Mechanics of Fluids
Solutions Manual
Mechanics of Fluids
Eighth edition
Solutions manual
Bernard Massey
Reader Emeritus in Mechanical Engineering
University College, London
Revised by
John Ward-Smith
Formerly Senior Lecturer in Mechanical Engineering
Brunel University
Seventh edition published by Stanley Thornes (Publishers) Ltd in 1998
Eighth edition published 2006
by Taylor & Francis
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Simultaneously published in the USA and Canada
by Taylor & Francis
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© 2006 Bernard Massey and John Ward-Smith
The right of B. S. Massey and J. Ward-Smith to be identified as authors of
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ISBN 0–415–36204–0
This edition published in the Taylor & Francis e-Library, 2005.
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(Print Edition)
ISBN 0-203-01231-3 Master e-book ISBN
Chapter 1
1.1 Since pV =mRT,V1
V1=T1p2
T2p1
∴V1=π
6(20 m)3288.15
233.15
1.1
101.3 =56.2m
3
1.2 =p
RT =1.4 ×105N·m−2
287 J ·kg−1·K−1×323.15 K =1.51 kg ·m−3
1.3 K=∂p
∂ Assume Kconstant. Then ln(/0)=p−p0
K
∴=0exp p−p0
K=1025 kg ·m−3exp 81.7 ×106
2.34 ×109
=1061 kg ·m−3
1.4 =µ
ν=2×10−5N·s·m−2
15 ×10−6m2·s−1=1.333 kg ·m−3
R=p
T=1.013 ×105N·m−2
1.333 kg ·m−3×293.15 K =259.2 J ·kg−1·K−1
∴M=8310
259.2 =32.06
1.5 µ=ν =400 ×10−6m2·s−1×850 kg ·m−3=0.34 Pa ·s
Velocity gradient =0.12 m ·s−1
0.1 ×10−3m=1200 s−1
Area =π0.2 ×1.2 m2=0.754 m2
Force =0.754 m2×0.34 Pa ·s×1200 s−1=307.6N
2Solutions manual
1.6 Total force on plate =Area ×µ∂u
∂yside A +∂u
∂yside B
=(0.25 m)2×0.7 Pa ·s0.15 m ·s−1
0.006 m +0.15 m ·s−1
0.019 m
=1.439 N
1.7 For annulus, radius r, width δr
Force =Area ×µ×Velocity
Clearance =2πrδrµωr
c
∴Torque =Force ×r=2πr3δrµω
c
Total torque =R
0
2πr3µω
cdr=πR4µω
2c
=π(0.1 m)40.14 Pa ·s×2π×7 rad ·s−1
2×0.00013 m =7.44 N ·m
1.8 p=2γ
d=2×0.073 N ·m−1
0.004 m =36.5Pa
1.9 h=4γcos θ
gd =4×0.073 N ·m−1×1
1000 kg ·m−3×9.81 N ·kg−1×0.005 m
=0.00595 m =5.95 mm
1.10 h=4×0.377 N ·m−1×cos 140◦
(13.56 −1)1000 kg ·m−3×9.81 N ·kg−1×0.006 m
=−1.563 mm
1.11 Re =ud
µ=4Q
πdµ=4×0.0025 m3·s−1×900 kg ·m−3
π0.05 m ×0.038 N ·s·m−2=1508
u=2000µ
d=2000 ×0.038 N ·s·m−2
0.05 m ×900 kg ·m−3=1.689 m ·s−1
1.12 Re =4Q
πdµ=4×0.01 m3·s−1
π0.08 m ×370 ×10−6m2·s−1=430 ∴Laminar
