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

The image above represents thickness of solidifying metals.

To compute for thickness of solidifying metals, six essential parameters are needed and these parameters are Melting Temperature of Metal (Tm), Initial Mould Temperature (To), Heat Diffusivity (α), Time (t), Density (ρ’) and Latent Heat of Fusion (Hf).

The formula for calculating thickness of solidifying metals:

M = 2(Tm – To)√(α)√(t) / √(π)ρ’Hf

Where:

M = Thickness of Solidifying Metal
Tm = Melting Temperature of Metal
To = Initial Mould Temperature
α = Heat Diffusivity
t = Time
ρ = Density
Hf = Latent Heat of Fusion

Let’s solve an example;
Find the thickness of solidifying metal when the melting temperature of metal is 4, the initial mould temperature is 8, the heat diffusivity is 2, the time is 6, the density is 3 and the latent heat of fusion is 7.

This implies that;

Tm = Melting Temperature of Metal = 4
To = Initial Mould Temperature = 8
α = Heat Diffusivity = 2
t = Time = 6
ρ = Density = 3
Hf = Latent Heat of Fusion = 7

M = 2(Tm – To)√(α)√(t) / √(π)ρ’Hf
M = 2(4 – 8)√(2)√(6) / √(π)(3)(7)
M = 2(-4)(1.414)(2.449) / (1.772)(3)(7)
M = -27.712 / 37.22
M = -0.744

Therefore, the thickness of solidifying metal is -0.744 m.

Continue reading How to Calculate and Solve for Thickness of Solidifying Metals | Solidification of Metals

How to Calculate and Solve for Total Heat Loss in Furnace | Fuel and Furnaces

The image above represents total heat loss in furnace.

To compute for total heat loss in furnace, four essential parameters are needed and these parameters are Absolute Temperature (Kelvin) (T), Factor of Total Radiation (a), Area of Opening (A) and Time (Hours) (H).

The formula for calculating total heat loss in furnace:

Q = 4.88(T/100)4 x a x AH

Where:

Q = Total Heat Loss in Furnace
T = Absolute Temperature (Kelvin)
a = Factor of Total Radiation
A = Area of Opening
H = Time (Hours)

Let’s solve an example;
Find the total heat loss in furnace when the absolute temperature is 22, the factor of total radiation is 14, the area of opening is 10 and the time is 18.

This implies that;

T = Absolute Temperature (Kelvin) = 22
a = Factor of Total Radiation = 14
A = Area of Opening = 10
H = Time (Hours) = 18

Q = 4.88(T/100)4 x a x AH
Q = 4.88(22/100)4 x 14 x (10)(18)
Q = 4.88(0.22)4 x 14 x 180
Q = 4.88(0.00234256) x 2520
Q = 28.807

Therefore, the total heat loss in furnace is 28.807 J/Kg K.

Continue reading How to Calculate and Solve for Total Heat Loss in Furnace | Fuel and Furnaces

How to Calculate and Solve for Infiltration Capacity | Methods of Application of Water

The image above represents infiltration capacity.

To compute for infiltration capacity, four essential parameters are needed and these parameters are Initial infiltration capacity (Fo), Final constant infiltration capacity (Fc), Time (t) and Empirical constant (k).

The formula for calculating infiltration capacity:

Fp = Fc + (Fo – Fc)-kt

Where:

Fp = Infiltration Capacity
Fo = Initial Infiltration Capacity
Fc = Final Constant Infiltration Capacity
t = Time
k = Empirical Constant

Let’s solve an example;
Find the infiltration capacity when the initial infiltration capacity is 16, the final constant infiltration capacity is 10, the time is 6 and the empirical constant is 21.

This implies that;

Fo = Initial Infiltration Capacity = 16
Fc = Final Constant Infiltration Capacity = 10
t = Time = 6
k = Empirical Constant = 21

Fp = Fc + (Fo – Fc)-kt
Fp = 10 + (16 – 10)-(21)(6)
Fp = 10 + (6)-126
Fp = 10 + 8.97e-99
Fp = 10

Therefore, the infiltration capacity is 10.

