Major and Minor Losses in Pipes 9/24/2012 Major and Minor Losses in Pipes Trans-Alaska Pipeline System Length 1287 km, D=1.22 m ME 322 THERMO-FLUIDS LAB-1 1/18/2019 ME 383 Fluid Mechanics

Major and Minor Losses in Pipes 9/24/2012 Major and Minor Losses in Pipes Energy Considerations in Pipe Flow 𝑝 1 𝜌 + 𝛼 1 𝑉 1 2 2 +𝑔 𝑧 1 − 𝑝 2 𝜌 + 𝛼 2 𝑉 2 2 2 +𝑔 𝑧 2 = ℎ 𝑙 𝑇 This equation enables us to calculate the losses occurring in a section of the pipe. The values of 𝛼 are usually close to 1. Each term in the equation has dimensions of 𝐿 2 𝑡 2 , so if we divide by 𝑔, it would have dimensions of length 𝐿. 𝑝 1 𝜌𝑔 + 𝛼 1 𝑉 1 2 2𝑔 + 𝑧 1 − 𝑝 2 𝜌𝑔 + 𝛼 2 𝑉 2 2 2𝑔 + 𝑧 2 = ℎ 𝑙 𝑇 𝑔 = 𝐻 𝑙 𝑇 𝑝 1 + 𝛼 1 𝜌 𝑉 1 2 2 + 𝑧 1 − 𝑝 2 + 𝛼 2 𝜌 𝑉 2 2 2 + 𝜌𝑔𝑧 2 =𝜌 ℎ 𝑙 𝑇 =𝐾 𝜌 𝑉 2 2 ME 322 THERMO-FLUIDS LAB-1 1/18/2019 ME 383 Fluid Mechanics

Major and Minor Losses in Pipes 9/24/2012 Major and Minor Losses in Pipes Energy Considerations in Pipe Flow 𝑝 1 + 𝛼 1 𝜌 𝑉 1 2 2 + 𝑧 1 − 𝑝 2 + 𝛼 2 𝜌 𝑉 2 2 2 + 𝜌𝑔𝑧 2 =𝜌 ℎ 𝑙 𝑇 =𝐾 𝜌 𝑉 2 2 Major losses are due to friction between fluid and pipe, hence we can write the losses as, ℎ 𝑙 =𝑓 𝐿 𝐷 𝑉 2 2 Where L and D are the pipe length and diameter, respectively. Minor losses are due to fittings and or area changes Inlets/Exits Enlargements and Contractions Pipe Bends Valves and fittings ℎ 𝑙 =𝐾 𝑉 2 2 =𝑓 𝐿 𝑒 𝐷 𝑉 2 2 We can define Le, equivalent length, for each type of fitting. ME 322 THERMO-FLUIDS LAB-1 1/18/2019 ME 383 Fluid Mechanics

Major and Minor Losses in Pipes 9/24/2012 Major and Minor Losses in Pipes Fittings: Area Change ME 322 THERMO-FLUIDS LAB-1 1/18/2019 ME 383 Fluid Mechanics

Major and Minor Losses in Pipes 9/24/2012 Major and Minor Losses in Pipes Fittings: Bends ME 322 THERMO-FLUIDS LAB-1 1/18/2019 ME 383 Fluid Mechanics

Major and Minor Losses in Pipes 9/24/2012 Major and Minor Losses in Pipes Fittings: Equivalent Length The equivalent length is calculated using the flow velocity and Reynolds number to get an estimate for f using Moody chart Using the estimated value of K we can estimate Le/D ME 322 THERMO-FLUIDS LAB-1 1/18/2019 ME 383 Fluid Mechanics