Flow Through Pipes free study notes for Diploma / BTech.

1. Introduction

Flow through pipes deals with the movement of fluids (liquids or gases) inside closed conduits. It is a fundamental topic in fluid mechanics, widely applied in water supply systems, oil pipelines, HVAC systems, and industrial processes.

Pipes usually run completely full, and the flow is driven by pressure differences.

2. Types of Flow in Pipes

(a) Laminar Flow

• Fluid particles move in smooth, parallel layers.
• No mixing between layers.
• Occurs at low velocities.

Condition:$$Re < 2000$$Re<2000

(b) Turbulent Flow

• Irregular motion with eddies and mixing.
• High energy losses.

Condition:$$Re > 4000$$Re>4000

(c) Transitional Flow

• Between laminar and turbulent flow.

$$2000 < Re < 4000$$2000<Re<4000

3. Reynolds Number

It determines the type of flow:$$Re = \frac{\rho V D}{\mu}$$Re=μρVD​

Where:

• $\rho$ρ = Density of fluid
• $V$V = Velocity
• $D$D = Diameter of pipe
• $\mu$μ = Dynamic viscosity

4. Velocity Distribution in Pipes

Laminar Flow

• Parabolic velocity profile
• Maximum velocity at center
• Zero velocity at walls (due to no-slip condition)

Turbulent Flow

• Flatter velocity profile
• Higher velocity near pipe walls compared to laminar flow

5. Head Loss in Pipes

Energy loss occurs due to friction and disturbances.

(a) Major Loss (Friction Loss)

$h_f = \frac{f L V^2}{2 g D}$hf​=2gDfLV2​

Where:

• $h_f$hf​ = Head loss due to friction
• $f$f = Friction factor
• $L$L = Length of pipe
• $D$D = Diameter
• $V$V = Velocity
• $g$g = Acceleration due to gravity

(b) Minor Losses

Due to:

• Bends
• Valves
• Fittings
• Sudden expansion/contraction

$$h_m = \frac{K V^2}{2g}$$hm​=2gKV2​

Where $K$K is loss coefficient.

6. Darcy-Weisbach Equation

Used to calculate frictional losses in pipes (already shown above).

• Valid for both laminar and turbulent flow.
• Most widely used formula.

7. Friction Factor (f)

For Laminar Flow

$$f = \frac{64}{Re}$$f=Re64​

For Turbulent Flow

• Depends on:
  • Reynolds number
  • Pipe roughness
• Determined using:
  • Moody Chart
  • Empirical equations (e.g., Colebrook equation)

8. Energy Equation for Pipe Flow

Bernoulli’s equation with losses:$$\frac{P_1}{\gamma} + \frac{V_1^2}{2g} + Z_1 = \frac{P_2}{\gamma} + \frac{V_2^2}{2g} + Z_2 + h_f + h_m$$

9. Pipes in Series and Parallel

(a) Pipes in Series

• Same flow rate through all pipes
• Total head loss = sum of individual losses

$$h_{total} = h_1 + h_2 + h_3$$

(b) Pipes in Parallel

• Same head loss across each branch
• Total discharge = sum of individual discharges

$$Q = Q_1 + Q_2 + Q_3$$Q=Q1​+Q2​+Q3​

10. Hydraulic Gradient Line (HGL) & Total Energy Line (TEL)

• HGL: Represents pressure head + elevation head
• TEL: Represents total energy (pressure + velocity + elevation)

Difference between TEL and HGL = Velocity head

11. Flow Measurement in Pipes

Devices used:

• Venturimeter
• Orifice meter
• Pitot tube

12. Practical Applications

• Water distribution systems
• Oil and gas pipelines
• Irrigation systems
• Power plants
• Chemical industries

13. Key Points Summary

• Flow depends on Reynolds number.
• Head loss is crucial in pipe design.
• Friction factor varies with flow type.
• Darcy-Weisbach equation is most important.
• Energy losses must be minimized for efficiency.

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