Head Loss in Circular Pipe due to Friction

Given Data:
- Length of the pipe (L) = 800 meters
- Diameter of the pipe (D) = 30 cm
- Velocity of water (V) = 0.26 m/s
- Friction factor (f) = 0.016

Calculating Reynolds Number
Reynolds Number (Re) is a dimensionless quantity that helps determine the flow regime (laminar or turbulent). It is calculated using the formula:

Re = (V * D) / ν

Where:
- V is the velocity of water
- D is the diameter of the pipe
- ν is the kinematic viscosity of water (approximately 1.004 × 10^-6 m^2/s at 20°C)

Given that V = 0.26 m/s and D = 30 cm = 0.3 m, we can calculate the Reynolds number as follows:

Re = (0.26 * 0.3) / (1.004 × 10^-6)
= 773,360.95

Calculating Friction Factor
The friction factor (f) depends on the Reynolds number and the roughness of the pipe's internal surface. In this case, the value of f is given as 0.016.

Calculating Head Loss
The head loss (hL) due to friction is calculated using the Darcy-Weisbach equation:

hL = (f * (L/D) * (V^2) / (2 * g))

Where:
- f is the friction factor
- L is the length of the pipe
- D is the diameter of the pipe
- V is the velocity of water
- g is the acceleration due to gravity (approximately 9.81 m/s^2)

Substituting the given values into the equation, we have:

hL = (0.016 * (800/0.3) * (0.26^2) / (2 * 9.81))
= 3.56 meters

Explanation:
The head loss in a pipe due to friction is the energy loss experienced by the fluid as it flows through the pipe. This loss occurs because of the interaction between the fluid and the internal surface of the pipe, resulting in a pressure drop.

To calculate the head loss, we first determine the Reynolds number to determine the flow regime. In this case, the Reynolds number is high, indicating turbulent flow.

Using the given friction factor and the Darcy-Weisbach equation, we can calculate the head loss. The head loss depends on the length of the pipe, diameter, velocity of water, and friction factor. Finally, we substitute the values into the equation to obtain the head loss due to friction as 3.56 meters.

The head loss is an important parameter in fluid flow analysis as it helps determine the pressure drop and energy dissipation in a pipe network. It is crucial for designing efficient piping systems and ensuring the desired flow conditions are achieved.