How to Calculate and Solve for Total Storage | Hydrology

The image above represents total storage.

To compute for total storage, three essential parameters are needed and these paramters are Storage co-efficient (k), Dimensionless constant (x) and Average outflow rate (O).

The formula for calculating total storage:

s = k[x + (1 – x)O]

Where:

s = Total Storage
k = Storage Co-efficient
x = Dimensionless Constant
O = Average Outflow Rate

Let’s solve an example;
Find the total storage when the storage co-efficient is 12, the dimensionless constant is 10 and the average outflow rate is 6.

This implies that;

k = Storage Co-efficient = 12
x = Dimensionless Constant = 10
O = Average Outflow Rate = 6

s = k[x + (1 – x)O]
s = 12[10 + (1 – 10)6]
s = 12[10 + (-9)6]
s = 12[10 + -54]
s = 12[-44]
s = -528

Therefore, the total storage is -528.

Continue reading How to Calculate and Solve for Total Storage | Hydrology

How to Calculate and Solve for Average Outflow Rate | Hydrology II

The image above represents average outflow rate.

To compute for average outflow rate, three essential parameters are needed and these parameters are Average inflow rate (I), Change in storage during routing time (Δs) and Routing Time (Δt).

The formula for calculating average outflow rate:

O = I – Δs / Δt

Where:

O = Average Outflow Rate
I = Average Inflow Rate
Δs = Change in Storage during Routing Time
Δt = Routing Time

Let’s solve an example;
Given that the average inflow rate is 5, the change in storage during routing time is 2 and routing time is 10. Find the average outflow rate?

This implies that;

I = Average Inflow Rate = 5
Δs = Change in Storage during Routing Time = 2
Δt = Routing Time = 10

O = I – Δs / Δt
O = 5 – 2 / 10
O = 5 – 0.2
O = 4.8

Therefore, the average outflow rate is 4.8.

Calculating the Average Inflow Rate when the Average Outflow Rate, the Change in Storage during Routing Time and the Routing Time is Given.

I = O + Δs / Δt

Where;

I = Average Inflow Rate
O = Average Outflow Rate
Δs = Change in Storage during Routing Time
Δt = Routing Time

Let’s solve an example;
Find the Average Inflow Rate when the average outflow rate is 40, change in storage during routing time is 10 and the routing time is 5.

This implies that;

I = Average Inflow Rate = 40
Δs = Change in Storage during Routing Time = 10
Δt = Routing Time = 5

I = O + Δs / Δt
I = 40 + 105
I = 40 – 2
I = 38

Therefore, the average inflow rate is 38.

Continue reading How to Calculate and Solve for Average Outflow Rate | Hydrology II

How to Calculate and Solve for Average Inflow Rate | Hydrology II

The image above represents average inflow rate.

To compute for average inflow rate, three essential parameters are needed and these parameters are Average outflow rate (O), Change in storage during routing time (Δs) and Routing Time (Δt).

The formula for calculating average inflow rate:

I = O + Δs / Δt

Where:

I = Average Inflow Rate
O = Average Outflow Rate
Δs = Change in Storage during Routing Time
Δt = Routing Time

Let’s solve an example;
Find the Average Inflow Rate when the average outflow rate is 10, the change in storage during routing time is 5 and the routing time is 12.

This implies that;

O = Average Outflow Rate = 10
Δs = Change in Storage during Routing Time = 5
Δt = Routing Time = 12

I = O + Δs / Δt
I = 10 + 5 / 12
I = 10 + 0.416
I = 10.416

Therefore, the average inflow rate is 10.416.

Calculating the Average Outflow Rate when the Average Inflow Rate, the Change in Storage during Routing Time and the Routing Time is Given.

O = I – Δs / Δt

Where;

O = Average Outflow Rate
I = Average Inflow Rate
Δs = Change in Storage during Routing Time
Δt = Routing Time

Let’s solve an example;
Find the Average Outflow Rate when the average inflow rate is 50, change in storage during routing time is 20 and the routing time is 10.

