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

a solenoid is created by wrapping a l = 90 m long wire around a hollow tube of diameter d = 4.5 cm.   the wire diameter is d = 0.9 mm.   the solenoid wire is then connected to a power supply so that a current of i = 9 a flows through the wire.

randomized variablesl = 90 m

d = 4.5 cm

d = 0.9 mm

i = 9 a                                          

write an expression for the number of turns, n, in the solenoid. you do not need to take into account the diameter of the wire in this calculation.

calculate the number of turns, n, in the solenoid.

write an expression for the length of the solenoid (l2) in terms of the diameter of the hollow tube d.

calculate the length of the solenoid (l2)   in meters.

calculate the magnitude of the magnetic field at the center of the solenoid in teslas.

explanation:

e

explanation:

there is no change in the electric potential energy as it is in rest on both conditions.