Lesson 5.6: Pipe Flow & Losses

Pipe Flow is critical for water supply, hydraulic systems, and process industries. GATE and PSU exams often test flow rate, velocity, pressure drop, and head loss calculations.

🔹 1. Introduction

• Definition: Pipe flow is the movement of fluid through closed conduits.

• Applications: Piping networks, pumps, turbines, industrial fluid transport

• Flow Types:

  1. Laminar Flow: Smooth, orderly layers (Re < 2000)

  2. Turbulent Flow: Chaotic, mixed flow (Re > 4000)

  3. Transitional Flow: 2000 < Re < 4000

🔹 2. Velocity & Flow Rate

• Volumetric Flow Rate:

$$Q=AV$$

Where A = cross-sectional area, V = average velocity

• Mass Flow Rate:

m˙=ρQ\dot{m} = \rho Qm˙=ρQ

• Example: Pipe diameter 0.2 m, average velocity 2 m/s → Q = ?

A=πd2/4=0.0314m2,Q=AV=0.0314∗2≈0.0628m3/sA = \pi d^2 /4 = 0.0314 m^2, \quad Q = A V = 0.0314*2 ≈ 0.0628 m^3/sA=πd2/4=0.0314m2,Q=AV=0.0314∗2≈0.0628m3/s

🔹 3. Head Loss in Pipes

• Major Losses (Friction Loss):

  • Darcy-Weisbach Equation:

hf=fLDV22gh_f = f \frac{L}{D} \frac{V^2}{2g}hf​=fDL​2gV2​

Where f = friction factor, L = pipe length, D = diameter

• Minor Losses (Fittings, Bends, Valves):

hm=KV22gh_m = K \frac{V^2}{2g}hm​=K2gV2​

Where K = loss coefficient

• Example: Pipe 50 m long, diameter 0.1 m, V = 1 m/s, f = 0.02 → major loss:

hf=0.02∗50/0.1∗12/(2∗9.81)≈0.51mh_f = 0.02 * 50/0.1 * 1^2/(2*9.81) ≈ 0.51 mhf​=0.02∗50/0.1∗12/(2∗9.81)≈0.51m

🔹 4. Reynolds Number & Flow Regime

Re=VDνRe = \frac{VD}{\nu}Re=νVD​

• Re < 2000 → Laminar

• Re > 4000 → Turbulent

• 2000–4000 → Transitional

• Friction Factor (f):

  • Laminar: $f=64/Re$

  • Turbulent: Moody chart or empirical equations

🔹 5. Solved Examples (PYQ Style)

Example 1 (GATE ME 2018):
Water flows through 100 m long, 0.15 m diameter pipe, V = 2 m/s, f = 0.02 → calculate major head loss.

Example 2 (PSU Exam):
Determine total head loss for pipe system with 3 bends (K = 0.3 each), length 50 m, diameter 0.1 m, V = 1.5 m/s, f = 0.018.

Example 3:
Classify flow in a pipe with diameter 0.1 m, velocity 1 m/s, ν = 1e-6 m²/s.

🔹 6. Practice Exercises

1. Calculate volumetric and mass flow rate for given pipe and velocity.

2. Determine major and minor head losses for a pipe network.

3. Compute Reynolds number and identify flow type.

4. Use Darcy-Weisbach equation to find friction loss in turbulent flow.

5. Evaluate total energy loss in system with bends, valves, and expansions.

🔹 7. Summary

• Pipe Flow: Closed conduit, steady incompressible flow

• Head Losses: Major (friction) and minor (fittings, bends)

• Flow Regime: Laminar, turbulent, transitional (Reynolds number)

• Applications: Water supply, industrial piping, pumps, turbines