Drag force
 

Hi :D

I'm new in fluid mechanics so i hope you help me

Drag=0.5*row*C*A*V^n

the value of n = 1 or 2

what n value depending on ?? is the value of Reynolds number or what !!

and an small another question what is the viscosity value of air in SI units ??

Thanks all

Just by dimensional arguments n must be 2. Newton=kg/m^3*m^2*(m/sec)^2=kg*m/sec^2, while C is dimensionless.

C itself depends on reynolds number Re.

For big reynolds numbers Re>>1 dependence of C on Re is weak, that is why we choose this form of writing down the drag force with quadratic dependence on velocity.

For Re<<1 (stokes flow), the drag is lineraly dependent on velocity (you might think that n is still 2, but C is inversely proportional to Re in such cases).

I am sorry I didn't get it
I am new in fluid :D

n=2 and it is 2 in all time never changes

but what you meant by c is depending on Re

is c function of Re ??

or for the same object c1 constant in laminar flow ,c2 constant in turbulent

flow , c1 not equal c2 and the type of flow depending on Re ??

Yes C is a function of Re, i.e. C=C(Re). It is not a constant and it is generally a difficult problem to find dependence C(Re) for a given object. It is one of central problems of fluid mechanics and CFD.

For instance, for a laminar flow past flat plate C=const/sqrt(Re). The above example of laminar flow past flat plate is one of rare cases when you can get C(Re) analytically. In majority of cases, for objects of different shape, you should use numeric methods.

n is always 2, as you can see from dimensional arguments. The reason why sometimes people writes that n can be 1 is a case of stokes flow (very slow and viscous, so that Re is much less than 1). In such cases Drag is proportional to 1st power of velocity, but instead area in the Drag equation one should use characteristic size of the object. E.g drag for a small and vey sloooow spere is

Drag = 6*Pi*mu*r*v,

where r is the radius of spere. Note that in the last case n=1, but you have linear size r instead of area in this equation. You can rewrite it as

Drag = 6*Pi*mu*r*v = 6*Pi*mu*r*v *(r *v) /(r*v) = .5*C*rho*A*v^2

where A=Pi*r^2, ans C=12*Pi*mu/(rho*r*v)=12/Re,

so you get standard equation with n=2 in the cas of stokes flow too but this time C(Re)=12/Re (this is for a sphere only since function C(Re) is different for different shapes)