Essentials of Materials Science and Engineering, SI Edition
Essentials of Materials Science and Engineering, SI Edition
4th Edition
ISBN: 9781337672078
Author: ASKELAND, Donald R., WRIGHT, Wendelin J.
Publisher: Cengage Learning
Question
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Chapter 9, Problem 9.71P
Interpretation Introduction

Interpretation:

The volume, diameter, and height of cylinder riser to prevent shrinkage needs to be determined.

Concept introduction:

The riser is an extra source of molten metal connected to casting to avoid cavities being formed.

Solidification of casting material experiences shrinkage which results in the formation of pores.

Casting should freeze before freezing of riser to compensate for shrinkage.

Freezing of riser takes 25% more time than casting.

Time is calculated as follows:

   ts=B( V A)nHere,ts=Solidificationtime V=Volumeofcasting A=Areaofcasting B=Moldcasting

The volume of the riser can be calculated by using

  Vriser=πD24×H

Here,

D= Diameter of the riser

H= Height of riser

Expert Solution & Answer
Check Mark

Answer to Problem 9.71P

  Volume of cylinder riser=132.87  in3Diameter of cylinder riser=7.08inHeight of cylinder riser=10.62in

Explanation of Solution

Given Information:

The volume of casting = 4×10×20in3

And,

  HD=1.5

Calculation:

The time required to solidify the riser is 1.25 times more than that for casting.

  tRiser>1.25tcastingB( V A)nRiser>1.25B( V A)ncasting( V A)nRiser>1.25( V A)ncasting( V A)2Riser>1.25( V A)2casting( V A)Riser>1.25( V A)casting

Here,

The volume of casting = 4×10×20 in3=800 in3

The surface area of casting:

  Acasting=(2×4×10)+(2×4×20)+(2×10×10)πD24 =640πD24

The volume of the riser can be calculated by,

  Vriser=πD24×HVriser=πD24×1.5DVriser=1.5πD24

Area of riser can be calculated as follows:

  Ariser=2×πD24+πDH =πD24+1.5πD2Ariser=1.75πD2

And,

  ( V A)Riser>1.25( V A)casting( 1.5π D 3 4 )1.75πD2>1.25( 800 640 π D 2 4 )0.21D>( 894.42 640 π D 2 4 )(0.21D)(640 π D 2 4)>894.42134.4D0.164D3>894.420.164D3134.4D+894.42<0

Further solving,

  D=(7.08,894.42)

Taking smallest value for Diameter of the riser, D=7.08 in

But the diameter of riser = height of the riser

H = 1.5D inch = 10.62 in

The volume of a riser will be:

  Vriser=1.5π× 10.6224=132.87 in3

Conclusion

Thus, the volume, diameter, and height of cylindrical riser by using proper relation is as follows:

  Volume of cylinder riser=132.87  in3Diameter of cylinder riser=7.08inHeight of cylinder riser=10.62in

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Chapter 9 Solutions

Essentials of Materials Science and Engineering, SI Edition

Ch. 9 - Prob. 9.11PCh. 9 - Prob. 9.12PCh. 9 - Prob. 9.13PCh. 9 - Prob. 9.14PCh. 9 - Prob. 9.15PCh. 9 - Prob. 9.16PCh. 9 - Prob. 9.17PCh. 9 - Prob. 9.18PCh. 9 - Prob. 9.19PCh. 9 - Prob. 9.20PCh. 9 - Prob. 9.21PCh. 9 - Prob. 9.22PCh. 9 - Prob. 9.23PCh. 9 - Prob. 9.24PCh. 9 - Prob. 9.25PCh. 9 - Prob. 9.26PCh. 9 - Prob. 9.27PCh. 9 - Prob. 9.28PCh. 9 - Prob. 9.29PCh. 9 - Prob. 9.30PCh. 9 - Prob. 9.31PCh. 9 - Prob. 9.32PCh. 9 - Prob. 9.33PCh. 9 - Prob. 9.34PCh. 9 - Prob. 9.35PCh. 9 - Prob. 9.36PCh. 9 - Prob. 9.37PCh. 9 - Prob. 9.38PCh. 9 - Prob. 9.39PCh. 9 - Prob. 9.40PCh. 9 - Prob. 9.41PCh. 9 - Prob. 9.42PCh. 9 - Prob. 9.43PCh. 9 - Prob. 9.44PCh. 9 - Prob. 9.45PCh. 9 - Prob. 9.46PCh. 9 - Prob. 9.47PCh. 9 - Prob. 9.48PCh. 9 - Prob. 9.49PCh. 9 - Prob. 9.50PCh. 9 - Prob. 9.51PCh. 9 - Prob. 9.52PCh. 9 - Prob. 9.53PCh. 9 - Prob. 9.54PCh. 9 - Prob. 9.55PCh. 9 - Prob. 9.56PCh. 9 - Prob. 9.57PCh. 9 - Prob. 9.58PCh. 9 - Prob. 9.59PCh. 9 - Prob. 9.60PCh. 9 - Prob. 9.61PCh. 9 - Prob. 9.62PCh. 9 - Prob. 9.63PCh. 9 - Prob. 9.64PCh. 9 - Prob. 9.65PCh. 9 - Prob. 9.66PCh. 9 - Prob. 9.67PCh. 9 - Prob. 9.68PCh. 9 - Prob. 9.69PCh. 9 - Prob. 9.70PCh. 9 - Prob. 9.71PCh. 9 - Prob. 9.72PCh. 9 - Prob. 9.73PCh. 9 - Prob. 9.74PCh. 9 - Prob. 9.75PCh. 9 - Prob. 9.76PCh. 9 - Prob. 9.77PCh. 9 - Prob. 9.78PCh. 9 - Prob. 9.79PCh. 9 - Prob. 9.80PCh. 9 - Prob. 9.81PCh. 9 - Prob. 9.82PCh. 9 - Prob. 9.83PCh. 9 - Prob. 9.84PCh. 9 - Prob. 9.85PCh. 9 - Prob. 9.86PCh. 9 - Prob. 9.87PCh. 9 - Prob. 9.88PCh. 9 - Prob. 9.89PCh. 9 - Prob. 9.90PCh. 9 - Prob. 9.91PCh. 9 - Prob. 9.92PCh. 9 - Prob. 9.93PCh. 9 - Prob. 9.94PCh. 9 - Prob. 9.95PCh. 9 - Prob. 9.96PCh. 9 - Prob. 9.97PCh. 9 - Prob. 9.98PCh. 9 - Prob. 9.99PCh. 9 - Prob. 9.100PCh. 9 - Prob. 9.101PCh. 9 - Prob. 9.102PCh. 9 - Prob. 9.103PCh. 9 - Prob. 9.104PCh. 9 - Prob. 9.105PCh. 9 - Prob. 9.106PCh. 9 - Prob. 9.107PCh. 9 - Prob. 9.108PCh. 9 - Prob. 9.109PCh. 9 - Prob. 9.110PCh. 9 - Prob. 9.111DPCh. 9 - Prob. 9.112DPCh. 9 - Prob. 9.113DPCh. 9 - Prob. 9.114DPCh. 9 - Prob. 9.115DPCh. 9 - Prob. 9.116CPCh. 9 - Prob. 9.117CPCh. 9 - Prob. 9.118CPCh. 9 - Prob. K9.1KPCh. 9 - Prob. K9.2KP
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