How to Calculate and Solve for Freezing Time | Solidification of Metals

The image above represents freezing time.

To compute for freezing time, three essential parameters are needed and these parameters are Thickness of Solidified Metal (M), Constant (β) and Heat Diffusivity (α).

The formula for calculating freezing time:

t = / 4β²α

Where:

t = Freezing Time
M = Thickness of Solidified Metal
β = Constant
α = Heat Diffusivity

Let’s solve an example;
Find the freezing time when the thickness of solidified metal is 8, the constant is 10 and the heat diffusivity is 2.

This implies that;

M = Thickness of Solidified Metal = 8
β = Constant = 10
α = Heat Diffusivity = 2

t = / 4β²α
t = / 4(10)²(2)
t = 64 / 4(100)(2)
t = 64 / 800
t = 0.08

Therefore, the freezing time is 0.08 s.

Calculating the Thickness of Solidified Metal when the Freezing Time, the Constant and the Heat Diffusivity is Given.

M = t x 4β²α

Where:

M = Thickness of Solidified Metal
t = Freezing Time
β = Constant
α = Heat Diffusivity

Let’s solve an example;
Find the thickness of solidified metal when the freezing time is 21, the constant is 9 and the heat diffusivity is 2.

This implies that;

t = Freezing Time = 21
β = Constant = 9
α = Heat Diffusivity = 2

M = t x 4β²α
M = 21 x 4(9²)(2)
M = 21 x 4(81)(2)
M = 21 x 4(162)
M = 21 x 648
M = 13668

Therefore, the thickness of solidified metal is 13668.

Continue reading How to Calculate and Solve for Freezing Time | Solidification of Metals

How to Calculate and Solve for Permeability | Mass Transfer

The image above represents permeability.

To compute for permeability, five essential parameters are needed and these parameters are Constant (A), Partial Pressure (Po), Activation due to Permeation (Qp), Gas Constant (R) and Temperature (T).

The formula for calculating permeability:

P = APo0.5 . e-Qp/RT

Where:

P = Permeability
A = Constant
Po = Partial Pressure
Qp = Activation due to Permeation
R = Gas Constant
T = Temperature

Let’s solve an example;
Find the permeability when the constant is 12, the partial pressure is 22, the activation due to permeation is 10, the gas constant is 14 and the temperature is 2.

This implies that;

A = Constant = 12
Po = Partial Pressure = 22
Qp = Activation due to Permeation = 10
R = Gas Constant = 14
T = Temperature = 2

P = APo0.5 . e-Qp/RT
P = 12(22)0.5 . e-(10)/(14)(2)
P = 12(4.69) . e-10/28
P = 56.28 . e-0.357
P = 56.28 (0.699)
P = 39.38

Therefore, the permeability is 39.38.

Continue reading How to Calculate and Solve for Permeability | Mass Transfer

How to Calculate and Solve for Permeability due to Partial Pressure | Mass Transfer

The image above represents permeability due to partial pressure.

To compute for permeability due to partial pressure, three essential parameters are needed and these parameters are Diffusion Coefficient (D), Constant (K) and Partial Pressure (Po).

The formula for calculating permeability due to partial pressure:

P = DK / √(Po)

Where:

P = Permeability due to Partial Pressure
D = Diffusion Coefficient
K = Constant
Po = Partial Pressure

Let’s solve an example;
Find the permeability due to partial pressure when the diffusion coefficient is 12, the constant is 14 and the partial pressure is 17.

This implies that;

D = Diffusion Coefficient = 12
K = Constant = 14
Po = Partial Pressure = 17

P = DK / √(Po)
P = (12)(14) / √(17)
P = 168 / 4.12
P = 40.74

Therefore, the permeability due to partial pressure is 40.74.

Calculating the Diffusion Coefficient when the Permeability due to Partial Pressure, the Constant and the Partial Pressure is Given.

D = P x √(Po) / K

Where;

D = Diffusion Coefficient
P = Permeability due to Partial Pressure
K = Constant
Po = Partial Pressure

Let’s solve an example;
Find the diffusion coefficient when the permeability due to partial pressure is 12, the constant is 8 and the partial pressure is 16.

