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2
02
ft
2 2
0
1
2 2
p p q p V p p M
2 4
02
lb
2116 0.7(2116)(2) 0.804 10
ft
p
4
2
lb
1.656 10 ,
ft
2
1
12 1
ee
pM
p
PROPRIETARY MATERIAL. © 2012 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual may be
displayed, reproduced, or distributed in any form or by any means, without the prior written permission of the publisher, or used
beyond the limited distribution to teachers and educators permitted by McGraw-Hill for their individual course preparation. A
student using this manual is using it without permission.
4
3
1.37 10 0.267 kg/m
(287)(178.6)
e
e
c
p
RT
PROPRIETARY MATERIAL. © 2012 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual may be
displayed, reproduced, or distributed in any form or by any means, without the prior written permission of the publisher, or used
beyond the limited distribution to teachers and educators permitted by McGraw-Hill for their individual course preparation. A
student using this manual is using it without permission.
32
1
2
0
1
12
ee
pM
p
t
/( 1)
2 2 2 2 2 3.5
0 0
1
1 0.7 (1 0.2 )
2 2 2
q p M M M M M
p p
M M2q/p
0
0 0 0
0.2 0.04 0.027
0.4 0.16 0.100
0.6 0.36 0.198
PROPRIETARY MATERIAL. © 2012 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual may be
displayed, reproduced, or distributed in any form or by any means, without the prior written permission of the publisher, or used
beyond the limited distribution to teachers and educators permitted by McGraw-Hill for their individual course preparation. A
student using this manual is using it without permission.
7
5
(1, 225)(200)(3)
Re 4.10 10
(1.7894 10 )
L
V L
2 2 4 2
1 1 (1.225)(200) 2.45 10 N/m
2 2
q V
5.2 5.2(3) 0.0024 m 0.24 cm
L
L
f
0.2 7 0.2
0.37 0.37(3) 0.033 m 3.3 cm
(Re ) (4.1 10 )
L
L
turbulent laminar
3.3
/ 13.75
0.24
0.2 7 0.2
0.074 0.074 0.0022
(Re ) (4.1 10 )
f
L
C
4
(2/45 10 )(3)(17.5)(0.0022)
f f
D q Sc
PROPRIETARY MATERIAL. © 2012 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual may be
displayed, reproduced, or distributed in any form or by any means, without the prior written permission of the publisher, or used
beyond the limited distribution to teachers and educators permitted by McGraw-Hill for their individual course preparation. A
student using this manual is using it without permission.
PROPRIETARY MATERIAL. © 2012 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual may be
displayed, reproduced, or distributed in any form or by any means, without the prior written permission of the publisher, or used
beyond the limited distribution to teachers and educators permitted by McGraw-Hill for their individual course preparation. A
student using this manual is using it without permission.
35
cr
cr
x
e
V x
R
6 5
(10 )(1.789 10 )
Re (1.225)(200)
xV
0.2
c
4 2
0.074 (on one side)
(Re )
0.074 (2.45 10 )(7.3 10 )(17.5)
A
f A
D q S
D
B
f
0.5
cr
1.328
(Re )
A
f
D q S
4 2
6 0.5
1.328
(2.45 10 )(7.3 10 )(17.5)
(10 )
A
f
D
42 N
A
f
D
(laminar) (turbulent)
42 2684 2726 N
A B
f f f
f
D D D
D
PROPRIETARY MATERIAL. © 2012 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual may be
displayed, reproduced, or distributed in any form or by any means, without the prior written permission of the publisher, or used
beyond the limited distribution to teachers and educators permitted by McGraw-Hill for their individual course preparation. A
student using this manual is using it without permission.
36
dp VdV
7.0121 10 N/m
p
4
4 2
(0.65)(7.0121 10 ) 4.555 10 N/mp
1/2
1/2 3
3
1.0663 10
(800) 535.8ft.sec
2.3769 10
e
s
V V
PROPRIETARY MATERIAL. © 2012 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual may be
displayed, reproduced, or distributed in any form or by any means, without the prior written permission of the publisher, or used
beyond the limited distribution to teachers and educators permitted by McGraw-Hill for their individual course preparation. A
student using this manual is using it without permission.
37
1
21
2
2
6
2 5
2
1 2 1
1
1 2
1 2 1 0.2 (10) 2.87 10
2.4
(10)
ee
te
AM
AM
t
1
2 2 3.5
4
01
1 [1 0.2(10) ] 4.244 10
2e
e
pM
p
4 6 2
0(4.244 10 )(48.373) 2.053 10 N/m 20.3atmp
e
(1.4)(287)(275.78) 332.9 m/sec.
e e
a RT
10(332.9) 3329 m/sec
e e e
V M a
PROPRIETARY MATERIAL. © 2012 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual may be
displayed, reproduced, or distributed in any form or by any means, without the prior written permission of the publisher, or used
beyond the limited distribution to teachers and educators permitted by McGraw-Hill for their individual course preparation. A
student using this manual is using it without permission.
38
6
2 8
2
1 2 [1 0.2 (20) ] 2.365 10
2.4
(20)
te
15,377
e
t
A
A
1
2 2 1
01
1 [1 (0.2)(20) ] 0.01235
2e
e
TM
T
PROPRIETARY MATERIAL. © 2012 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual may be
displayed, reproduced, or distributed in any form or by any means, without the prior written permission of the publisher, or used
beyond the limited distribution to teachers and educators permitted by McGraw-Hill for their individual course preparation. A
student using this manual is using it without permission.
