# How to Calculate and Solve for Standard Permeability of Sand | Solidification of Metals

**Last Updated on May 13, 2024**

The image above represents standard permeability of sand. To calculate standard permeability of sand, five essential parameters are needed and these parameters are **Volume of Area (V), Height of Sand Specimen (H), Pressure (P _{r}), Cross-Sectional Area of Sand Specimen (A) **and

**Time (t).**

**The formula for calculating the standard permeability of sand:**

P = ^{VH} / _{PrAt}

Where:

P = Standard Permeability of Sand

V = Volume of Air

H = Height of Sand Specimen

P_{r} = Pressure

A = Cross-Sectional Area of Sand Specimen

t = Time

Let’s solve an example;

Find the standard permeability of sand when the volume of air is 6, the height of sand specimen is 3, the pressure is 8, the cross-sectional area of sand specimen is 5 and the time is 2.

This implies that;

V = Volume of Air = 6

H = Height of Sand Specimen = 3

P_{r} = Pressure = 8

A = Cross-Sectional Area of Sand Specimen = 5

t = Time = 2

P = ^{VH} / _{PrAt}

That is, P = ^{6 x 3} / _{8 x 5 x 2}

P = ^{18} / _{80}

P = 0.225

Therefore, the **standard permeability of sand **is **0.225.**

Read more: How to Calculate and Solve for Heat Flux | Solidification of Metals

**Calculating the Volume of Air when the Standard Permeability of Sand, the Height of Sand Specimen, the Pressure, the Cross-Sectional Area of Sand Specimen and the Time are Given**

V = ^{P x PrAt} / _{H}

Where:

V = Volume of Air

P = Standard Permeability of Sand

H = Height of Sand Specimen

P_{r} = Pressure

A = Cross-Sectional Area of Sand Specimen

t = Time

Let’s solve an example;

Find the volume of air when the standard permeability of sand is 10, the height of sand specimen is 2, the pressure is 4, the cross-sectional area of sand specimen is 8 and the time is 1.

This implies that;

P = Standard Permeability of Sand = 10

H = Height of Sand Specimen = 2

P_{r} = Pressure = 4

A = Cross-Sectional Area of Sand Specimen = 8

t = Time = 1

V = ^{P x PrAt} / _{H}

So, V = ^{10 x (4)(8)(1)} / _{2}

V = ^{320} / _{2}

V = 160

Therefore, the **volume of air **is **160.**

Read more: How to Calculate and Solve for Volume Shrinkage | Solidification of Metals

**Calculating the Height of Sand Specimen when the Standard Permeability of Sand, the Volume of Air, the Pressure, the Cross-Sectional Area of Sand Specimen and the Time are Given**

H = ^{P x PrAt} / _{V}

Where:

H = Height of Sand Specimen

P = Standard Permeability of Sand

V = Volume of Air

P_{r} = Pressure

A = Cross-Sectional Area of Sand Specimen

t = Time

Let’s solve an example;

Find the height of sand specimen when the standard permeability of sand is 4, the volume of air is 12, the pressure is 6, the cross-sectional area of sand specimen is 3 and the time is 5.

This implies that;

P = Standard Permeability of Sand = 4

V = Volume of Air = 12

P_{r} = Pressure = 6

A = Cross-Sectional Area of Sand Specimen = 3

t = Time = 5

H = ^{P x PrAt} / _{V}

H = ^{4 x (6)(3)(5)} / _{12}

So, H = ^{360} / _{12}

H = 30

Therefore, the **height of sand specimen **is **30.**

**Calculating the Pressure when the Standard Permeability of Sand. the Volume of Air, the Height of Sand Specimen, the Cross-Sectional Area of Sand Specimen and the Time are Given**

P_{r} = ^{VH} / _{P x At}

Where:

P_{r} = Pressure

P = Standard Permeability of Sand

V = Volume of Air

H = Height of Sand Specimen

A = Cross-Sectional Area of Sand Specimen

t = Time

Let’s solve an example;

Find the pressure when the standard permeability of sand is 14, the volume of air is 20, the height of sand specimen is 12, the cross-sectional area of sand specimen is 4 and the time is 3.

