9.2 Major and Minor Losses in Pipe Systems

Pipe systems experience major and minor losses due to friction and fittings. The Darcy-Weisbach equation calculates major losses, while minor losses are determined using loss coefficients. Understanding these losses is crucial for designing efficient pipe systems.

Total head loss combines major and minor losses. Factors like pipe roughness, diameter, and flow rate affect the overall loss. Engineers use the concept of equivalent length to simplify complex systems, aiding in design and optimization of piping networks.

Major Losses in Pipe Systems

Darcy-Weisbach equation for friction losses

Top images from around the web for Darcy-Weisbach equation for friction losses

• 

  Darcy–Weisbach equation - Wikipedia View original

  Is this image relevant?

• 

  Reynolds number - Wikipedia View original

  Is this image relevant?

• 

  Experiment #4: Energy Loss in Pipes – Applied Fluid Mechanics Lab Manual View original

  Is this image relevant?

• 

  Darcy–Weisbach equation - Wikipedia View original

  Is this image relevant?

• 

  Reynolds number - Wikipedia View original

  Is this image relevant?

1 of 3

Top images from around the web for Darcy-Weisbach equation for friction losses

• 

  Darcy–Weisbach equation - Wikipedia View original

  Is this image relevant?

• 

  Reynolds number - Wikipedia View original

  Is this image relevant?

• 

  Experiment #4: Energy Loss in Pipes – Applied Fluid Mechanics Lab Manual View original

  Is this image relevant?

• 

  Darcy–Weisbach equation - Wikipedia View original

  Is this image relevant?

• 

  Reynolds number - Wikipedia View original

  Is this image relevant?

1 of 3

• Calculates head loss due to friction in pipe systems using the Darcy-Weisbach equation $h_f = f \frac{L}{D} \frac{V^2}{2g}$
  • $h_f$ represents the head loss due to friction measured in meters (m)
  • $f$ is the Darcy friction factor, a dimensionless quantity that depends on the Reynolds number ($Re$) and relative roughness ($\varepsilon/D$) of the pipe
  • $L$ is the length of the pipe (m)
  • $D$ is the diameter of the pipe (m)
  • $V$ is the average flow velocity through the pipe (m/s)
  • $g$ is the gravitational acceleration, typically taken as 9.81 m/s²
• Friction factor ($f$) is influenced by the Reynolds number ($Re$), which characterizes the flow regime, and the relative roughness ($\varepsilon/D$), which accounts for the pipe's internal surface irregularities
  • $\varepsilon$ is the pipe roughness, a measure of the internal surface irregularities (m)
  • Relative roughness is the ratio of the pipe roughness to the pipe diameter
• For laminar flow conditions ($Re < 2300$), the friction factor is solely dependent on the Reynolds number and can be calculated using the equation $f = \frac{64}{Re}$
• In turbulent flow conditions ($Re > 4000$), the friction factor depends on both the Reynolds number and the relative roughness, and can be determined using the Moody diagram or the Colebrook-White equation
  • The Moody diagram is a graphical representation of the relationship between the friction factor, Reynolds number, and relative roughness
  • The Colebrook-White equation is an implicit equation that can be solved iteratively to find the friction factor

Minor losses in pipe systems

• Minor losses in pipe systems are caused by various fittings, valves, and sudden changes in the pipe geometry, such as expansions, contractions, bends, and tees
• The head loss due to minor losses is calculated using the equation $h_m = K \frac{V^2}{2g}$
  • $h_m$ is the head loss due to minor losses (m)
  • $K$ is the minor loss coefficient, a dimensionless quantity that depends on the type of fitting or valve
  • $V$ is the average flow velocity in the pipe (m/s)
  • $g$ is the gravitational acceleration (m/s²)
• Minor loss coefficients ($K$) are specific to each type of fitting or valve and can be found in engineering reference tables or handbooks
  • Sudden expansion: When the pipe diameter abruptly increases, causing a loss of kinetic energy (flow separation)
  • Sudden contraction: When the pipe diameter abruptly decreases, leading to a loss of pressure (vena contracta)
  • Bends and elbows: Curved sections of the pipe that change the direction of the flow (90° elbow, 45° bend)
  • Tees and wyes: Junctions where the flow is split or combined (regular tee, bullhead tee)
  • Valves: Devices used to control the flow rate or pressure in the pipe system (gate valve, globe valve, check valve)

Total Losses and Equivalent Length

Equivalent length of pipe systems

• The equivalent length ($L_e$) of a pipe system is the length of a straight pipe that would cause the same head loss as the actual pipe system, considering both major and minor losses
• It is calculated using the equation $L_e = L + \sum \frac{K_i D}{f}$
  • $L$ is the actual length of the pipe (m)
  • $K_i$ is the minor loss coefficient for each fitting or valve in the system
  • $D$ is the pipe diameter (m)
  • $f$ is the Darcy friction factor (dimensionless)
• The equivalent length concept simplifies the analysis of complex pipe systems by converting minor losses into an equivalent length of straight pipe

Factors affecting pipe head loss

• The total head loss in a pipe system is the sum of the head losses due to friction (major losses) and the head losses caused by fittings and valves (minor losses), given by the equation $h_L = h_f + \sum h_m$
  • $h_L$ is the total head loss (m)
  • $h_f$ is the head loss due to friction (m)
  • $h_m$ is the head loss due to minor losses (m)
• Several factors influence the total head loss in a pipe system:
  • Pipe roughness ($\varepsilon$): A higher pipe roughness increases the friction factor and, consequently, the head loss due to friction (cast iron pipes vs. PVC pipes)
  • Pipe diameter ($D$): A smaller pipe diameter results in a higher flow velocity for a given flow rate, leading to increased head loss (2-inch vs. 4-inch diameter pipes)
  • Flow rate ($Q$): A higher flow rate increases the flow velocity and, therefore, the head loss in the pipe system (doubling the flow rate quadruples the head loss)
    • The flow velocity is related to the flow rate by the equation $V = \frac{Q}{A}$, where $A$ is the cross-sectional area of the pipe (m²)
• Understanding the impact of these factors on head loss is crucial for designing efficient and economical pipe systems, as well as for troubleshooting and optimizing existing installations (industrial process lines, water distribution networks, HVAC systems)