This implies that;

P = Permeability due to Partial Pressure = 12
K = Constant = 8
Po = Partial Pressure = 16

D = P x √(Po) / K
D = 12 x √(16) / 8
D = 12 x 4 / 8
D = 48 / 8
D = 6

Therefore, the diffusion constant is 6.

Continue reading How to Calculate and Solve for Permeability due to Partial Pressure | Mass Transfer

How to Calculate and Solve for Diffusion Coefficient | Mass Transfer

The image above represents diffusion coefficient.

To compute for diffusion coefficient, three essential parameters are needed and these parameters are Constant (BA), Boltzmann’s Constant (KB) and Temperature (T).

The formula for calculating diffusion coefficient:

DA = BAKBT

Where:

DA = Diffusion Coefficient | Nernst-Einstein Equation
BA = Constant
KB = Boltzmann’s Constant
T = Temperature

Let’s solve an example;
Find the diffusion coefficient when the constant is 21, the boltzmann’ s constant is 1.39e-23 and temperature is 12.

This implies that;

BA = Constant = 21
KB = Boltzmann’s Constant = 1.3806e-23
T = Temperature = 12

DA = BAKBT
DA = (21)(1.38e-23)(12)
DA = 3.47

Therefore, the diffusion coefficient is 3.47e-21 cm²/s.

Calculating the Constant when the Diffusion Coefficient and the Temperature is Given.

BA = DA / KB x T

Where;

BA = Constant
DA = Diffusion Coefficient | Nernst-Einstein Equation
KB = Boltzmann’s Constant
T = Temperature

Let’s solve an example;
Find the constant when the diffusion coefficient is 10 and the temperature is 3.

This implies that;

DA = Diffusion Coefficient | Nernst-Einstein Equation = 10
KB = Boltzmann’s Constant = 1.3806e-23
T = Temperature = 12

BA = DA / KB x T
BA = 10 / 1.3806e-23 x 12
BA = 10 / 1.70e-9
BA = 5.88e+9

Therefore, the constant is 5.88e+9.

Continue reading How to Calculate and Solve for Diffusion Coefficient | Mass Transfer

How to Calculate and Solve for Concentration of Particles | Fluidization

The image above represents concentration of particles.

To compute for concentration of particles, three essential parameters are needed and these parameters are Initial Concentration of Particles (Co), Constant (M) and Time of Elutriation (t).

The formula for calculating concentration of particles:

C = Coe-Mt

Where:

C = Concentration of Particles
Co = Initial Concentration of Particles
M = Constant
t = Time of Elutriation

Let’s solve an example;
Find the concentration of particles when the initial concentration of particles is 10, the constant is 5 and the time of elutriation is 2.

This implies that;

Co = Initial Concentration of Particles = 10
M = Constant = 5
t = Time of Elutriation = 2

C = Coe-Mt
C = 10e-(5)(2)
C = 10e-10
C = 10(0.000045)
C = 0.00045

Therefore, the concentration of particles is 0.00045 mol/m³.

Continue reading How to Calculate and Solve for Concentration of Particles | Fluidization

How to Calculate and Solve for Expected Discharge | Flood Formulae | Irrigation Water Requirement

The image above represents expected discharge.

To compute for expected discharge, three essential parameters are needed and these parameters are Constant (c), Constant (n) and Drainage Basin Area (Ad).

The formula for calculating expected discharge:

Qp = cAdn

Where:

Qp = Expected Discharge | Flood Formulae
c = Constant
n = Constant
Ad = Drainage Basin Area

Let’s solve an example;
Find the expected discharge when the constant is 8, the constant is 2 and the drainage basin area is 4.

This implies that;

c = Constant = 8
n = Constant = 2
Ad = Drainage Basin Area = 4

Qp = cAdn
Qp = (8) . (4)2
Qp = (8) . (16)
Qp = 128

Therefore, the expected discharge is 128.

Calculating the Constant when the Expected Discharge, the Constant and the Drainage Basin Area is Given.

c = Qp / Adn

Where;

c = Constant
Qp = Expected Discharge | Flood Formulae
n = Constant
Ad = Drainage Basin Area

Let’s solve an example;
Find the constant when the expected discharge is 30, the constant is 3 and the drainage basin area is 2.