This implies that;

P = Standard Permeability of Sand = 14

V = Volume of Air = 20

H = Height of Sand Specimen = 12

A = Cross-Sectional Area of Sand Specimen = 4

t = Time = 3

P_{r} = ^{VH} / _{P x At}

P_{r} = ^{(20)(12)} / _{14 x (4)(3)}

So. P_{r} = ^{240} / _{168}

P_{r} = 1.428

Therefore, the **pressure **is **1.428.**

**Calculating the Cross-Sectional Area of Sand Specimen when the Standard Permeability of Sand, the Volume of Air, the Height of Sand Specimen, the Pressure and the Time are Given**

A = ^{VH} / _{P x Prt}

Where:

A = Cross-Sectional Area of Sand Specimen

P = Standard Permeability of Sand

V = Volume of Air

H = Height of Sand Specimen

P_{r} = Pressure

t = Time

Let’s solve an example;

Find the cross-sectional area of sand specimen when the standard permeability of sand is 15, the volume of air is 32, the height of sand specimen is 20, the pressure is 18 and the time is 10.

This implies that;

P = Standard Permeability of Sand = 15

V = Volume of Air = 32

H = Height of Sand Specimen = 20

P_{r} = Pressure = 18

t = Time = 10

A = ^{VH} / _{P x Prt}

A = ^{(32)(20)} / _{15 x (18)(10)}

Then, A = ^{640} / _{2700}

A = 0.237

Therefore, the **cross-sectional area of sand specimen **is **0.237.**

**Calculating the Time when the Standard Permeability of Sand, the Volume of Air, the Height of Sand Specimen, the Pressure and the Cross-Sectional Area of Sand Specimen are Given**

t = ^{VH} / _{P x PrA}

Where:

t = Time

P = Standard Permeability of Sand

V = Volume of Air

H = Height of Sand Specimen

P_{r} = Pressure

A = Cross-Sectional Area of Sand Specimen

Let’s solve an example;

Find the time when the standard permeability of sand is 10, the volume of air is 24, the height of sand specimen is 9, the pressure is 12 and the cross-sectional area of sand specimen is 2.

This implies that;

P = Standard Permeability of Sand = 10

V = Volume of Air = 24

H = Height of Sand Specimen = 9

P_{r} = Pressure = 12

A = Cross-Sectional Area of Sand Specimen = 2

t = ^{VH} / _{P x PrA}

t = ^{(24)(9)} / _{10 x (12)(2)}

So, t = ^{216} / _{240}

t = 0.9

Therefore, the **time **is **0.9.**

**How to Calculate Standard Permeability of Sand Using Nickzom Calculator**

Nickzom Calculator – **The Calculator Encyclopedia** is capable of calculating the standard permeability of sand.

To get the answer and workings of the standard permeability of sand 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 **Materials and Metallurgical **under **Engineering****.**

Now, Click on **Solidification of Metal **under **Materials and Metallurgical**

Now, Click on **Standard Permeability of Sand **under **Solidification of Metal**

The screenshot below displays the page or activity to enter your values, to get the answer for the standard permeability of sand according to the respective parameter which is the **Volume of Area (V), Height of Sand Specimen (H), Pressure (P _{r}), Cross-Sectional Area of Sand Specimen (A) and Time (t).**

Now, enter the values appropriately and accordingly for the parameters as required by the **Volume of Area (V)** is **6**,** Height of Sand Specimen (H)** is **3**,** Pressure (P _{r})** is

**8**,

**Cross-Sectional Area of Sand Specimen (A)**is

**5**and

**Time (t)**is

**2**.

Finally, Click on Calculate

As you can see from the screenshot above, **Nickzom Calculator**– The Calculator Encyclopedia solves for the standard permeability of sand and presents the formula, workings and steps too.