You are trying to calculate the Reynolds Number, not the Reynold number.
Please explain what you mean by writing: “Renold number is < 2,100: laminar flow > 4,200 : turbulent flow”. Your symbology is confusing and it's not clear as to what you are saying.
You state “but it is not possible for Re > 10000. You are wrong; it is very possible for the Reynolds Number to be as great as 10,000 – and even greater! Where do you obtain such an assertion?
Your answer for the Reynolds Number (Re) is correct. To prove this to you, I calculated the Re as follows, in U.S. customary units:
D = 2.06693 inches = 0.172244 ft
v = 4.8546 ft/s
rho = 2.68519 lb/ft-h
mu = 62.36557 lb/ft3
Re = D*v*rho/mu = 69,619
I personally have resolved this very value every time I’ve employed 2” schedule 40 pipe in the past 47 years – and that’ s a lot of times! – and I know that a Re of 70,000 with a velocity of around 5 ft/s is what I would expect for a sound installation for water flowing at 50-60 gpm (which this is).
I don't know what else you may be doing that is wrong, but your Reynolds Number is correct. I suspect your understanding of where the Reynolds Number originates and its use may be strange and not well understood. You need more practice and research into the Reynolds to understand its significance and importance in fluid mechanics - that's what I think will cure your bad feelings about how you are doing your problem calculations. With practice and experience you will learn to have the confidence you need.
Good Luck.