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Chapter 3: Q14E (page 575)

Aluminium rivets used in airplane construction are made slightly larger than the rivet holes and cooled by 鈥渄ry ice鈥� (solid CO2) before being driven. If the diameter of a hole is 4.500 mm, what should be the diameter of a rivet at 23.0潞C if its diameter is to equal that of the hole when the rivet is cooled to -78.0潞C, the temperature of dry ice? Assume that the expansion coefficient remains constant at the value given in Table 17.1.

Short Answer

Expert verified

The diameter value of the rivet is4.511mm.

Step by step solution

01

Concept of Linear Expansion in solids.

The linear change in length when the temperature change is given by the linear expansion expression,

L=L0(1+伪鈭�T) ...(i)

Here, L is the expanded length, L0 is the original length, 伪 is the coefficient of expansion of the material and T is the absolute temperature.

02

 Determination of the diameter value of the rivet following the conditions mentioned.

For aluminium, the coefficient of linear expansion,

伪=2.4脳10-5C掳-1

Take the diameter of rivet at -78.0潞C as D0and the diameter at 23.0潞C is D. Then,

D=D0+鈭�D=D01+伪鈭�T

Substitute all the values in the above equation,

D=0.4500cm1+2.4脳10-5C掳-123.0C掳--78.0C掳=0.4511cm=4.511mm

Thus, the expanded diameter value of the rivet is 4.511mm

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