**Friction Loss Calculation in Cast Iron Pipe**

To calculate the friction loss in a cast iron (CI) pipe, we can use the Darcy-Weisbach equation, which relates the friction loss to the pipe diameter, discharge, distance, roughness coefficient, and viscosity.

The Darcy-Weisbach equation is given by:

𝑓 = (𝑓𝑟𝑖𝑐𝑡𝑖𝑜𝑛 𝑓𝑎𝑐𝑡𝑜𝑟 × 𝐿 × 𝑉^2) / (2 × 𝑔 × 𝐷)

Where:
- 𝑓 is the friction factor
- 𝑓𝑟𝑖𝑐𝑡𝑖𝑜𝑛 𝑓𝑎𝑐𝑡𝑜𝑟 is the friction factor based on the flow regime (laminar or turbulent)
- 𝐿 is the length of the pipe (1000 m in this case)
- 𝑉 is the velocity of flow (discharge divided by pipe cross-sectional area)
- 𝑔 is the acceleration due to gravity (9.81 m/s^2)
- 𝐷 is the diameter of the pipe (300 mm)

**Determining the Flow Regime:**

To determine the flow regime, we can use the Reynolds number (Re), which is given by:

𝑅𝑒 = (𝑉 × 𝐷) / 𝑣

Where:
- 𝑣 is the kinematic viscosity (viscosity divided by density)

For laminar flow, Re < 2000,="" and="" for="" turbulent="" flow,="" re="" /> 4000. Between 2000 and 4000, the flow is transitional, and we need to use a different friction factor calculation.

**Calculating the Velocity:**

The velocity (V) can be calculated by dividing the discharge by the cross-sectional area of the pipe. The cross-sectional area (A) is given by:

𝐴 = 𝜋 × (𝐷/2)^2

**Calculating the Friction Factor:**

For turbulent flow, we can use the Colebrook-White equation to calculate the friction factor:

1 / √𝑓 = -2 × log10((𝑘/3.7) + (2.51 / (𝑅𝑒 × √𝑓)))

Where:
- 𝑘 is the roughness coefficient (0.25 mm)
- 𝑅𝑒 is the Reynolds number
- 𝑓 is the friction factor (to be solved iteratively)

For laminar flow, the friction factor can be calculated using:

𝑓 = 16 / 𝑅𝑒

**Calculating the Friction Loss:**

Once we have the friction factor, we can calculate the friction loss using the Darcy-Weisbach equation mentioned earlier.

𝑓 = (𝑓𝑟𝑖𝑐𝑡𝑖𝑜𝑛 𝑓𝑎𝑐𝑡𝑜𝑟 × 𝐿 × 𝑉^2) / (2 × 𝑔 × 𝐷)

Substituting the values, we can calculate the friction loss in the cast iron pipe