How to Calculate and Solve for Discharge | Chezy’s Equation | Water Budget

The image above represents discharge | Chezy’s Equation.

To compute for discharge, four essential parameters are needed and these parameters are Area (A), Chezy’s Constant (C), Hydraulic Radius (R) and Slope (S).

The formula for calculating discharge:

Q = AC√(RS)

Where;

Q = Discharge
A = Area
C = Chezy’s Constant
R = Hydraulic Radius
S = Slope

Let’s solve an example;
Find the discharge when the area is 25, the chezy’s constant is 16, the hydraulic radius is 9 and the slope is 21.

This implies that;

A = Area = 25
C = Chezy’s Constant = 16
R = Hydraulic Radius = 9
S = Slope = 21

Q = AC√(RS)
Q = (25)(16)√((9)(21))
Q = (25)(16)√(189)
Q = (25)(16)(13.74)
Q = 5499.09

Therefore, the discharge according to Chezy’s equation is 5499.09.

Calculating the Area when the Discharge, the Chezy’s Constant, the Hydraulic Radius and the Slope is Given.

A = Q / C √RS

Where;

A = Area
Q = Discharge
C = Chezy’s Constant
R = Hydraulic Radius
S = Slope

Let’s solve an example;
Find the area when the discharge is 40, the chezy’s constant is 10, the hydraulic radius is 5 and the slope is 9.

This implies that;

Q = Discharge = 40
C = Chezy’s Constant = 10
R = Hydraulic Radius = 5
S = Slope = 9

A = Q / C √RS
A = 40 / 10 √(5)(9)
A = 40 / 10 √45
A = 40 / 10 (6.708)
A = 40 / 67.08
A = 0.596

Therefore, the area is 0.596.

Continue reading How to Calculate and Solve for Discharge | Chezy’s Equation | Water Budget

How to Calculate and Solve for Discharge | Slope Area Method | Water Budget

The image above represents discharge | slope area method.

To compute for discharge | slope area method, four essential parameters are needed and these parameters are Manning’s Co-efficient (N), Area (A), Hydraulic Radius (R) and Slope (S).

The formula for calculating discharge | slope area method:

Q = (A / N) R2/3 S1/2

Where;

Q = Discharge
N = Manning’s Co-efficient
A = Area
R = Hydraulic Radius
S = Slope

Let’s solve an example;
Find the discharge when the manning’s co-efficient is 4, the area is 30, the hydraulic radius is 15 and the slope is 22.

This implies that;

N = Manning’s Co-efficient = 4
A = Area = 30
R = Hydraulic Radius = 15
S = Slope = 22

Q = (A / N) R2/3 S1/2
Q = (30 / 4) (15)2/3 (22)1/2
Q = (7.5) (6.08) (4.69)
Q = 213.96

Therefore, the discharge is 213.96.

Continue reading How to Calculate and Solve for Discharge | Slope Area Method | Water Budget

How to calculate and Solve for Shear Stress | Rock Mechanics

The image above represents shear stress.

To compute for shear stress, two essential parameters are needed and these parameters are Shear Force (ΔS) and Area (ΔA).

The formula for calculating the shear stress:

τ = ΔS / ΔA

Where:

τ = Shear Stress
ΔS = Shear Force
ΔA = Area

Let’s solve an example;
Find the shear stress when the shear force is 16 with an area of 30.

This implies that;

ΔS = Shear Force = 16
ΔA = Area = 30

τ = ΔS / ΔA
τ = 16 / 30
τ = 0.53

Therefore, the shear stress is 0.53 Pa.

Calculating the Shear Force when the Shear Stress and Area is Given.

ΔS = τ x ΔA

Where;

ΔS = Shear Force
τ = Shear Stress
ΔA = Area

Let’s solve an example;
Find the shear force with a shear stress of 40 and an area of 12.

This implies that;

τ = Shear Stress = 40
ΔA = Area = 12

ΔS = τ x ΔA
ΔS = 40  x 12
ΔS = 480

Therefore, the Shear Force is 480.

Continue reading How to calculate and Solve for Shear Stress | Rock Mechanics

How to Calculate and Solve for Normal Stress | Rock Mechanics

The image above represents normal stress.

To calculate for normal stress, two essential parameters are needed and these parameters are normal force (ΔN) and area (ΔA).

The formula for calculating the normal stress:

σn = ΔN / ΔA

Where;

σn = Normal Stress
ΔN = Normal Force
ΔA = Area

Let’s solve an example;
Calculate the normal stress with a normal force of 12 and an area of 22.

This implies that;

ΔN = Normal Force = 12
ΔA = Area = 22

σn = ΔN / ΔA
σn = 12 / 22
σn = 0.54

Therefore, the normal stress is 0.54 Pa.

