Alexander Fufaev

Formula: Poiseuille's Equation

Pipe with Fluid and a Volumetric Flow Rate

Volumetric Flow Rate

Unit
Volumetric Flow Rate (Volume velocity) is the volume of a fluid (e.g. water) that passes through a cross-sectional area of a pipe per second. The volume flow is due to a pressure difference \( \Delta \mathit{\Pi} = \mathit{\Pi}_1 - \mathit{\Pi}_2 \) between the ends of the pipe.

Length

Unit
Length of a pipe through which a fluid moves.

Dynamic viscosity

Unit
Viscosity \( \eta \) (pronounced: Eta) is a property of a fluid (liquid or gas) and describes how difficult it is to move a body through this fluid.

Liquid Viscosity \( \eta \)
Olive oil\( 108 \cdot 10^{-3} \, \frac{\mathrm{kg}}{ \mathrm{m}\cdot \mathrm{s} } \)
Honey\( 10\,000 \cdot 10^{-3} \, \frac{\mathrm{kg}}{ \mathrm{m}\cdot \mathrm{s} } \)
Glycerin\( 1500 \cdot 10^{-3} \, \frac{\mathrm{kg}}{ \mathrm{m}\cdot \mathrm{s} } \)
Water\( 1.008 \cdot 10^{-3} \, \frac{\mathrm{kg}}{ \mathrm{m}\cdot \mathrm{s} } \)
Tar\( 100\,000 \cdot 10^{-3} \, \frac{\mathrm{kg}}{ \mathrm{m}\cdot \mathrm{s} } \)
Viscosity of some liquids.

Radius

Unit
Radius of the pipe through which a fluid moves. If you double the radius, then the flow rate becomes 16 times larger!

Pressure at one end

Unit
Pressure at one end of the pipe. \(\Pi\) is pronounced as "Pi".

Pressure at the other end

Unit
Pressure at the other end of the pipe.