The stokes-oseen formula for drag force, f, on a sphere of diameter d in a fluid stream of low velocity, v, density rho and viscosity µ is is this formula dimensionally consistent?

the equation is dimensionally consistent

Explanation:

To verify that the formula is dimensionally consistent, we must verify the two terms of the sum and verify that they are units of force. We achieve this by putting the units of each dimensional term of the equation and verifying that the answer is in units of force

μ=viscosity=Ns/m^2

D=diameter

V=velocity

ρ=density=Kg/m^3π

First term

3πμDV==N

the first term is  dimensionally consistent

second term

(9π/16)ρV^2D^2=

.

as the two terms are in Newtons it means that the equation is dimensionally consistent

air exerts forces on falling objects near earth’s surface.

explanation:

the term 'free falls' refer to object that are falling towards the earth, in a situation in which gravity is the only force acting on the object.

for an object in free fall, the acceleration is constant (g, the gravitational acceleration), and so the velocity of the object constantly increases.

for objects near earth's surface, there is always another force acting on the object: the resistance due to the air. this force is opposed to the direction of fall of the object, and it is proportional to the velocity of the object, so as the object falls down, this force increases up to a point when it balances the force of gravity, and the object continues its motion at constant velocity (called terminal velocity). since in this case gravity is not the only force acting on the object, we are not in a situation of free fall.

causes

fossil fuels burn

cities become more industrialized

human population grows worldwide