Pearson eText for Manufacturing Processes for Engineering Materials -- Instant Access (Pearson+)
Pearson eText for Manufacturing Processes for Engineering Materials -- Instant Access (Pearson+)
6th Edition
ISBN: 9780137503520
Author: Serope Kalpakjian, Steven Schmid
Publisher: PEARSON+
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Chapter 5, Problem 5.75P
To determine

The solidification time for tripled height and diameter.

Expert Solution & Answer
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Answer to Problem 5.75P

Time required to solidify the metal if the height is tripled is 6.612 min.

Time required to solidify the metal if the diameter is tripled is 12.96 min.

Explanation of Solution

Given Information:

  Diameter to heght ratio:d1h1=1Then, Solidification time, t=4min

The volume of the cylinder is,

  V=π4d2h

The area of the cylinder is,

  A=πdh+2×π4d2A=πdh+π2d2

The solidification is given as,

  t=C( V A)2t=C( π 4 d 2 h πdh+ π 2 d 2 )2t=C( dh 4h+2d)2.......(1)

From the given data, h1=d1&t1=4min

Then, solidification becomes,

  t1=C( d 1 h 1 4 h 1 +2 d 1 )24=C( d 1 2 4 d 1 2 +2 d 1 2 )24=C( d 1 6)2=C( h 1 6)2.....(2)

Now if the height is tripled

  h2=3h1h2=3d1&d2=d1

  t2=C( d 2 h 2 4 h 2 +2 d 2 )2t2=C( d 1 ×3 h 1 4×3 h 1 +2× d 1 )2t2=C( 3 d 1 h 1 12 h 1 +2 d 1 )2t2=C( 3 d 1 2 12 d 1 +2 d 1 )2t2=C( 3 14 d 1)2......(3)

From

Equation (2) & (3)

  4=C( d 1 6)2t2=C( 3 14 d 1)2Dividing both the equations,4t2=C ( d 1 6 )2C ( 3 14 d 1 )24t2= ( 1 6 )2 ( 3 14 )24t2=( 7 9)24t2=4981t2=81×449t2=6.612min

Hence, the time required to solidify the metal if the height is tripled is 6.612 min.

Now, if the diameter is tripled then,

  d3=3d1&h3=h1h3=d1

  t3=C( d 3 h 3 4 h 3 +2 d 3 )2t3=C( 3 d 1 × d 1 4 d 1 +2×3 d 1 )2t3=C( 3 d 1 2 4 d 1 +6 d 1 )2t2=C( 3 d 1 2 10 d 1 )2t3=C( 3 10 d 1)2......(4)

From

Equation (2) & (4)

  4=C( d 1 6)2t3=C( 3 10 d 1)2Dividing both the equations,4t3=C ( d 1 6 )2C ( 3 10 d 1 )24t3= ( 1 6 )2 ( 3 10 )24t3=( 5 9)24t3=2581t3=4×8125t3=12.96min

Hence, the time required to solidify the metal if the diameter is tripled is 12.96 min.

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Chapter 5 Solutions

Pearson eText for Manufacturing Processes for Engineering Materials -- Instant Access (Pearson+)

Ch. 5 - Prob. 5.11QCh. 5 - Prob. 5.12QCh. 5 - Prob. 5.13QCh. 5 - Prob. 5.14QCh. 5 - Prob. 5.15QCh. 5 - Prob. 5.16QCh. 5 - Prob. 5.17QCh. 5 - Prob. 5.18QCh. 5 - Prob. 5.19QCh. 5 - Prob. 5.20QCh. 5 - Prob. 5.21QCh. 5 - Prob. 5.22QCh. 5 - Prob. 5.23QCh. 5 - Prob. 5.24QCh. 5 - Prob. 5.25QCh. 5 - Prob. 5.26QCh. 5 - Prob. 5.27QCh. 5 - Prob. 5.28QCh. 5 - Prob. 5.29QCh. 5 - Prob. 5.30QCh. 5 - Prob. 5.31QCh. 5 - Prob. 5.32QCh. 5 - Prob. 5.33QCh. 5 - Prob. 5.34QCh. 5 - Prob. 5.35QCh. 5 - Prob. 5.36QCh. 5 - Prob. 5.37QCh. 5 - Prob. 5.38QCh. 5 - Prob. 5.39QCh. 5 - Prob. 5.40QCh. 5 - Prob. 5.41QCh. 5 - Prob. 5.42QCh. 5 - Prob. 5.43QCh. 5 - Prob. 5.44QCh. 5 - Prob. 5.45QCh. 5 - Prob. 5.46QCh. 5 - Prob. 5.47QCh. 5 - Prob. 5.48QCh. 5 - Prob. 5.49QCh. 5 - Prob. 5.50QCh. 5 - Prob. 5.51QCh. 5 - Prob. 5.52QCh. 5 - Prob. 5.53QCh. 5 - Prob. 5.54QCh. 5 - Prob. 5.55QCh. 5 - Prob. 5.56QCh. 5 - Prob. 5.57QCh. 5 - Prob. 5.58QCh. 5 - Prob. 5.59QCh. 5 - Prob. 5.60QCh. 5 - Prob. 5.61PCh. 5 - Prob. 5.62PCh. 5 - Prob. 5.63PCh. 5 - Prob. 5.64PCh. 5 - Prob. 5.65PCh. 5 - Prob. 5.66PCh. 5 - Prob. 5.67PCh. 5 - Prob. 5.68PCh. 5 - Prob. 5.69PCh. 5 - Prob. 5.70PCh. 5 - Prob. 5.71PCh. 5 - Prob. 5.72PCh. 5 - Prob. 5.73PCh. 5 - Prob. 5.74PCh. 5 - Prob. 5.75PCh. 5 - Prob. 5.76PCh. 5 - Prob. 5.77PCh. 5 - Prob. 5.78PCh. 5 - Prob. 5.79PCh. 5 - Prob. 5.80PCh. 5 - Prob. 5.81PCh. 5 - Prob. 5.82PCh. 5 - Prob. 5.83PCh. 5 - Prob. 5.84PCh. 5 - Prob. 5.85PCh. 5 - Prob. 5.86PCh. 5 - Prob. 5.87PCh. 5 - Prob. 5.88PCh. 5 - Prob. 5.89PCh. 5 - Prob. 5.90PCh. 5 - Prob. 5.91PCh. 5 - Prob. 5.92PCh. 5 - Prob. 5.93DCh. 5 - Prob. 5.94DCh. 5 - Prob. 5.95DCh. 5 - Prob. 5.96DCh. 5 - Prob. 5.97DCh. 5 - Prob. 5.98DCh. 5 - Prob. 5.99DCh. 5 - Prob. 5.100DCh. 5 - Prob. 5.101DCh. 5 - Prob. 5.102DCh. 5 - Prob. 5.103DCh. 5 - Prob. 5.104DCh. 5 - Prob. 5.105DCh. 5 - Prob. 5.106DCh. 5 - Prob. 5.107DCh. 5 - Prob. 5.108DCh. 5 - Prob. 5.109DCh. 5 - Prob. 5.110DCh. 5 - Prob. 5.111DCh. 5 - Prob. 5.112DCh. 5 - Prob. 5.113DCh. 5 - Prob. 5.114DCh. 5 - Prob. 5.115D
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