Understanding Viscosity Units: Poiseuille and Poise

Viscosity is a measure of a fluid's resistance to flow. It describes the internal friction of a moving fluid. The question asks about the equivalence between two units of dynamic viscosity: the Poiseuille and the Poise.

The standard SI unit for dynamic viscosity is the pascal-second ($\text{Pa} \cdot \text{s}$). This unit is sometimes referred to as the Poiseuille ($\text{Pl}$).

The CGS unit for dynamic viscosity is the poise ($\text{P}$). One poise is defined as one dyne-second per square centimetre ($\text{dyne} \cdot \text{s}/\text{cm}^2$).

To find the relationship between Poiseuille and poise, we need to convert between the SI and CGS units.

Converting Poiseuille (Pa·s) to Poise (dyne·s/cm²)

We know the definitions of the units:

• $\text{1 Poiseuille} = \text{1 Pa} \cdot \text{s}$
• $\text{1 Poise} = \text{1 dyne} \cdot \text{s}/\text{cm}^2$

Let's convert the Pascal ($\text{Pa}$) unit to the dyne per square centimetre ($\text{dyne}/\text{cm}^2$) unit. A Pascal is defined as one Newton per square metre ($\text{1 Pa} = \text{1 N}/\text{m}^2$).

We need the conversion factors between Newton and dyne, and between metre and centimetre:

• $\text{1 Newton} = \text{10}^5 \text{ dynes}$
• $\text{1 metre} = \text{100 centimetres}$

Now, let's convert $\text{1 Pa}$:

$\text{1 Pa} = \text{1 N}/\text{m}^2$

Substitute the conversion factors:

$\text{1 Pa} = \frac{10^5 \text{ dynes}}{(100 \text{ cm})^2}$

$\text{1 Pa} = \frac{10^5 \text{ dynes}}{10000 \text{ cm}^2}$

$\text{1 Pa} = \frac{10^5}{10^4} \frac{\text{dynes}}{\text{cm}^2}$

$\text{1 Pa} = 10^{5-4} \frac{\text{dynes}}{\text{cm}^2}$

$\text{1 Pa} = 10 \frac{\text{dynes}}{\text{cm}^2}$

So, one Pascal is equivalent to 10 dyne/cm². Now, let's relate this back to the viscosity units:

$\text{1 Poiseuille} = \text{1 Pa} \cdot \text{s}$

Substitute the equivalent for Pascal:

$\text{1 Poiseuille} = \left(10 \frac{\text{dynes}}{\text{cm}^2}\right) \cdot \text{s}$

$\text{1 Poiseuille} = 10 \frac{\text{dynes} \cdot \text{s}}{\text{cm}^2}$

Since $\text{1 Poise} = \text{1 dyne} \cdot \text{s}/\text{cm}^2$, we can see the relationship:

$\text{1 Poiseuille} = 10 \times (\text{1 Poise})$

Therefore, one Poiseuille is equivalent to 10 poise.

Summary of Viscosity Unit Conversion

The conversion shows that 1 Poiseuille is equal to 10 poise.

Revision Table: Key Viscosity Unit Conversions

Additional Information on Dynamic Viscosity

Dynamic viscosity, often denoted by the Greek letter $\mu$ (mu) or $\eta$ (eta), quantifies a fluid's resistance to shear flow. Imagine two parallel layers of fluid moving at different speeds. Dynamic viscosity describes the force per unit area required to maintain a certain velocity gradient between these layers. A higher dynamic viscosity means the fluid is thicker or more resistant to flow.

Understanding dynamic viscosity units is crucial in various fields, including fluid mechanics, chemical engineering, mechanical engineering, and physics. Many standard measurements, especially older ones or those in certain industries, are still reported in poise or centipoise, making the conversion to the standard SI unit (Poiseuille or Pa·s) essential for calculations and comparisons.

Centipoise (cP) is a commonly used unit because the viscosity of water at 20°C is approximately 1 cP, which is a convenient reference point. Since 1 Poise = 100 cP, and 1 Poiseuille = 10 Poise, we also get the relationship 1 Poiseuille = 1000 cP.