Solution

658 Solutions Manual • Fluid Mechanics, Fifth Edition
(c) Assume ρ = ρ o = ρ tire , for how would we know ρ exit if we didn’t use compressibleflow
theory Then the incompressible Bernoulli relation predicts
po
169120 kg
ρ o = = = 1.945
3
RT 287(303) m
o
V
einc ,
2∆p
2(169120 −100000)
≈ = ≈
ρ
1.945
o
m
267 s
Ans. (c)
This is 8% lower than the “exact” estimate in part (a).
9.43 Air flows isentropically through a duct with T o = 300°C. At two sections with
identical areas of 25 cm 2 , the pressures are p 1 = 120 kPa and p 2 = 60 kPa. Determine (a) the
mass flow; (b) the throat area, and (c) Ma 2 .
Solution: If the areas are the same and the pressures different, than section (1)
must be subsonic and section (2) supersonic. In other words, we need to find
where
p 1/po
120
= = 2.0 for the same A 1/A* = A 2/A*—search Table B.1 (isentropic)
p/p 60
2 o
After laborious but straightforward iteration, Ma = 0.729, Ma ≈ 1.32 Ans. (c)
1 2
A/A* = 1.075 for both sections, A* = 25/1.075 = 23.3 cm Ans. (b)
With critical area and stagnation conditions known, we may compute the mass flow:
2 3.5
p = 120[1 + 0.2(0.729) ] ≈ 171 kPa and T = 300 + 273 = 573 K
o
1/2 1/2
m
= 0.6847poA*/[RT o] = 0.6847(171000)(0.00233)/[287(573)]
kg
m ≈ 0.671 Ans. (a) s
o
2
9.44 In Prob. 3.34 we knew nothing about compressible flow at the time so merely assumed
exit conditions p 2 and T 2 and computed V 2 as an application of the continuity equation. Suppose