How to Calculate Porosity
Extract useful values from the given information., Set up the appropriate equation., Find values for your volume variables., Plug your known volume variables into the porosity equation., Solve the equation to obtain a porosity value.
Step-by-Step Guide
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Step 1: Extract useful values from the given information.
When calculating porosity theoretically, you will be given an example situation that contains some of the values you need.
Read your question carefully and look for values such as total volume (Vt{\displaystyle Vt}), solid volume (Vs{\displaystyle Vs}), and pore volume (Vp{\displaystyle Vp}).
Always pay close attention to the units of these values.
It will help to write these values out separately.
For example, if your question provides Vt{\displaystyle Vt} and Vs{\displaystyle Vs}, you would write:
Vt{\displaystyle Vt} =
5.00 cm^3 Vs{\displaystyle Vs} =
3.00 cm^3 -
Step 2: Set up the appropriate equation.
By definition, porosity (Pt{\displaystyle Pt}) is equal to the pore volume (Vp{\displaystyle Vp}) divided by the total volume (Vt{\displaystyle Vt}), or Pt{\displaystyle Pt} = Vp{\displaystyle Vp}/Vt{\displaystyle Vt}.
Keep in mind that this is not the only equation that can find porosity.
If values are given for bulk density and particle density rather than values for volumes, you should use a different equation., It is helpful to keep in mind that Vt{\displaystyle Vt} is the sum of solid and pore volumes, or Vt{\displaystyle Vt} = Vs{\displaystyle Vs} + Vp{\displaystyle Vp}.
This relationship can be rearranged to allow you to solve for the any of the volume variables, as long as the other two are known.
For example, and Vt{\displaystyle Vt}
- Vp{\displaystyle Vp} = Vs{\displaystyle Vs}.Using the same values as listed in previous steps, Vt{\displaystyle Vt} =
5.00 cm^3 and Vs{\displaystyle Vs} =
3.00 cm^3, we can solve Vt{\displaystyle Vt}
- Vs{\displaystyle Vs} = Vp{\displaystyle Vp} to find that Vp{\displaystyle Vp} =
5.00 cm^3
-
3.00 cm^3 =
2.00 cm^3. , Once you have determined a value for Vp{\displaystyle Vp} and a value for Vt{\displaystyle Vt}, you can plug them into the porosity equation, Pt{\displaystyle Pt} = Vp{\displaystyle Vp}/Vt{\displaystyle Vt}.
Be sure that you include units for Vp{\displaystyle Vp} and Vt{\displaystyle Vt}.
Also, you should be sure that the units match, if not, you will need to do dimensional analysis to make them match. , Now that your equation is totally set up and has the appropriate values in place, you can solve by doing simple arithmetic.
It might help to have a calculator handy for this part.
You should also note that the units for Vt{\displaystyle Vt} and Vp{\displaystyle Vp} are the same and cancel out by division.
This is exactly what you want to happen since porosity is a unitless value.Since porosity is often expressed as a percent, once you have found the decimal value, it is common to multiply this value by 100%.
Using the same values from the above examples, your equation will look similar to this:
Pt{\displaystyle Pt} =
2.00 cm^3 /
5.00 cm^3 =
0.400.
If you would like to express that value as a percent, you would multiply it by 100% to yield Pt{\displaystyle Pt} = 40%. -
Step 3: Find values for your volume variables.
-
Step 4: Plug your known volume variables into the porosity equation.
-
Step 5: Solve the equation to obtain a porosity value.
Detailed Guide
When calculating porosity theoretically, you will be given an example situation that contains some of the values you need.
Read your question carefully and look for values such as total volume (Vt{\displaystyle Vt}), solid volume (Vs{\displaystyle Vs}), and pore volume (Vp{\displaystyle Vp}).
Always pay close attention to the units of these values.
It will help to write these values out separately.
For example, if your question provides Vt{\displaystyle Vt} and Vs{\displaystyle Vs}, you would write:
Vt{\displaystyle Vt} =
5.00 cm^3 Vs{\displaystyle Vs} =
3.00 cm^3
By definition, porosity (Pt{\displaystyle Pt}) is equal to the pore volume (Vp{\displaystyle Vp}) divided by the total volume (Vt{\displaystyle Vt}), or Pt{\displaystyle Pt} = Vp{\displaystyle Vp}/Vt{\displaystyle Vt}.
Keep in mind that this is not the only equation that can find porosity.
If values are given for bulk density and particle density rather than values for volumes, you should use a different equation., It is helpful to keep in mind that Vt{\displaystyle Vt} is the sum of solid and pore volumes, or Vt{\displaystyle Vt} = Vs{\displaystyle Vs} + Vp{\displaystyle Vp}.
This relationship can be rearranged to allow you to solve for the any of the volume variables, as long as the other two are known.
For example, and Vt{\displaystyle Vt}
- Vp{\displaystyle Vp} = Vs{\displaystyle Vs}.Using the same values as listed in previous steps, Vt{\displaystyle Vt} =
5.00 cm^3 and Vs{\displaystyle Vs} =
3.00 cm^3, we can solve Vt{\displaystyle Vt}
- Vs{\displaystyle Vs} = Vp{\displaystyle Vp} to find that Vp{\displaystyle Vp} =
5.00 cm^3
-
3.00 cm^3 =
2.00 cm^3. , Once you have determined a value for Vp{\displaystyle Vp} and a value for Vt{\displaystyle Vt}, you can plug them into the porosity equation, Pt{\displaystyle Pt} = Vp{\displaystyle Vp}/Vt{\displaystyle Vt}.
Be sure that you include units for Vp{\displaystyle Vp} and Vt{\displaystyle Vt}.
Also, you should be sure that the units match, if not, you will need to do dimensional analysis to make them match. , Now that your equation is totally set up and has the appropriate values in place, you can solve by doing simple arithmetic.
It might help to have a calculator handy for this part.
You should also note that the units for Vt{\displaystyle Vt} and Vp{\displaystyle Vp} are the same and cancel out by division.
This is exactly what you want to happen since porosity is a unitless value.Since porosity is often expressed as a percent, once you have found the decimal value, it is common to multiply this value by 100%.
Using the same values from the above examples, your equation will look similar to this:
Pt{\displaystyle Pt} =
2.00 cm^3 /
5.00 cm^3 =
0.400.
If you would like to express that value as a percent, you would multiply it by 100% to yield Pt{\displaystyle Pt} = 40%.
About the Author
Jose Young
With a background in education and learning, Jose Young brings 9 years of hands-on experience to every article. Jose believes in making complex topics accessible to everyone.
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