This implies that;

I = Average Inflow Rate = 50
Δs = Change in Storage during Routing Time =20
Δt = Routing Time = 10

O = I – Δs / Δt
O = 50 – 20 / 10
O = 50 – 2
O = 48

Therefore, the average outflow rate is 48.

Continue reading How to Calculate and Solve for Average Inflow Rate | Hydrology II

How to Calculate and Solve for Unit Hydrograph | Hydrology II

The image above represents unit hydrograph.

To compute for unit hydrograph, two essential parameters are needed and these parameters are Direct run off (DRO) and Effective depth (ED).

The formula for calculating unit hydrograph:

UHG = DRO / ED

Where:

UHG = Unit Hydrograph
DRO = Direct Run Off
ED = Effective Depth

Let’s solve an example;
Find the unit hydrograph when the direct run off is 11 and the effective depth is 13.

This implies that:

DRO = Direct Run Off = 11
ED = Effective Depth = 13

UHG = DRO / ED
UHG = 11 / 13
UHG = 0.846

Therefore, the unit hydrograph is 0.846.

Calculating the Direct Run Off when the Unit Hydrograph and the Effective Depth is Given.

DRO = UHG x ED

Where;

DRO = Direct Run Off
UHG = Unit Hydrograph
ED = Effective Depth

Let’s solve an example;
Find the direct run off when the unit hydrograph is 21 and the effective depth is 10.

This implies that;

UHG = Unit Hydrograph = 21
ED = Effective Depth = 10

DRO = UHG x ED
DRO = 21 x 10
DRO = 210

Therefore, the direct run off is 210.

Continue reading How to Calculate and Solve for Unit Hydrograph | Hydrology II

How to Calculate and Solve for Length of Well Screen | Water Budget

The image above represents length of well screen.

To compute for length of well screen, three essential parameters are needed and these parameters are Maximum Expected Discharge Capacity of Well (Qo), Effective Open Area per Metre (Ao) and Entrance Velocity at the Screen (Ve).

The formula for calculating length of well screen:

L = Qo / AoVe

Where:

L = Length of Well Screen
Qo = Maximum Expected Discharge Capacity of Well
Ao = Effective Open Area per Metre
Ve = Entrance Velocity at the Screen

Let’s solve an example;
Find the length of well screen when the maximum expected discharge capacity of well is 12, the effective open area per metre is 24 and the entrance velocity at the screen is 18.

This implies that;

Qo = Maximum Expected Discharge Capacity of Well
Ao = Effective Open Area per Metre
Ve = Entrance Velocity at the Screen

L = Qo / AoVe
L = 12 / (24)(18)
L = 12 / 432
L = 0.027

Therefore, the length of well screen is 0.027.

Calculating the Maximum Expected Discharge Capacity of Well when the Length of Well Screen, the Effective Open Area per Metre and the Entrance Velocity at the Screen is Given.

Qo = L x (AoVe)

Where;

Qo = Maximum Expected Discharge Capacity of Well
L = Length of Well Screen
Ao = Effective Open Area per Metre
Ve = Entrance Velocity at the Screen

Let’s solve an example;
Find the maximum expected discharge capacity of well with a length of well screen as 21, effective open area per metre as 10 and entrance velocity at the screen as 5.

This implies that;

L = Length of Well Screen = 21
Ao = Effective Open Area per Metre = 10
Ve = Entrance Velocity at the Screen = 5

Qo = L x (AoVe)
Qo = 21 x (10 x 5)
Qo = 21 x 50
Qo = 1050

Therefore, the maximum expected discharge capacity of well is 1050.

Continue reading How to Calculate and Solve for Length of Well Screen | Water Budget

How to Calculate and Solve for Hydrostatic Pressure of a Dam | Water Budget

The image above represents hydrostatic pressure of a dam.

To compute for hydrostatic pressure of a dam, two essential parameters are needed and these parameters are Specific Weight of Water (γ) and Depth of water (h).

