# How to Calculate and Solve for Knudsen Diffusion of Moulding Sand | Mass Transfer

**Last Updated on August 1, 2021**

The image above represents knudsen diffusion of moulding sand.

To compute for knudsen diffusion of moulding sand, three essential parameters are needed and these parameters are **Pore Radius (r), Temperature (T) **and **Molecular Weight (M).**

The formula for calculating knudsen diffusion of moulding sand:

D_{k} = 9700r√(^{T}/_{M})

Where:

D_{k} = Knudsen Diffusion of Moulding Sand

r = Pore Radius

T = Temperature

M = Molecular Weight

Let’s solve an example;

Find the knudsen diffusion of moulding sand when the pore radius is 24, the temperature is 18 and the molecular weight is 12.

This implies that;

r = Pore Radius = 24

T = Temperature = 18

M = Molecular Weight = 12

D_{k} = 9700r√(^{T}/_{M})

D_{k} = 9700(24)√(^{18}/_{12})

D_{k} = 9700(24)√(1.5)

D_{k} = 9700(24)(1.22)

D_{k} = 285120.6

Therefore, the **knudsen diffusion of moulding sand** is **285120.6 cm²/s.**

**Calculating the Pore Radius when the Knudsen Diffusion of Moulding Sand, the Temperature and the Molecular Weight is Given.**

r = ^{Dk} / _{9700 √(T / M)}

Where:

r = Pore Radius

D_{k} = Knudsen Diffusion of Moulding Sand

T = Temperature

M = Molecular Weight

Let’s solve an example;

Find the pore radius when the knudsen diffusion of moulding sand is 20, the temperature is 14 and the molecular weight is 10.

This implies that;

D_{k} = Knudsen Diffusion of Moulding Sand = 20

T = Temperature = 14

M = Molecular Weight = 10

r = ^{Dk} / _{9700 √(T / M)}

r = ^{20} / _{9700 √(14 / 10)}

r = ^{20} / _{9700 √(1.4)}

r = ^{20} / _{11446}

r = 0.00174

Therefore, the **pore radius **is **0.00174.**

**Calculating the Temperature when the Knudsen Diffusion of Moulding Sand, the Pore Radius and the Molecular Weight is Given.**

T = M x (^{Dk} / _{9700r})^{2}

Where:

T = Temperature

D_{k} = Knudsen Diffusion of Moulding Sand

r = Pore Radius

M = Molecular Weight

Let’s solve an example;

Find the temperature when the knudsen diffusion of moulding sand is 2700, the pore radius is 6 and the molecular weight is 14.

This implies that;

D_{k} = Knudsen Diffusion of Moulding Sand = 2700

r = Pore Radius = 6

M = Molecular Weight = 14

T = M x (^{Dk} / _{9700r})^{2}

T = 14 x (^{2700} / _{9700(6)})^{2}

T = 14 x (^{2700} / _{58200})^{2}

T = 14 x (0.046)^{2}

T = 14 x 0.002116

T = 0.0296

Therefore, the **temperature **is **0.0296 s.**

**Calculating the Molecular Weight when the Knudsen Diffusion of Moulding Sand, the Temperature and the Pore Radius is Given.**

M = ^{T} / (^{Dk} / _{9700r})^{2}

Where:

M = Molecular Weight

D_{k} = Knudsen Diffusion of Moulding Sand

r = Pore Radius

T = Temperature

Let’s solve an example;

Find the molecular weight when the knudsen diffusion of moulding sand is 3000, the pore radius is 8 and the temperature is 4.

This implies that;

D_{k} = Knudsen Diffusion of Moulding Sand = 3000

r = Pore Radius = 8

T = Temperature = 4

M = ^{T} / (^{Dk} / _{9700r})^{2}

M = ^{4} / (^{3000} / _{9700(8)})^{2}

M = ^{4} / (^{3000} / _{77600})^{2}

M = ^{4} / _{0.00148}

M = 2702.7

Therefore, the **molecular weight **is **2702.7 cm.**

Nickzom Calculator – **The Calculator Encyclopedia** is capable of calculating the knudsen diffusion of moulding sand.

To get the answer and workings of the knudsen diffusion of moulding 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 **Mass Transport **under **Materials and Metallurgical**

Now, Click on **Knudsen Diffusion of Moulding Sand **under **Mass Transport**

The screenshot below displays the page or activity to enter your values, to get the answer for the knudsen diffusion of moulding sand according to the respective parameter which is the **Pore Radius (r), Temperature (T) **and **Molecular Weight (M).**

Now, enter the values appropriately and accordingly for the parameters as required by the **Pore Radius (r)** is **24**,** Temperature (T)** is **18 **and **Molecular Weight (M)** is **12**.

Finally, Click on Calculate

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