 L s...
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 Spring '08
 Sakar
 Fluid Dynamics, eText Main Menu, Osborne Reynolds

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