Question

What is Hagen – Poiseuille law and why is it important? Show that it is dimensionally

consistent.​

Answer 1

*The Hagen – Poiseuille law*

The Poiseuile law states that the flow(Q) of any liquid depends on many factors such as viscosity (n), the pressure gradient across the tubing (P), and the length (L) and diameter(r) of the tubing.

It is dynamically consistent. Let the dimension of Dynamic viscosity =ML-1T-1 , Volumetric flow=L3T-1 Radius=L and pressure difference=M1L-1T-2.

We know that the equation is equal If both sides of the equation are familiar and satisfy dimensionally then the formula is dimensionally consistent. M1L-1T-2=( ML-1T-1×L× L3T-1)/L4 M1L-1T-2=(MT-2L3)/L4 M1L-1T-2=M1L-1T-2

Since ,R.H.S is equal to L.H.S

Hence proved