Continue reading How to Calculate and Solve for Infiltration Capacity | Methods of Application of Water

How to Calculate and Solve for Age Determination | Radiometric Method

The image above represents age determination.

To compute for age determination, two essential parameters are needed and these parameters are Decay Constant (λ) and Time (t).

The formula for calculating age determination:

AD = eλt – 1

Where:

AD = Age Determination
l = Decay Constant
t = Time

Let’s solve an example;
Find the age determination when the decay constant is 6 and the time is 20.

This implies that;

l = Decay Constant = 6
t = Time = 20

AD = eλt – 1
AD = e(6)(20) – 1
AD = e120 – 1
AD = 1.304e+52 – 1
AD = 1.304e+52

Therefore, the age determination is 1.304e+52.

Continue reading How to Calculate and Solve for Age Determination | Radiometric Method

How to Calculate and Solve for Number of Atoms Present | Radiometric Method

The image above represents number of atoms present.

To compute for number of atoms present, three essential parameters are needed and these parameters are Number of Atoms Present at t = 0 (No), Time (t) and Decay Constant (λ).

The formula for calculating number of atoms present:

N = Noe-λt

Where:

N = Number of Atoms Present
No = Number of Atoms Present at t = 0
t = Time
λ = Decay Constant

Let’s solve an example;
Find the number of atoms present when the number of atoms present at t=0 is 10, time is 5 and decay constant is 14.

This implies that;

No = Number of Atoms Present at t = 0 = 10
t = Time = 15
λ = Decay Constant = 14

N = Noe-λt
N = 10e-(14)(5)
N = 10e-(70)
N = 10e-70
N = 10(3.97e-31)
N = 3.97e-30

Therefore, the number of atoms present is 3.97e-30.

Continue reading How to Calculate and Solve for Number of Atoms Present | Radiometric Method

How to Calculate and Solve for Impulse | Motion

The image above represents impulse.

To compute for impulse, two essential parameters are needed and these parameters are force (f) and time (t).

The formula for calculating impulse:

I = Ft

Where;

I = Impulse
F = Force
t = Time

Let’s solve an example;
Given that the force is 28 and the time is 14. Find the impulse?

This implies that;

F = Force = 28
t = Time = 14

I = Ft
I = 28 x 14
I = 392

Therefore, the impulse is 392 Ns.

Calculating the Force when the Impulse and the Time is Given.

F = I / t

Where;

F = Force
I = Impulse
t = Time

Let’s solve an example;
Given that the impulse is 60 and the time is 10. Find the force?

This implies that;

I = Impulse = 60
t = Time = 10

F = I / t
F = 60 / 10
F = 6

Therefore, the force is 6 N.

Continue reading How to Calculate and Solve for Impulse | Motion

How to Calculate and Solve for Final Velocity | Motion

The image above represents final velocity.

To compute for final velocity, three essential parameters are needed and these parameters are initial velocity (u), acceleration (a) and time (t).

The formula for calculating final velocity:

v = u + at

Where;

v = Final Velocity
u = Initial Velocity
a = Acceleration
t = Time

Let’s solve an example;
Find the Final velocity when the initial velocity is 12, acceleration is 9 and the time is 24.

This implies that;

u = Initial Velocity = 12
a = Acceleration = 9
t = Time = 24

v = u + at
v = 12 + (9 x 24)
v = 12 + 216
v = 228

Therefore, the final velocity is 228 m/s.

Calculating the Initial Velocity when the Final Velocity, the Acceleration and the Time is Given.

u = v – at

Where;

u = Initial Velocity
v = Final Velocity
a = Acceleration
t = Time

Let’s solve an example;
Find the Initial Velocity when the Final Velocity is 32, the acceleration is 12 and the time is 2.

This implies that;

v = Final Velocity = 32
a = Acceleration = 12
t = Time = 2

u = v – at
u = 32 – (12 x 2)
u = 32 – 24
u = 8

Therefore, the initial velocity is 8 m/s.

Continue reading How to Calculate and Solve for Final Velocity | Motion

How to Calculate and Solve for Acceleration | Motion

The image above represents acceleration.

To compute for acceleration, three essential parameters are needed and these parameters are initial velocity (u), final velocity (v) and time (t).

