Question

If there was a small sphere freely suspended in plane poiseuille flow, how would you go about using linearity to prove that the sphere will not migrate?

Answer 1

Answer Explanation :

Poiseuille equation: this equation is used for non ideal flow this is used for the calculation of pressure in laminar flow it is physical law we know that fluid in laminar flow, flows across the pipe whose diameter is larger than the length of pipe

in mathematical form the equation can be expressed as

Q = $\frac{(P_2-P_1) r^{4}\times \pi}{8\times\eta \times l }$

where η is the cofficient of viscosity

now if we assume a small sphere of radius a is suspended freely in the plane of the laminar flow then for assuring that the sphere does not migrate with the flow we have to calculate the rate of flow of the liquid