Chapter 9, Problem 9.61P

Interpretation Introduction

(a)

Interpretation:

The pouring temperature in the cooling curve needs to be determined.

Concept Introduction:

The cooling curve represents a change in temperature as a function of time. Cooling curve is of two types: Curve for metals having no inoculation and curve for metals with inoculation.

Answer to Problem 9.61P

Pouring temperature is ${900}^0\text{C}$

Explanation of Solution

The figure shows the cooling curve for casting.

  

Pouring temperature is the temperature of the liquid at which liquid is added in the mold.Hence from the graph shown, temperature ${900}^0\text{C}$

Interpretation Introduction

(b)

Interpretation:

Solidification temperature of the metal in cooling curves needs to be determined.

Concept Introduction:

Solidification is a process of forming crystal structure from molten metal during cooling.The temperature at which molten metal starts forming crystal is solidification temperature.

Answer to Problem 9.61P

Solidification temperature of metal is ${\text{320}}^{\text{0}}\text{C}$.

Explanation of Solution

Solidification temperature at which solidification starts.Hence from the graph, solidification temperature is ${420}^0\text{C}$.

Or,

  $T_{\text{solidification}}={420}^0\text{C}$

Interpretation Introduction

(c)

Interpretation:

The superheat temperature of the metal needs to be determined.

Concept Introduction:

Difference between pouring temperature and freezing temperature is known as superheating.

Pouring temperature is the temperature at which metal is introduced in a casting.

Freezing temperature is the temperature at which metal solidifies.

Answer to Problem 9.61P

Superheat temperature is ${480}^0\text{C}$.

Explanation of Solution

Superheat is a temperature between pouring temperature and freezing temperature.

Pouring temperature, $T_{pouring=}{900}^{0}c$

Freezing temperature, $T_{freezing}={420}^{0}c$

Thus,

  $\begin{array}{l}{T}_{\sup erheat}=T_{pouring}-T_{freezing}\\ =900-420\\ T_{\sup erheat}={480}^{0}c\end{array}$

Interpretation Introduction

(d)

Interpretation:

At the starting of the solidification, thecooling rate needs to be determined.

Concept Introduction:

Cooling curves are of two types of metal- for metal with no inoculation and for metal with inoculation.

Cooling curve represents different temperatures.

The cooling curve shows different regions according to change in temperature at a specific time.

Answer to Problem 9.61P

Cooling rate of metal is ${250}^{\text{0}}\text{C/sec}$

Explanation of Solution

The cooling rate is the rate of change in temperature with respect to time.

According to the graph,the slope of the curve from pouring temperature to freezing temperature shows the rate of cooling.

It is denoted by $\frac{\text{ΔT}}{\text{Δt}}$

Thus,

  $\frac{\Delta T}{\Delta t}=\frac{125}{0.5\min }={250}^0\text{C/min}$

Cooling rate $={250}^0\text{C/min}$

Interpretation Introduction

(e)

Interpretation:

The total solidification time needs to be determined.

Concept Introduction:

Solidification is a process of forming crystal structure from molten metal during cooling. The time required to form crystal structure from molten metal is solidification time.

Answer to Problem 9.61P

Total solidification time of metal is $9.7\min$

Explanation of Solution

The time required to remove specific heat and latent heat of fusion during cooling of metal is total solidification time.It is the time between the pouring of metal to the completion of solidification.

From the graph,

  $t_{TST}=9.7\min$

Interpretation Introduction

(f)

Interpretation:

The local solidification time of metal needs to be determined.

Concept Introduction:

Solidification is a process of forming crystal structure from molten metal during cooling. The time required to form crystal structure from molten metal is solidification time.

Answer to Problem 9.61P

Local solidification time of metal is 7.2 min.

Explanation of Solution

The time required to remove latent heat of fusion is at specific casting location is local solidification time.

It is the time between the start of solidification and the end of solidification.

Hence from the graph,

  $\begin{array}{l}{t}_{LST}=t_{TST}-\text{start}\text{of}\text{freezing}\\ =9.7-2.5\\ =7.2\min \end{array}$

Interpretation Introduction

(g)

Interpretation:

The identity of metal needs to be determined.

Concept Introduction:

Cooling curves are of two types of metal- for metal with no inoculation and for metal with inoculation.

Cooling curve represents different temperatures.The cooling curve represents charge in temperature as a function of time.

Answer to Problem 9.61P

Probable metal should be Zinc.

Explanation of Solution

Given the cooling curve is for metal having well inoculation.For this metal, solidification starts at melting temperature.Solidification of the temperature of this metal is ${420}^0\text{C}$ Zinc has the same solidification temperature

Hence, the probable metal should be zinc.

Interpretation Introduction

(h)

Interpretation:

The mold constant of metal needs to be determined.

Concept Introduction:

As per Chvorinov's rule, solidification time is directly proportional to the square of volume- area ratio of cast metal.

  $t_s=B{(\frac{V}{A})}^n$

Here,

  $\begin{array}{l}{\text{t}}_{\text{s}}\text{=Solidification time=470sec}\hfill \\ \text{B=Mold Constant}\hfill \\ \text{v=Volume of casting}\hfill \\ \text{A=Area of casting}\hfill \\ \text{n=Constant=2}\hfill \end{array}$

Answer to Problem 9.61P

Mold constant is $87.3\min /i{n}^2$

Explanation of Solution

As per Chvorinov's rule,

  $t_s=B{(\frac{V}{A})}^n$

Volume of casting can be calculated as follow:

  $\begin{array}{l}V=2\times 2\times 2\\ =8i{n}^3\end{array}$

Area of castingcan be calculated as follow:

  $\begin{array}{l}A=6\times (2\times 2)\\ =24i{n}^2\end{array}$

Putting the value.

  $t_s=B{(\frac{V}{A})}^n$

  $9.7=B{(\frac{8}{24})}^2$

  $B=87.3\min /i{n}^2$