# How do I calculate the yield pressure for a Bingham plastic in a tube?

• Peter Hessellund
In summary: Hi ChesterUgh. Most Bingham plastics are typically going to be suspensions. I was thinking of something like drilling mud, which is a suspension of bentonite clay particles. You need to find something that forms a gel, so maybe something with polar molecules with ends that attract. Unfortunately, this is about all that I can help. I don't know much more.
Peter Hessellund
I have three questions.
1. How do I calculate the yield pressure for a Bingham plastic in a tube if I am given:
Length of tube
Diameter of tube
Yield stress of liquid

2. Is it possible to engineer a liquid to have a specific yield stress ?
3. What kind of material would be suited for engineering a specific yield stress? Could it be done with silicon oils or could it be done with additives to water?

Peter Hessellund said:
I have three questions.
1. How do I calculate the yield pressure for a Bingham plastic in a tube if I am given:
Length of tube
Diameter of tube
Yield stress of liquid

2. Is it possible to engineer a liquid to have a specific yield stress ?
3. What kind of material would be suited for engineering a specific yield stress? Could it be done with silicon oils or could it be done with additives to water?
I don't quite understand your first question. Are you asking how much of a pressure difference is required before the bingham plastic begins to flow?

Peter Hessellund
Yes I am asking how much pressure difference is required for flow. I think that I have read somewhere that a larger initial pressure is required for small diameters.

Hi Chester
You already answered the first question for me. I was googeling yield pressure and getting nothing. The right words were the ones you used in your reply to me:)
I still need answers for the two last questions.
The formula is:

Found in this PDF
http://onlinelibrary.wiley.com/doi/10.1002/9780470516430.app7/pdf

Peter Hessellund said:
Hi Chester
You already answered the first question for me. I was googeling yield pressure and getting nothing. The right words were the ones you used in your reply to me:)
I still need answers for the two last questions.
The formula is:
View attachment 110883
Found in this PDF
http://onlinelibrary.wiley.com/doi/10.1002/9780470516430.app7/pdf
Nicely done. For questions 2 and 3, I recommend that you google Bingham plastics and dilatent fluids and see what you come up with.

Hi Chester

I have already been googeling for hours on question 2 and 3 but the only thing that comes up is general stuff about ketchup or specific stuff about solving the governing equations or simulations. I have so far been unable to find a nice catalogue from a supplier producing a liquid with the desired yield stress or a company claiming to be able to make tailor made liquids with the desired properties. I have not been able to find a chemical formulation of a liquid with at attached yield stress number at all. I am looking for a liquid with a yield stress in the range of 150 Pa to 250 Pa with as low a viscosity as possible or maybe even a shear thinning liquid. The liquid can not be a suspension.

Peter Hessellund said:
Hi Chester

I have already been googeling for hours on question 2 and 3 but the only thing that comes up is general stuff about ketchup or specific stuff about solving the governing equations or simulations. I have so far been unable to find a nice catalogue from a supplier producing a liquid with the desired yield stress or a company claiming to be able to make tailor made liquids with the desired properties. I have not been able to find a chemical formulation of a liquid with at attached yield stress number at all. I am looking for a liquid with a yield stress in the range of 150 Pa to 250 Pa with as low a viscosity as possible or maybe even a shear thinning liquid. The liquid can not be a suspension.
Ugh. Most Bingham plastics are typically going to be suspensions. I was thinking of something like drilling mud, which is a suspension of bentonite clay particles. You need to find something that forms a gel, so maybe something with polar molecules with ends that attract. Unfortunately, this is about all that I can help. I don't know much more.

## 1. What is a Bingham plastic?

A Bingham plastic is a type of non-Newtonian fluid that exhibits both solid and liquid-like behavior. It has a yield stress, meaning that it will not flow until a certain amount of force is applied.

## 2. What is yield pressure?

Yield pressure is the amount of pressure required to make a Bingham plastic begin to flow. It is measured in units of pressure, such as pounds per square inch (psi) or pascals (Pa).

## 3. How do I calculate the yield pressure for a Bingham plastic in a tube?

The yield pressure for a Bingham plastic in a tube can be calculated using the formula P = τ0 + μγ, where P is the yield pressure, τ0 is the yield stress, μ is the plastic viscosity, and γ is the shear rate. The shear rate can be calculated by dividing the flow rate by the tube diameter.

## 4. What units should I use for the yield pressure calculation?

The units used for the yield pressure calculation will depend on the units used for the other variables in the formula. It is important to ensure that all units are consistent in order to get an accurate calculation.

## 5. Are there any other factors that may affect the yield pressure calculation?

Yes, there are other factors that may affect the yield pressure calculation, such as the temperature of the Bingham plastic, the size and shape of the tube, and the presence of any additives or impurities in the fluid. These factors may alter the yield stress or plastic viscosity, thus affecting the overall yield pressure calculation.

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