The formula for calculating hydrostatic pressure of a dam:

Hn = γh² / 2

Where:

Hn = Hydrostatic Pressure of a Dam
γ = Specific Weight of Water
h = Depth of Water

Let’s solve an example;
Find the hydrostatic pressure of a dam when the specific weight of water is 10 and the depth of water is 5.

This implies that;

γ = Specific Weight of Water = 10
h = Depth of Water = 5

Hn = γh² / 2
Hn = (10)(5)² / 2
Hn = 10(25) / 2
Hn = 250 / 2
Hn = 125

Therefore, the hydrostatic pressure of the dam is 125.

Calculating the Specific Weight of Water when the Hydrostatic Pressure of the Dam and the Depth of Water is Given.

γ = Hn x 2 / h2

Where;

γ = Specific Weight of Water
Hn = Hydrostatic Pressure of a Dam
h = Depth of Water

Let’s solve an example;
Find the specific weight of water when the hydrostatic pressure of a dam is 30 and the depth of water is 6.

This implies that;

Hn = Hydrostatic Pressure of a Dam = 30
h = Depth of Water = 6

γ = Hn x 2 / h2
γ = 30 x 2 / 62
γ = 60 / 36
γ = 1.667

Therefore, the specific weight of water is 1.667.

Continue reading How to Calculate and Solve for Hydrostatic Pressure of a Dam | Water Budget

How to Calculate and Solve for Entrance Velocity | Darcy’s Law | Water Budget

The image above represents entrance velocity.

To compute for entrance velocity, one essential parameters are needed and these parameters are Hydraulic Conductivity (ki).

The formula for calculating entrance velocity:

Ve = ki

Where:

Ve = Entrance Velocity
ki = Hydraulic Conductivity

Let’s solve an example;
Find the entrance velocity when the hydraulic conductivity is 8.\

This implies that;

ki = Hydraulic Conductivity = 8

Ve = ki
Ve = 8

Therefore, the entrance velocity is 8.

Continue reading How to Calculate and Solve for Entrance Velocity | Darcy’s Law | Water Budget

How to Calculate and Solve for Storage Co-efficient for a Confined Aquifer | Water Budget

The image above represents storage co-efficient for a confined aquifer.

To compute for storage co-efficient for a confined aquifer, five essential parameters are needed and these parameters are Unit Weight of Water (γw), Confined Aquifer Thickness (H), Compressibility of the Aquifer Material (α), Porosity of Aquifer Material (n) and Compressibility of Water (β).

The formula for calculating storage co-efficient for a confined aquifer:

S = γw(α + nβ)H

Where;

S = Storage Co-efficient for a Confined Aquifer
γw = Unit Weight of Water
H = Confined Aquifer Thickness
α = Compressibility of the Aquifer Material
n = Porosity of Aquifer Material
β = Compressibility of Water

Let’s solve an example;
Find the storage co-efficient for a confined aquifer when the unit weight of water is 8, confined aquifer thickness is 12, the compressibility of the aquifer material is 21, the porosity of aquifer material is 18 and the compressibiity of water is 14.

This implies that;

γw = Unit Weight of Water = 8
H = Confined Aquifer Thickness = 12
α = Compressibility of the Aquifer Material = 21
n = Porosity of Aquifer Material = 18
β = Compressibility of Water = 14

S = γw(α + nβ)H
S = 8(21 + 18(14))12
S = 8(21 + 252)12
S = 8(273)12
S = 26208

Therefore, the storage co-efficient for a confined aquifer is 26208.

Calculating the Unit Weight of Water when the Storage Co-efficient for a Confined Aquifer, the Confined Aquifer Thickness, the Compressibility of the Aquifer Material, the Porosity of Aquifer Material and the Compressibility of Water is Given.

γw = S / (a + nβ)H

Where;

γw = Unit Weight of Water
S = Storage Co-efficient for a Confined Aquifer
H = Confined Aquifer Thickness
α = Compressibility of the Aquifer Material
n = Porosity of Aquifer Material
β = Compressibility of Water

Let’s solve an example;
Find the unit weight of water when the storage co-efficient for a confined aquifer is 20, the confined aquifer thickness is 10, the compressibility of the aquifer material is 8, the porosity of aquifer material is 3 and the compressibility of water is 4.

