Question

check the validity of the two equations... if u give the right answer.. I will give u 100 thanks​

Answer 1

Answer: First one valis but the second one is not valid.

Explanation:

First part:

The first equation is F = 6πηrv

this is valid and dimensionally correct. This is actually viscous force by Stokes law.

F is the force of viscosity known as Stokes' drag on a small sphere moving through a viscous fluid and η is the dynamic viscosity, r is the radius of the spherical object, v is the flow velocity relative to the object.

Dimension of 6πηrv is actually the dimension of ηrv which is given by,

[η][r][v]= [ML⁻¹T⁻¹] [L] [LT⁻¹] = [ MLT⁻²]; which is exactly same as the dimension of force.

so the first equation is valid.

Second part:

But the second equation is not dimensionally correct:

p = Fv + ρΑ³v

because p is pressure, its dimension is equivalent to force / area, i.e. [MLT⁻² / L²] = [ML⁻¹T⁻²]

But F v = force x velocity has dimension [MLT⁻² LT⁻¹] = [ML²T⁻³].

and the term ρΑ³v has dimension [ML⁻³ L⁶ LT⁻¹] = [ML⁴T⁻¹].

So this equation is not dimensionally correct. it is not valid.