How to Calculate and Solve for the Total Volume Shrinkage | Solidification of Metals

The image above represents total volume shrinkage.

To compute for total volume shrinkage, three essential parameters are needed and these parameters are Liquid Shrinkage of Metal or Alloy (εv.l), Freezing Shrinkage (εv.f) and Solid Shrinkage (εv.s).

The formula for calculating the total volume shrinkage:

εv.t = εv.l + εv.f + εv.s

Where:

εv.t = Total Volume Shrinkage
εv.l = Liquid Shrinkage of Metal or Alloy
εv.f = Freezing Shrinkage
εv.s = Solid Shrinkage

Let’s solve an example;
Find the total volume shrinkage when the liquid shrinkage of metal or alloy is 14, the freezing shrinkage is 7 and the solid shrinkage is 2.

This implies that;

εv.l = Liquid Shrinkage of Metal or Alloy = 14
εv.f = Freezing Shrinkage = 7
εv.s = Solid Shrinkage = 2

εv.t = εv.l + εv.f + εv.s
εv.t = 14 + 7 + 4
εv.t = 25

Therefore, the total volume shrinkage is 25.

Calculating the Liquid Shrinkage of Metal or Alloy when the Total Volume Shrinkage, the Freezing Shrinkage and the Solid Shrinkage is Given.

εv.l = εv.t – εv.f – εv.s

Where:

εv.l = Liquid Shrinkage of Metal or Alloy
εv.t = Total Volume Shrinkage
εv.f = Freezing Shrinkage
εv.s = Solid Shrinkage

Let’s solve an example;
Find the liquid shrinkage of metal or alloy when the total volume shrinkage is 44, the freezing shrinkage is 12 and the solid shrinkage is 6.

This implies that;

εv.t = Total Volume Shrinkage = 44
εv.f = Freezing Shrinkage = 12
εv.s = Solid Shrinkage = 6

εv.l = εv.t – εv.f – εv.s
εv.l = 44 – 12 – 6
εv.l = 26

Therefore, the liquid shrinkage of metal or alloy is 26.

How to Calculate and Solve for Volume Shrinkage | Solidification of Metals

The image above represents volume shrinkage.

To compute for volume shrinkage, two essential parameters are needed and these parameters are Mould Volume (Vm) and Volume of Casting at 20°C (Vo).

The formula for calculating the volume shrinkage:

εv= Vm – Vo / Vo x 100%

Where:

εv = Volume Shrinkage
Vm = Mould Volume
Vo = Volume of Casting at 20°C

Let’s solve an example;
Find the volume shrinkage where the mould volume is 30 and the volume of casting at 20°C.

This implies that;

Vm = Mould Volume = 30
Vo = Volume of Casting at 20°C = 3

εv= Vm – Vo / Vo x 100%
εv = 30 – 3 / 3 x 100%
εv = 27 / 3 x 100%
εv = 9 x 100%
εv = 900%

Therefore, the volume shrinkage is 900%.

How to Calculate and Solve for Temperature of Solidifying Metals | Solidification of Metals

The image above represents temperature of solidifying metals.

To compute for temperature of solidifying metals, three essential parameters are needed and these parameters are Surface Temperature (T), Melting Temperature of Metal (Tm) and Initial Temperature of Environment or Mould (To).

The formula for calculating temperature of solidifying metals:

Tsm = T – Tm / To – Tm

Where:

Tsm = Temperature of Solidifying Metals
T = Surface Temperature
Tm = Melting Temperature of Metal
To = Initial Temperature of Environment or Mould

Let’s solve an example;
Find the temperature of solidifying metals when the surface temperature is 12, the melting temperature of metal is 9 and the initial temperature of environment or mould is 10.

This implies that;

T = Surface Temperature = 12
Tm = Melting Temperature of Metal = 9
To = Initial Temperature of Environment or Mould = 10

Tsm = T – Tm / To – Tm
Tsm = 12 – 9 / 10 – 9
Tsm = 3 / 1
Tsm = 3

Therefore, the temperature of solidifying metals is 3 K.

Calculating for Surface Temperature when the Temperature of Solidifying Metals, the Melting Temperature of Metal and the Initial Temperature of Environment or Mould is Given.

T = Tsm (To – Tm) + Tm

Where;

T = Surface Temperature
Tsm = Temperature of Solidifying Metals
Tm = Melting Temperature of Metal
To = Initial Temperature of Environment or Mould

Let’s solve an example;
Find the surface temperature when the temperature of solidifying metals is 10, the melting temperature of metal is 8 and the initial temperature of environment or mould is 14.

This implies that;

Tsm = Temperature of Solidifying Metals = 10
Tm = Melting Temperature of Metal = 8
To = Initial Temperature of Environment or Mould = 14

T = Tsm (To – Tm) + Tm
T = 10 (14 – 8) + 8
T = 10 (6) + 8
T = 68

Therefore, the surface temperature is 68 K.