How to Calculate and Solve for Total Head | Hydrology II

The image above represents total head. To calculate total head, three essential parameters are needed and these parameters are Elevation above the Choosen Datum (z), Unit Weight of Water (γ_w) and Total Pressure (μ).

The formula for calculating total head:

h = z + ^μ / _γw

Where:

h = Total Head
z = Elevation above the Choosen Datum
μ = Unit Weight of Water
γ_w = Total Pressure

Let’s solve an example;
Find the total head when the elevation above the choosen datum is 14, unit weight of water is 21 and the total pressure is 10.

This implies that;

z = Elevation above the Choosen Datum = 14
μ = Unit Weight of Water = 21
γ_w = Total Pressure = 10

h = z + ^μ / _γw
That is, h = 14 + ¹⁰ / ₂₁
h = 14 + 0.47
h = 14.47

Therefore, the total head is 14.47.

Calculating for the Elevation above the Choosen Datum when the Total Head, the Unit Weight of Water and the Total Pressure are Given

z = h – ^μ / _γw

Where;

z = Elevation above the Choosen Datum
h = Total Head
μ = Unit Weight of Water
γ_w = Total Pressure

Let’s solve an example;
Find the elevation above the choosen datum when the total head is 32, the unit weight of water is 12 and the total pressure is 6.

This implies that;

h = Total Head = 32
μ = Unit Weight of Water = 12
γ_w = Total Pressure = 6

z = h – ^μ / _γw
z = 32 – ¹² / ₆
Then, z = 32 – 2
z = 30

Therefore, the elevation above the choosen datum is 30.

Read more: How to Calculate and Solve for Permeability | Hydrology II

Calculating for the Unit Weight of Water when the Total Head, the Elevation above the Choosen Datum and the Total Pressure are Given

μ = (h – z) γ_w

Where;

μ = Unit Weight of Water
h = Total Head
z = Elevation above the Choosen Datum
γ_w = Total Pressure

Let’s solve an example;
Find the unit weight of water when the total head is 40, the elevation above the choosen datum is 10 and the total pressure is 5.

This implies that;

h = Total Head = 40
z = Elevation above the Choosen Datum = 10
γ_w = Total Pressure = 5

μ = (h – z) γ_w
μ = (40 – 10) 5
So, μ = (30) 5
μ = 150

Therefore, the unit weight of water is 150.

Calculating for the Total Pressure when the Total Head, the Elevation above the Choosen Datum and the Unit weight of Water are Given

γ_w  = ^μ / _{(h – z)}

Where;

γ_w = Total Pressure
h = Total Head
z = Elevation above the Choosen Datum
μ = Unit Weight of Water

Let’s solve an example;
Find the total pressure when the total head is 36, the elevation above the choosen datum is 12 and the unit weight of water is 60.

This implies that;

h = Total Head = 36
z = Elevation above the Choosen Datum = 12
μ = Unit Weight of Water = 60

γ_w  = ^μ / _{(h – z)}
Then, γ_w  = ⁶⁰ / _{(36 – 12)}
γ_w  = ⁶⁰ / ₂₄
γ_w  = 2.5

Therefore, the total pressure is 2.5.

How to Calculate Total Head in Hydrology Using Nickzom Calculator

Nickzom Calculator – The Calculator Encyclopedia is capable of calculating the total head.

To get the answer and workings of the total head using the Nickzom Calculator – The Calculator Encyclopedia. First, you need to obtain the app.

You can get this app via any of these means:

Web – https://www.nickzom.org/calculator-plus

To get access to the professional version via web, you need to register and subscribe for NGN 2,000 per annum to have utter access to all functionalities.
You can also try the demo version via https://www.nickzom.org/calculator

Android (Paid) – https://play.google.com/store/apps/details?id=org.nickzom.nickzomcalculator
Android (Free) – https://play.google.com/store/apps/details?id=com.nickzom.nickzomcalculator
Apple (Paid) – https://itunes.apple.com/us/app/nickzom-calculator/id1331162702?mt=8
Once, you have obtained the calculator encyclopedia app, proceed to the Calculator Map, then click on Agricultural under Engineering.

Now, Click on Hydrology II under Agricultural

Now, Click on Total Head under Hydrology II

The screenshot below displays the page or activity to enter your values, to get the answer for the total head according to the respective parameters which is the Elevation above the Choosen Datum (z), Unit Weight of Water (γ_w) and Total Pressure (μ).

Now, enter the values appropriately and accordingly for the parameters as required by the Elevation above the Choosen Datum (z) is 14, Unit Weight of Water (γ_w) is 21 and Total Pressure (μ) is 10.

Finally, Click on Calculate

As you can see from the screenshot above, Nickzom Calculator– The Calculator Encyclopedia solves for the total head and presents the formula, workings and steps too.