Physics Help (Calculating Drag from pressure and Viscosity)

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Some Context:
I study Computing in Games Development and for one of my assignments I have to write a program to simulate a little physics. Assuming the object is a sphere you enter its: Starting Position,
Starting Velocity,
Acceleration,
mass,
radius,
Density and Viscosity of fluid its passing through,
and the program hammers out the location of the object against time.

I'm a little stuck on calculating the drag of the object.
In my notes it says that "Force of Drag = Drag Viscosity + Drag Pressure"

Which breaks down into:
Drag Viscosity = C1*radius*Velocity;
Drag Pressure = C2*radius^2*VelocityMagnitude*Velocity;

I understand most of it, except C1 and C2.

I figure they must be a variation of the coefficient of drag or something but I've no idea how to calculate them. Everything I've found calculates the coefficient of drag once you know the force of drag, but I don't know what my force of drag will be.

Can I calculate them using Reynolds Number ?

Assuming they are some variation of the coefficient of drag, why would they be different for Viscosity and Pressure?

I know this area of physics is very broad and complicated so getting assistance may be unlikely. But any help would be really appreciated. I've scoured the internet but the only help I've gotten is a drag formula stating : CD * 0.5 * rho * v^2 * A;

Since this formula doesn't take into account Viscosity I don't think I can use it.
Am I being really dumb and overlooking something ?

Thanks again on any help.