The formula for calculating acceleration:

a = (v – u) / t

Where;

a = Acceleration
v = Final Velocity
u = Initial Velocity
t = Time

Let’s solve an example;
Find the acceleration when the final velocity is 21, the initial velocity is 10 and time is 8.

This implies that;

v = Final Velocity =21
u = Initial Velocity = 10
t = Time = 8

a = (v – u) / t
a = (21 – 10) / 8
a = 11 / 8
a = 1.375

Therefore, the acceleration is 1.375 m/s².

Calculating the Initial Velocity when the Acceleration, the Final Velocity and the Time is Given.

u = v – at

Where;

u = Initial Velocity
a = Acceleration
v = Final Velocity
t = Time

Let’s solve an example;
Find the initial velocity when the acceleration is 14, the final velocity is 34 and the time is 2.

This implies that;

a = Acceleration = 14
v = Final Velocity = 34
t = Time = 2

u = v – at
u = 34 – (14 x 2)
u = 34 – 28
u = 6

Therefore, the initial velocity is 6 m/s.

Continue reading How to Calculate and Solve for Acceleration | Motion

How to Calculate and Solve for Distance Covered | Motion

The image above represents distance covered.

To compute for distance covered, three essential parameters are needed and these parameters are initial velocity (u), acceleration (a) and time (t).

The formula for calculating distance covered:

S = ut + 0.5at²

Where;

S = Distance Covered
u = Initial Velocity
t = Time
a = Acceleration

Let’s solve an example;
Find the distance covered when the initial velocity is 21, acceleration is 10 and the time is 15.

This implies that;

u = Initial Velocity = 21
t = Time = 15
a = Acceleration = 10

S = ut + 0.5at²
S = (21 x 15) + (0.5 x 10 x 15²)
S = 315 + (0.5 x 10 x 225)
S = 315 + (1125)
S = 1440

Therefore, the distance covered is 1440 m .

Calculating the Initial Velocity when the Distance Covered, the Acceleration and the Time is Given.

u = S – 0.5at2 / t

Where;

u = Initial Velocity
S = Distance Covered
t = Time
a = Acceleration

Let’s solve an example;
Find the initial velocity when the distance covered is 48 with a time of 8 and an acceleration of 9.

This implies that;

S = Distance Covered = 48
t = Time = 8
a = Acceleration = 9

u = S – 0.5at2 / t
u = 48 – 0.5(9)(82) / 8
u = 48 – 0.5(9)(64) / 8
u = 48 – 288 / 8
u = – 240 / 8
u = – 30

Therefore, the initial velocity is – 30 m/s.

Continue reading How to Calculate and Solve for Distance Covered | Motion

How to Calculate and Solve for Distance Covered | Motion

The image above represents distance covered.

To compute for distance covered, three essential parameters are needed and these parameters are final velocity (v), initial velocity (u) and time (t).

The formula for calculating distance covered:

S = ((u + v) / 2) t

Where;

S = Distance Covered
u = Initial Velocity
v = Final Velocity
t = Time

Let’s solve an example;
Find the distance covered when the initial velocity is 6, final velocity is 11 and time is 14.

This implies that;

u = Initial Velocity = 6
v = Final Velocity = 11
t = Time = 14

S = ((u + v) / 2) t
S = ((6 + 11) / 2) 14
S = ((17) / 2) 14
S = (8.5) 14
S = 119

Therefore, the distance covered is 119 m.

Calculating the Initial Velocity when the Distance Covered, the Final Velocity and the Time is Given.

u = (2S / t) – v

Where;

u = Initial Velocity
S = Distance Covered
v = Final Velocity
t = Time

Let’s solve an example;
Find the initial velocity when the distance covered is 48, the final velocity is 20 and the time is 4.

This implies that;

S = Distance Covered = 48
v = Final Velocity = 20
t = Time = 4

u = (2S / t) – v
u = (2(48) / 4) – 20
u = (96 / 4) – 20
u = 24 – 20
u = 4

Therefore, the initial velocity is 4 m/s.

Continue reading How to Calculate and Solve for Distance Covered | Motion