Final answer:
The friction factor for fluid flow through a pipe can be determined by first calculating the Reynolds number using the velocity, diameter, and kinematic viscosity of the fluid, and then using this value along with the pipe's relative roughness to find the friction factor from a Moody chart or an empirical equation.
Step-by-step explanation:
To determine the friction factor for fluid flow through a pipe, we typically use the Darcy-Weisbach equation, which requires the calculation of Reynolds number and the use of a Moody chart or an appropriate equation for friction factor determination. Given the values, we have a fluid with a kinematic viscosity (ν) of 5 x 10⁻⁶ m²/s, flowing through a pipe with a diameter (D) of 5 cm and a roughness (ε) of 0.1 mm, with an average velocity (V) of 1 m/s. To calculate the Reynolds number (Re), the formula Re = VD/ν is used.
First, we find the Reynolds number for the flow:
- Re = (1 m/s * 0.05 m) / (5 x 10⁻⁶ m²/s) = 10,000
With the Reynolds number calculated, we use the relative roughness (ε/D) and the Reynolds number to find the appropriate friction factor (f) from a Moody chart or using an empirical correlation such as the Colebrook-White equation.
The process involves iteration or the use of a suitable computational tool or approximation to determine the friction factor, which is not directly calculable from the given data alone without a graph or an equation.