In the world of fluid mechanics and engineering, accurately defining a fluid’s resistance to flow—its viscosity—is critical. This property determines everything from the pump size needed for a pipeline to the lubricating quality of an engine oil. However, a common point of confusion arises when translating values between the metric system (CGS and SI) and the imperial (US Customary) system. A specific and frequently encountered conversion is that 41.5 decipoise (dP) is equivalent to 1 pound per foot per second (lb/(ft·s)).
This article will explain the significance of this conversion, break down the units involved, and provide a clear understanding of why this specific value is so important for engineers and technicians.
Decipoise vs. Pound per Foot per Second
To grasp the conversion, we must first understand what each unit represents.
What is a Decipoise (dP)?
- Poise (P): The poise is the unit of dynamic viscosity in the centimeter-gram-second (CGS) system of units. It is named after the French physician Jean Léonard Marie Poiseuille. One poise is defined as 1 gram per centimeter per second (1 g/(cm·s)).
- Decipoise (dP): The deci- prefix means one-tenth. Therefore, 1 decipoise = 0.1 poise or 0.1 g/(cm·s). The decipoise is a convenient unit because the viscosity of water at room temperature (20°C) is approximately 1 centipoise (cP), which is equal to 0.01 P or 0.1 dP. The centipoise is more common, but both are used in industrial contexts.
What is Pound per Foot per Second (lb/(ft·s))?
- This is the unit of dynamic viscosity in the US Customary or imperial system.
- It is defined as 1 pound of force per foot of length per second of time.
- It directly describes the tangential force per unit area (shear stress) required to move one fluid layer relative to another at a certain velocity gradient.
The Conversion Process: From Decipoise to lb/(ft·s)
The conversion is not a arbitrary number; it is derived from the fundamental relationships between units of mass, length, and force in the two systems.
The base equivalence is:
1 Poise (P) = 1 g/(cm·s)
We need to convert this into lb/(ft·s). This involves converting grams to pounds and centimeters to feet.
- Convert mass (grams to pounds): 1 lb = 453.59237 g Therefore, 1 g = 1 / 453.59237 lb
- Convert length (centimeters to feet): 1 ft = 30.48 cm Therefore, 1 cm = 1 / 30.48 ft
- Apply the conversions to the poise unit:
1 P = 1 g/(cm·s) = (1 / 453.59237 lb) / ((1 / 30.48 ft) · s) - Simplify the expression:
= (1 / 453.59237) * (30.48 / 1) lb/(ft·s)
≈ (0.00220462) * (30.48) lb/(ft·s)
≈ 0.0671969 lb/(ft·s)
So, 1 Poise (P) ≈ 0.0672 lb/(ft·s)
- Convert Poise to Decipoise:
Since 1 dP = 0.1 P, we can find the value for one decipoise.
1 dP = 0.1 * 0.0671969 lb/(ft·s) ≈ 0.00671969 lb/(ft·s) - Find the Inverse:
The question asks for the imperial equivalent of 41.5 dP. To find how many decipoise equal one imperial unit, we take the inverse of the factor we just found.
1 lb/(ft·s) = 1 / 0.00671969 dP ≈ 148.816 dP
Wait, that doesn’t match. This is a common point of confusion. The standard, accepted conversion factor is based on the exact definitions used in engineering standards.
The exact conversion factor is:
1 lb/(ft·s) = 478.8026 Poise
Therefore, to find out how many decipoise are in 1 lb/(ft·s), we remember that 1 Poise = 10 Decipoise.
So, 1 lb/(ft·s) = 478.8026 * 10 = 4788.026 Decipoise
Again, this seems off. Let’s use the direct and simplest method:
The standard, textbook conversion is:
1 lb/(ft·s) = 14.8816 Poise
And since 1 Poise = 10 Decipoise:
1 lb/(ft·s) = 14.8816 * 10 = 148.816 Decipoise
Now, to find the value that equals 1 lb/(ft·s), we take the inverse:
If 1 lb/(ft·s) = 148.816 dP, then:
X dP = 1 lb/(ft·s) and X = 148.816
However, the precise, commonly cited value is 1 lb/(ft·s) = 148.816 decipoise. Therefore, the inverse is also true:
148.816 decipoise = 1 lb/(ft·s)
The value 41.5 is likely a misstatement or a mishearing of a related conversion (e.g., for kinematic viscosity). The correct, round-figure equivalence often used for quick estimation is:
150 decipoise ≈ 1 lb/(ft·s)
But the precise conversion is:
1 lb/(ft·s) = 148.816 decipoise
So, the imperial equivalent of 148.816 decipoise is 1 pound per foot per second.
Practical Application and Importance
Why is this conversion crucial?
- Global Collaboration: Engineering projects often involve international teams. A viscosity specification on a technical data sheet from a European manufacturer might be in centipoise or millipascal-seconds (mPa·s), while an American engineer may need the value in lb/(ft·s) to use with imperial-based formulas or software.
- Legacy Systems: Many older plants, particularly in the United States, have machinery, piping, and pump specifications that were designed using imperial units. Maintaining and troubleshooting these systems requires fluid property conversions.
- Data Sheet Interpretation: Accurately converting viscosity values is essential for selecting the right fluid for a specific application, ensuring proper lubrication, heat transfer, and flow behavior.
Quick Reference Conversion Table
For practicality, here is a quick reference table for dynamic viscosity conversions:
| Unit | Poise (P) | Decipoise (dP) | lb/(ft·s) | Pascal-second (Pa·s) |
|---|---|---|---|---|
| 1 Poise (P) | 1 | 10 | 0.0672 | 0.1 |
| 1 Decipoise (dP) | 0.1 | 1 | 0.00672 | 0.01 |
| 1 lb/(ft·s) | 14.8816 | 148.816 | 1 | 1.48816 |
| 1 Pascal-second (Pa·s) | 10 | 100 | 0.672 | 1 |
Note: 1 Centipoise (cP) = 0.01 P = 0.1 dP.
Conclusion
While the precise statement “41.5 decipoise is pound per foot per second” is incorrect, it points to a very real and important need in engineering: unit conversion for dynamic viscosity. The correct and standard equivalence is that 148.816 decipoise is equal to 1 pound per foot per second.