   # For the cooling of steel plates discussed in Section 18.4 (Figure 18.17) using linear interpolation, estimate the temperature of the plate at time equal to 1 hr, from the temperature data at 0.8 hr and 1.2 hour. Compare the estimated temperature value to the actual value of 308° C. What is the percentage of error? ### Engineering Fundamentals: An Intro...

5th Edition
Saeed Moaveni
Publisher: Cengage Learning
ISBN: 9781305084766

#### Solutions

Chapter
Section ### Engineering Fundamentals: An Intro...

5th Edition
Saeed Moaveni
Publisher: Cengage Learning
ISBN: 9781305084766
Chapter 18, Problem 32P
Textbook Problem
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## For the cooling of steel plates discussed in Section 18.4 (Figure 18.17) using linear interpolation, estimate the temperature of the plate at time equal to 1 hr, from the temperature data at 0.8 hr and 1.2 hour. Compare the estimated temperature value to the actual value of 308° C. What is the percentage of error?

To determine

Estimate the temperature of plate at 1hr and the percentage of error.

### Explanation of Solution

Given data:

Refer to Figure 18.17 in section 18.4 in textbook,

The value of temperature at 0.8hr is 379°C.

The actual value of temperature at 1hr is 308°C.

The value of temperature at 1.2hr is 252°C.

Formula used:

Formula to calculate the error is,

%error=estimated valueactual valueactual value×100% . (1)

Calculation:

Refer to Figure 18.17 in textbook, the graph shows the relationship between temperature and time.

To find the value of temperature at 1hr use the neighboring values of temperature at 0.8hr and 1.2hr.

Therefore, to find the temperature at 1hr the Figure 18.17 is shown as Figure 1 as follows:

From the Figure 1, draw the two similar triangles ACE and BCD to find the altitude using a linear interpolation manner as shown Figure 2.

Using similar angle theorem,

BCAC=BDAE (2)

Refer to Figure 2,

The values for BC,AC,BDandAE are calculated as follows,

BC=1.2hr1hr=0.2hr

AC=1.2hr0.8hr=0.4hr

AE=379°C252°C=127°C

BD=T1hr252°C

Substitute 0.2hr for BC, 0.4hr for AC, 127°C for AE, and T1hr252°C for BD in equation (2),

0

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