Water flows through a 100 m long, 200 mm diameter pipe with a head loss of 4 m. Find the flow rate (Q) using Darcy-Weisbach equation: h f = f L D v 2 2 g hf​=fDL​2gv2​ Assume friction factor f = 0.02 f=0.02, g = 9.81 m / s 2 g=9.81m/s2.

 Problem:

Water flows through a 100 m long, 200 mm diameter pipe with a head loss of 4 m. Find the flow rate (Q) using Darcy-Weisbach equation:

$$h_f = f \frac{L}{D} \frac{v^2}{2g}$$

Assume friction factor $f = 0.02$, $g = 9.81 m/s^2$.

Solution:

1. Velocity (v):

$$v = \sqrt{\frac{2 g h_f D}{f L}} = \sqrt{\frac{2 \cdot 9.81 \cdot 4 \cdot 0.2}{0.02 \cdot 100}}$$ $$v = \sqrt{\frac{15.696}{2}} = \sqrt{7.848} \approx 2.8 m/s$$

2. Flow rate (Q):

$$Q = A \cdot v = \pi \frac{D^2}{4} \cdot v = \pi \frac{0.2^2}{4} \cdot 2.8$$ $$Q = 0.0314 \cdot 2.8 \approx 0.088 m^3/s \approx 88 L/s$$

✅ Answer: Flow rate = 0.088 m³/s (88 L/s)

Label for blog: Fluid Mechanics / Pipe Flow