Mecanica De Fluidos

02 Solutions 46060

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2–1. An air-filled rubber ball has a diameter of 6 in. If theair pressure within it is increased until the ball’s diameter becomes 7 in., determine the average normal strain in the rubber. d0 = 6 in. d = 7 in. e = pd - pd0 7 - 6 = = 0.167 in./in. pd0 6 Ans.

2–2. A thin strip of rubber has an unstretched length of 15 in. If it is stretched around a pipe having an outer diameter of 5 in., determine the average normal strain in the strip. L0 = 15 in. L = p(5in.) e = L - L0 5p - 15 = = 0.0472 in.>in. L0 15 Ans.

2–3. The rigid beam is supported by a pin at A and wires BD and CE. If the load P on the beam causes the end C to be displaced 10 mm downward, determine the normal strain developed in wires CE and BD.

D

E

4m

P

¢LBD ¢LCE = 3 7 ¢LBD = eCE 3 (10) = 4.286 mm 7 ¢LCE 10 = = = 0.00250 mm>mm L 4000 ¢LBD 4.286 = = 0.00107 mm>mm L 4000A

B

C

3m

2m

2m

Ans. Ans.

eBD =

1

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© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.*2–4. The two wires are connected together at A. If the force P causes point A to be displaced horizontally 2 mm, determine the normal strain developed in each wire.
œ LAC = 23002 + 22 - 2(300)(2) cos 150° = 301.734 mm

C
300

mm

eAC = eAB

œ LAC - LAC 301.734 - 300 = = = 0.00578 mm>mm LAC 300

30

Ans.
mm

30

A

P

300
B

•2–5. The rigid beam is supported by a pin atA and wires BD and CE. If the distributed load causes the end C to be displaced 10 mm downward, determine the normal strain developed in wires CE and BD.

E D 2m 1.5 m 2m A B 3m C

w

Since the vertical displacement of end C is small compared to the length of member AC, the vertical displacement dB of point B, can be approximated by referring to the similar triangle shown in Fig. a dB 10 = ;dB = 4 mm 2 5 The unstretched lengths of wires BD and CE are LBD = 1500 mm and LCE = 2000 mm. dB 4 Ans. = = 0.00267 mm>mm A eavg B BD = LBD 1500

A eavg B CE =

dC 10 = = 0.005 mm>mm LCE 2000

Ans.

2

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© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws asthey currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

2–6. Nylon strips are fused to glass plates. When moderately heated the nylon will become soft while the glass stays approximately rigid. Determine the average shear strain in the nylon due to the load P when the assembly deforms as indicated.

y 2mm 3 mm 5 mm 3 mm 5 mm 3 mm x P

g = tan - 1 a

2 b = 11.31° = 0.197 rad 10

Ans.

2–7. If the unstretched length of the bowstring is 35.5 in., determine the average normal strain in the string when it is stretched to the position shown.
18 in.

6 in. 18 in.

Geometry: Referring to Fig. a, the stretched length of the string is

L = 2L¿ = 2 2182 + 62 = 37.947 in.

Average NormalStrain: eavg = L - L0 37.947 - 35.5 = = 0.0689 in.>in. L0 35.5 Ans.

3

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© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the...