Calculating the Normal Force when the Normal Stress and Area is Given.

ΔN = σn x ΔA

Where;

ΔN = Normal Force
σn = Normal Stress
ΔA = Area

Let’s solve an example;
Calculate the normal force when the normal stress is 25 with an area of 10.

This implies that;

σn = Normal Stress = 25
ΔA = Area = 10

ΔN = σn x ΔA
ΔN = 25 x 10
ΔN = 250

Therefore, the normal force is 250.

Continue reading How to Calculate and Solve for Normal Stress | Rock Mechanics

How to Calculate and Solve for Infinite Acting Period | The Calculator Encyclopedia

The image represents the infinite acting period.

To compute the infinite acting period, six essential parameters are needed and these parameters are permeability (k), porosity (φ), well drainage area (A), viscosity (μ), Dimensionless Time to End of Infinite Acting Period ((tDA)eia) and total compressibility (CT).

The formula for calculating the infinite acting period:

teia = [φ μ CT A / 0.000263K] (tDA)eia

Where;

teia = Infinite Acting Period
K = Permeability
φ = Porosity
A = Well Drainage Area
μ = Viscosity
(tDA)eia = Dimensionless Time to End of Infinite Acting Period
CT = Total Compressibility

Let’s solve an example;
Given that the permeability is 21, porosity is 15, well drainage area is 32, viscosity is 26, dimensionless time to end of infinite acting period is 44 and total compressibility is 34.
Find the infinite acting period?

This implies that;

K = Permeability = 21
φ = Porosity = 15
A = Well Drainage Area = 32
μ = Viscosity = 26
(tDA)eia = Dimensionless Time to End of Infinite Acting Period = 44
CT = Total Compressibility = 34

teia = [φ μ CT A / 0.000263K] (tDA)eia
teia = [15 x 26 x 34 x 32 / 0.000263 x 21] 44
teia = [424320 / 0.005523] 44
teia = [76827810.972] 44
teia = 3380423682.78

Therefore, the infinite acting period is 3380423682.78 s.

Continue reading How to Calculate and Solve for Infinite Acting Period | The Calculator Encyclopedia

How to Calculate and Solve for True Stress | The Calculator Encyclopedia

The image above represents the true stress.

To compute for the true stress, two essential parameters are needed and these parameters are force (F) and instantaneous area (Ai).

The formula for calculating true stress:

σT = F / Ai

Where;
T = True Stress
F = Force
Ai = Instantaneous Area

Let’s solve an example;
Find the true stress when the instantaneous area is 60 with a force of 25.

This implies that;
F = Force = 25
Ai = Instantaneous Area = 60

σT = F / Ai
σT = 25 / 60
σT = 0.416

Therefore, the true stress is 0.416 Pa.

Calculating the Force when True Stress and Instantaneous Area is Given.

F = Ai x σT

Where;
F = Force
σT = True Stress
Ai = Instantaneous Area

Let’s solve an example;
Find the force when the instantaneous area is 30 with a true stress of 15.

This implies that;
σT = True Stress = 15
Ai = Instantaneous Area = 30

F = Ai x σT
F = 30 x 15
F = 450

Therefore, the force is 450.

Continue reading How to Calculate and Solve for True Stress | The Calculator Encyclopedia

How to Calculate and Solve for the Height, Base Edge and Area of a Square Pyramid | Nickzom Calculator

The image above is a square pyramid.

To compute the area of a square pyramid, two essential parameters are needed and this parameters are base edge (a) and height (h).

The formula for calculating the area of a square pyramid:

A = a² + 2a√(( / 4) + h²)

Where;
A = Area of a square pyramid
a = Base edge of the square pyramid
h = Height of the square pyramid

Let’s solve for an example;
Find the area of a square pyramid when the base edge (a) given is 8 cm with a height (h) of 12 cm.

This implies that;
a = Base edge of the square pyramid = 8 cm
h = Height of the square pyramid = 12 cm

A = a² + 2a√(( / 4) + h²)
A = 8² + 2 x 8√(( / 4) + 12²)
A = 64 + 16√((64 / 4) + 144)
A = 64 + 16√(16 + 144)
A = 64 + (16)(√160)
A = 64 + (16)(12.65)
A = 64 + 202.3857
A = 266.386

Therefore, the area of the square pyramid is 266.386 cm2.

Continue reading How to Calculate and Solve for the Height, Base Edge and Area of a Square Pyramid | Nickzom Calculator

How to Calculate and Solve for the Area of an Ellipsoid | The Calculator Encyclopedia

The image above is an ellipsoid.

To compute the area of an ellipsoid, three essential parameters are needed and this parameters are axis (a)axis (b) and axis (c).