This implies that;

Qp = Expected Discharge | Flood Formulae = 30
n = Constant = 3
Ad = Drainage Basin Area = 2

c = Qp / Adn
c = 30 / 23
c = 30 / 8
c = 3.75

Therefore, the constant is 3.75.

Continue reading How to Calculate and Solve for Expected Discharge | Flood Formulae | Irrigation Water Requirement

How to Calculate and Solve for Flexural Strength with Relation to Volume Fraction | Ceramics

The image above represents Flexural strength with relation to volume.

To compute for flexural strength with relation to volume, three essential parameters are needed and these parameters are Initial Stress (σo), Constant (n) and Volume fraction porosity (P).

The formula for calculating flexural strength with relation to volume:

σfs = σo exp (-nP)

Where:

σfs = Flexural Strength
σo = Initial Stress
n = Constant
P = Volume Fraction Porosity

Let’s solve an example;
Find the flexural strength when the initial stress is 11, the constant is 8 and the volume fraction porosity is 22.

This implies that;

σo = Initial Stress = 11
n = Constant = 8
P = Volume Fraction Porosity = 22

σfs = σo exp (-nP)
σfr = (11)exp(-(8)(22))
σfr = (11)exp(-176)
σfr = (11)(3.665e-77)
σfr = 4.032e-76

Therefore, the flexural strength is 4.032e-76 Pa.

Calculating the Initial Stress when the Flexural Strength, the Constant and the Volume Fraction Porosity is Given.

σo = σfr / exp (-nP)

Where;

σo = Initial Stress
σfs = Flexural Strength
n = Constant
P = Volume Fraction Porosity

Let’s solve an example;
Find the initial stress when the flexural strength is 20, the constant is 10 and the volume fraction porosity is 8.

This implies that;

σfs = Flexural Strength = 20
n = Constant = 10
P = Volume Fraction Porosity = 8

σo = σfr / exp (-nP)
σo = 20 / exp (-10 x 8)
σo = 20 / exp (-80)
σo = 20 / – 5.54e+34
σo = – 3.61e-34

Therefore, the initial stress is 3.61e-34.

Continue reading How to Calculate and Solve for Flexural Strength with Relation to Volume Fraction | Ceramics

How to Calculate and Solve for Relative Freezing Time | Foundry Technology

The image above represents relative freezing time.

To compute for relative freezing time, four essential parameters are needed and these parameters are Constant (L), Constant (C), Volume of Riser/Volume of Casting (y) and Relative Contraction of Freezing (B).

The formula for calculating relative freezing time:

x = L / y – B + C

Where:

x = Relative Freezing Time
y = Volume of Riser / Volume of Casting
B = Relative Contraction on Freezing
C = Constant
L = Constant

Let’s solve an example;
Find the relative freezing time when the volume of riser/volume of casting is 26, the relative contraction on freezing is 21, the constant is 8 and the constant is 11.

This implies that;

y = Volume of Riser / Volume of Casting = 26
B = Relative Contraction on Freezing = 21
C = Constant = 11
L = Constant = 8

x = L / y – B + C
x = 8 / 26 – 21 + 11
x = 8 / 5 + 11
x = 1.6 + 11
x = 12.6

Therefore, the relative freezing time is 12.6 s.

Calculating the Constant (L) when the Relative Freezing Time, Constant (C), the Volume of riser/Volume of Casting and the Relative Contraction on Freezing is Given.

L = x (y – B) – C

Where;

L = Constant
x = Relative Freezing Time
y = Volume of riser / Volume of Casting
B = Relative Contraction on Freezing
C = Constant

Let’s solve an example;
Find the Constant when the relative freezing time is 24, the volume of riser / volume of casting is 14, the relative contraction on freezing is 8 and the constant is 10.

This implies that;

x = Relative Freezing Time = 24
y = Volume of riser / Volume of Casting = 14
B = Relative Contraction on Freezing = 8
C = Constant = 10

L = x (y -B) – C
L = 24 (14 – 8) – 10
L = 24 (6) – 10
L = 144 – 10
L = 134

Therefore, the constant is 134.

Continue reading How to Calculate and Solve for Relative Freezing Time | Foundry Technology