Question

Which among the following is an assumption of Hagen–Poiseuille equation?

• A. Fluid is uniform
• B. Fluid is laminar
• C. Fluid is turbulent
• D. Fluid is compressible

Hint:

Always check if the flow is laminar (Reynolds number > 2000) before applying the Hagen–Poiseuille equation.

Answer 1

The Correct Option is B

The Hagen–Poiseuille equation describes the pressure drop of a viscous fluid flowing through a long cylindrical pipe. It is applicable under specific assumptions and is used primarily in fluid dynamics and engineering calculations involving laminar flow.
The equation is given as:
\[ Q = \frac{\pi r^4 \Delta P}{8 \mu L} \]
Where:
$Q$ = volumetric flow rate
$r$ = radius of the pipe
$\Delta P$ = pressure difference across the pipe
$\mu$ = dynamic viscosity
$L$ = length of the pipe
Key assumptions of the Hagen–Poiseuille equation include:
- The flow is steady and incompressible
- The fluid is Newtonian
- The pipe is circular and has constant cross-section
- The flow is laminar, not turbulent
Hence, the assumption that is explicitly true among the options is:
Fluid is laminar — making option (2) correct.
Reviewing the incorrect options:
- (1) Fluid is uniform — vague and not a standard assumption in this context
- (3) Fluid is turbulent — violates the fundamental condition; the equation fails under turbulent flow
- (4) Fluid is compressible — the equation assumes incompressibility