In a circular tube of diameter 100 mm and length 15 m with laminar flow, the Darcy friction factor is estimated to be 0.05. Calculate the Reynolds number.
- A900
- B1280Correct
- C2500
- D1000
Solution
Concept
For laminar flow in a circular pipe, the Darcy friction factor depends only on Reynolds number: f = 64/Re.
Formula
f = 64/Re, so Re = 64/f
Step-by-step solution
1. Flow is laminar, so use f = 64/Re. 2. Given f = 0.05. 3. Re = 64/f = 64/0.05. 4. Re = 1280.
Explanation
In laminar pipe flow, the Darcy friction factor is 64/Re. Diameter and length are not needed. Re = 64/0.05 = 1280.
Why the other options are wrong
A (900): gives f = 0.071, not 0.05. C (2500): is above about 2000, so the flow is not laminar, and f would be 0.0256. D (1000): gives f = 0.064, not 0.05.
Shortcut
Re = 64/f directly. Ignore D and L.
Common mistake
Using the Fanning factor relation f = 16/Re gives Re = 320, which is not an option. Some students also try to use the extra data (D, L), which is not needed.
Correct answer: B) 1280