This implies that;

S = Storage Co-efficient for a Confined Aquifer = 20
H = Confined Aquifer Thickness = 10
α = Compressibility of the Aquifer Material = 8
n = Porosity of Aquifer Material = 3
β = Compressibility of Water = 4

γw = S / (a + nβ)H
γw = 20 / (8 + (3 x 4))10
γw = 20 / (8 + 12)10
γw = 20 / (20)10
γw = 20 / 200
γw = 0.1

Therefore, the unit weight of water is 0.1.

Continue reading How to Calculate and Solve for Storage Co-efficient for a Confined Aquifer | Water Budget

How to Calculate and Solve for Discharge Current | Unconfined Aquifer | Water Budget

The image above represents discharge current.

To compute for discharge current, five essential parameters are needed and these parameters are Hydraulic conductivity (k), Elevate from impermeable to surface (H), Depth of water in the well (hw), Radius of influence (R) and Radius of well (γw).

The formula for calculating discharge current:

Q = πk(H² – hw²) / In[R/γw]

Where:

Q = Discharge Current
k = Hydraulic Conductivity
H = Elevate from Impermeable to Surface
hw = Depth of Water in the Well
R = Radius of Influence
γw = Radius of Well

Let’s solve an example;
Find the discharge current when the hydraulic conductivity is 10,the elevate from impermeable to surface is 4, the depth of water in the well is 20, the radius of influence is 5 and the radius of well is 10.

This implies that;

k = Hydraulic Conductivity = 10
H = Elevate from Impermeable to Surface = 4
hw = Depth of Water in the Well = 20
R = Radius of Influence = 5
γw = Radius of Well = 10

Q = πk(H² – hw²) / In[R/γw]
Q = π(10)[(4)² – (20)²] / In[5/10]
Q = 31.415[16 – 400] / In[0.5]
Q = 31.415[-384] / -0.693
Q = -12063.7 / -0.69
Q = 17404.26

Therefore, the discharge current is 17404.26.

Continue reading How to Calculate and Solve for Discharge Current | Unconfined Aquifer | Water Budget

How to Calculate and Solve for Rate | Salt Trace Method | Water Budget

The image above represents rate.

To compute for rate, three essential parameters are needed and these parameters are Rate of injection for salt solution (q), Concentration of salt solution (c1) and Concentration of river downstream (c2).

The formula for calculating rate:

Q = q(c1 – c2)

Where:

Q = Rate
q = Rate of Injection for Salt Solution or Trace
c1 = Concentration of Salt Solution or Trace
c2 = Concentration of River Downstream

Let’s solve an example;
Find the rate when the rate of injection for salt solution is 12, the concentration of salt solution is 20 and the concentration of river downstream is 18.

This implies that;

q = Rate of Injection for Salt Solution or Trace = 12
c1 = Concentration of Salt Solution or Trace = 20
c2 = Concentration of River Downstream = 18

Q = q(c1 – c2)
Q = 12(20 – 18)
Q = 12(2)
Q = 24

Therefore, the rate is 24.

Calculating the Rate of Injection for Salt Solution when the Rate, the Concentration of Salt Solution and the Concentration of River Downstream is Given.

q = Q / (c1 – c2)

Where;

q = Rate of Injection for Salt Solution or Trace
Q = Rate
c1 = Concentration of Salt Solution or Trace
c2 = Concentration of River Downstream

Let’s solve an example;
Find the rate of injection for salt solution when the rate is 40, the concentration of salt solution is 32 and the concentration of river downstream is 14.

This implies that;

Q = Rate = 40
c1 = Concentration of Salt Solution or Trace = 32
c2 = Concentration of River Downstream = 14

q = Q / (c1 – c2)
q = 40 / (32 – 14)
q = 40 / 18
q = 2.2

Therefore, the rate of injection for salt solution is 2.2.

Continue reading How to Calculate and Solve for Rate | Salt Trace Method | Water Budget