2
02
ft
2 2
0
1
2 2
p p q p V p p M
2 4
02
lb
2116 0.7(2116)(2) 0.804 10
ft
p
4
2
lb
1.656 10 ,
ft
2
1
12 1
ee
pM
p
PROPRIETARY MATERIAL. © 2012 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual may be
displayed, reproduced, or distributed in any form or by any means, without the prior written permission of the publisher, or used
beyond the limited distribution to teachers and educators permitted by McGraw-Hill for their individual course preparation. A
student using this manual is using it without permission.
4
3
1.37 10 0.267 kg/m
(287)(178.6)
e
e
c
p
RT
PROPRIETARY MATERIAL. © 2012 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual may be
displayed, reproduced, or distributed in any form or by any means, without the prior written permission of the publisher, or used
beyond the limited distribution to teachers and educators permitted by McGraw-Hill for their individual course preparation. A
student using this manual is using it without permission.
32
1
2
0
1
12
ee
pM
p
t
/( 1)
2 2 2 2 2 3.5
0 0
1
1 0.7 (1 0.2 )
2 2 2
q p M M M M M
p p
M M2q/p
0
0 0 0
0.2 0.04 0.027
0.4 0.16 0.100
0.6 0.36 0.198
PROPRIETARY MATERIAL. © 2012 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual may be
displayed, reproduced, or distributed in any form or by any means, without the prior written permission of the publisher, or used
beyond the limited distribution to teachers and educators permitted by McGraw-Hill for their individual course preparation. A
student using this manual is using it without permission.
7
5
(1, 225)(200)(3)
Re 4.10 10
(1.7894 10 )
L
V L
2 2 4 2
1 1 (1.225)(200) 2.45 10 N/m
2 2
q V
5.2 5.2(3) 0.0024 m 0.24 cm
L
L
f
0.2 7 0.2
0.37 0.37(3) 0.033 m 3.3 cm
(Re ) (4.1 10 )
L
L
turbulent laminar
3.3
/ 13.75
0.24
0.2 7 0.2
0.074 0.074 0.0022
(Re ) (4.1 10 )
f
L
C
4
(2/45 10 )(3)(17.5)(0.0022)
f f
D q Sc
PROPRIETARY MATERIAL. © 2012 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual may be
displayed, reproduced, or distributed in any form or by any means, without the prior written permission of the publisher, or used
beyond the limited distribution to teachers and educators permitted by McGraw-Hill for their individual course preparation. A
student using this manual is using it without permission.
PROPRIETARY MATERIAL. © 2012 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual may be
displayed, reproduced, or distributed in any form or by any means, without the prior written permission of the publisher, or used
beyond the limited distribution to teachers and educators permitted by McGraw-Hill for their individual course preparation. A
student using this manual is using it without permission.
35
cr
cr
x
e
V x
R
6 5
(10 )(1.789 10 )
Re (1.225)(200)
xV
0.2
c
4 2
0.074 (on one side)
(Re )
0.074 (2.45 10 )(7.3 10 )(17.5)
A
f A
D q S
D
B
f
0.5
cr
1.328
(Re )
A
f
D q S
4 2
6 0.5
1.328
(2.45 10 )(7.3 10 )(17.5)
(10 )
A
f
D
42 N
A
f
D
(laminar) (turbulent)
42 2684 2726 N
A B
f f f
f
D D D
D
PROPRIETARY MATERIAL. © 2012 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual may be
displayed, reproduced, or distributed in any form or by any means, without the prior written permission of the publisher, or used
beyond the limited distribution to teachers and educators permitted by McGraw-Hill for their individual course preparation. A
student using this manual is using it without permission.
36
dp VdV
7.0121 10 N/m
p
4
4 2
(0.65)(7.0121 10 ) 4.555 10 N/mp
1/2
1/2 3
3
1.0663 10
(800) 535.8ft.sec
2.3769 10
e
s
V V
PROPRIETARY MATERIAL. © 2012 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual may be
displayed, reproduced, or distributed in any form or by any means, without the prior written permission of the publisher, or used
beyond the limited distribution to teachers and educators permitted by McGraw-Hill for their individual course preparation. A
student using this manual is using it without permission.
37
1
21
2
2
6
2 5
2
1 2 1
1
1 2
1 2 1 0.2 (10) 2.87 10
2.4
(10)
ee
te
AM
AM
t
1
2 2 3.5
4
01
1 [1 0.2(10) ] 4.244 10
2e
e
pM
p
4 6 2
0(4.244 10 )(48.373) 2.053 10 N/m 20.3atmp
e
(1.4)(287)(275.78) 332.9 m/sec.
e e
a RT
10(332.9) 3329 m/sec
e e e
V M a
PROPRIETARY MATERIAL. © 2012 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual may be
displayed, reproduced, or distributed in any form or by any means, without the prior written permission of the publisher, or used
beyond the limited distribution to teachers and educators permitted by McGraw-Hill for their individual course preparation. A
student using this manual is using it without permission.
38
6
2 8
2
1 2 [1 0.2 (20) ] 2.365 10
2.4
(20)
te
15,377
e
t
A
A
1
2 2 1
01
1 [1 (0.2)(20) ] 0.01235
2e
e
TM
T
PROPRIETARY MATERIAL. © 2012 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual may be
displayed, reproduced, or distributed in any form or by any means, without the prior written permission of the publisher, or used
beyond the limited distribution to teachers and educators permitted by McGraw-Hill for their individual course preparation. A
student using this manual is using it without permission.
