Water flows through a straight smooth pipe at a Reynolds number of 800,000. What is the approximate friction factor?
a. 0.030
b. 0.014 —>
c. 0.012
d. 0.010
The correct answer and explanation is:
The correct answer is a. 0.030.
The friction factor for a flow in a smooth pipe can be determined using the Moody chart, which relates the Reynolds number and the relative roughness of the pipe to the friction factor. For flow in a smooth pipe, the friction factor depends on the Reynolds number. A Reynolds number of 800,000 falls into the turbulent flow region, where the friction factor is primarily determined by the Reynolds number itself rather than the pipe roughness.
In the turbulent flow regime, for smooth pipes (with no significant roughness), the friction factor can be approximated using the following empirical relationship from the Colebrook-White equation: f=0.079×Re−0.25f = 0.079 \times \text{Re}^{-0.25}
Where:
- ff is the friction factor
- Re\text{Re} is the Reynolds number
For Re=800,000\text{Re} = 800,000, we can plug this value into the equation: f=0.079×(800,000)−0.25f = 0.079 \times (800,000)^{-0.25} f≈0.030f \approx 0.030
This matches the value given in option a. 0.030.
The friction factor in the turbulent flow regime decreases as the Reynolds number increases. At high Reynolds numbers, like 800,000, the flow is fully developed, and the friction factor stabilizes and can be predicted accurately by such empirical formulas. This friction factor represents the energy losses due to the viscosity of the fluid and the velocity profile in the pipe.