The formula for calculating the area of an ellipsoid:

A = 4π((ab)1.6 + (ac)1.6 + (bc)1.63)1 / 1.6

Where;
A = Area of the ellipsoid
a = Axis of the ellipsoid
b = Axis of the ellipsoid
c = Axis of the ellipsoid

Let’s solve an example;
Find the the area of an ellipsoid when the axis (a) of the ellipsoid is 12 cm, axis (b) of the ellipsoid is 6 cm and axis (c) of the ellipsoid is 2 cm.

This implies that;
a = Axis of the ellipsoid = 12 cm
b = Axis of the ellipsoid = 6 cm
c = Axis of the ellipsoid = 2 cm

A = 4π((ab)1.6 + (ac)1.6 + (bc)1.63)1 / 1.6
A = 4π(((12)(6))1.6 + ((12)(2))1.6 + ((6)(2))1.63)1 / 1.6
A = 4π(((72)1.6 + (24)1.6 + (12)1.6)3)1 / 1.6
A = 4π(((936.98) + (161.56) + (53.29))3)1 / 1.6
A = 4π((1151.84)3)1 / 1.6
A = 4π(383.946)1 / 1.6
A = 4π(383.946)0.625
A = 4π(41.2258)
A = (12.566)(41.2258)
A = 518.059

Therefore, the area of the ellipsoid is 518.059 cm2.

Continue reading How to Calculate and Solve for the Area of an Ellipsoid | The Calculator Encyclopedia

How to Calculate and Solve for the Width, Height, Length and Area of a Rectangular Prism | The Calculator Encyclopedia

The image above is a rectangular prism.

To compute the area of a rectangular prism requires three essential parameters which are the length, width and height of the rectangular prism.

A = 2wl + 2hl + 2hw

Where;
A = Area of the rectangular prism
l = Length of the rectangular prism
w = Width of the rectangular prism
h = Height of the rectangular prism

Let’s solve an example;
Find the area of a rectangular prism with a width of 10 cm, a height of 17 cm and a length of 14 cm.

This implies that;
l = Length of the rectangular prism = 14 cm
w = Width of the rectangular prism = 10 cm
h = Height of the rectangular prism = 17 cm

A = 2wl + 2hl + 2hw
A = 2 x 10 x 14 + 2 x 17 x 14 + 2 x 17 x 10
A = 280 + 476 + 340
A = 1096

Therefore, the area of the rectangular prism is 1096 cm2.

Calculating the Length of a Rectangular Prism using the Area, Width and Height of the Rectangular Prism. 

l = A – 2hw / 2 (w + h)

Where;
l = Length of the rectangular prism
A = Area of the rectangular prism
w = Width of the rectangular prism
h = Height of the rectangular prism

Let’s solve an example;
Find the length of a rectangular prism with a width of 9 cm, a height of 12 cm and a Area of 250 cm2.

This implies that;
w = Width of the rectangular prism = 9 cm
h = Height of the rectangular prism = 12 cm
A = Area of the rectangular prism = 250 cm2

l = A – 2hw / 2 (w + h)
l = 250 – 2 x 12 x 9 / 2 (9 + 12)
l = 250 – 216 / 2 (21)
l = 34 / 42
l = 0.81

Therefore, the length of the rectangular prism is 0.81 cm.

Continue reading How to Calculate and Solve for the Width, Height, Length and Area of a Rectangular Prism | The Calculator Encyclopedia

How to Calculate and Solve for the Axis and Area of an Ellipse | Nickzom Calculator

The image above is an ellipse.

To compute the area of an ellipse, two essential parameters are needed and this parameters are axis (a) and axis (b).

A = πab

Where;
A = Area of the ellipse
a = Axis of the ellipse
b = Axis of the ellipse

Let’s solve an example;
Find the area of an ellipse when it has an axis (a) of 10 cm and an axis (b) of 17 cm.

This implies that;
a = Axis of the ellipse = 10 cm
b = Axis of the ellipse = 17 cm

A = πab
A = 3.142 x 10 x 17
A = 534.14

Therefore, the area of the ellipse is 534.14 cm2.

Calculating the Axis (a) of an ellipse using Area of the ellipse and Axis (b) of the ellipse.

a = A / πb

Where;
a = Axis of the ellipse
A = Area of the ellipse
b = Axis of the ellipse

Let’s solve an example;
Find the axis (a) of an ellipse when the area of the ellipse is 210 cm2 with an axis (b) of 19 cm.

This implies that;
A = Area of the ellipse = 210 cm2
b = Axis of the ellipse = 19 cm

a = A / πb
a = 210 / 3.142 x 19
a = 210 / 59.70
a = 3.52

Therefore, the axis (a) of an ellipse is 3.52 cm.

Continue reading How to Calculate and Solve for the Axis and Area of an Ellipse | Nickzom Calculator