Pressure Drop Calculation for Pipe Fitting

How to Determine Total Pressure Drop in Pipe Fitting?

  • The pressure drop in a pipe fitting is a result of various factors including fluid velocity, pipe geometry, viscosity of the fluid, and the type of fitting being used.
  • The pressure drop is essentially the difference in pressure between the inlet and outlet of the fitting due to these factors.
  • There are several methods to calculate pressure drop in pipe fittings, and the appropriate method depends on the specific situation and the accuracy required.
  • Based on flow resistances and flow rate, the pressure drop is calculated. Refer to the website for

Losses through Pipe
Losses through Pipe Fittings

 

  • The total pressure drop in ducting is the sum of various pressure losses that occur as air flows through the duct system. These pressure losses can be categorized into different components, and the total pressure drop is the sum of these individual losses. Here are the main components to consider when calculating total pressure drops in ducting:
  • To calculate the total pressure drop, simply add up the individual pressure drops from each component:

                       Total Pressure Drop = Σ pressure drops 

                   ΔP Total = ΔP friction+ ΔP fitting+ΔP expansion/contraction+ΔP entrance/exit+ΔP dynamic

  • Keep in mind that accurate calculations may require knowledge of factors such as duct roughness, temperature, and specific fittings used, so consulting relevant engineering standards or using specialized software can be beneficial.

Steps in Determining a Pressure Drop 

  • Calculating the total pressure drop in ducting involves considering several factors including the duct geometry, air velocity, friction losses, fittings, and any other obstructions present in the duct system.
  • The total pressure drop is the sum of all individual pressure drops along the duct system.
  • Here’s a general outline of the steps involved in calculating total pressure drop in ducting:
  1. Understand the Duct System:
    1. Familiarize yourself with the layout and components of the duct system including the lengths of straight ducts, elbows, bends, transitions, dampers, filters, grilles, etc.
  2. Determine Air Flow Rate:
    • Determine the air flow rate through the duct system.
    • This could be based on design specifications, HVAC load calculations, or measured flow rates.
  3. Calculate Air Velocity:
    • Calculate the air velocity in each section of the ducting. This is typically done using the formula:

W

where:

      • = Air velocity (m/s or ft/s)
      • = Air flow rate (m³/s or ft³/s)
      • = Cross-sectional area of the duct (m² or ft²)
  1. Determine Friction Losses: Use the Darcy-Weisbach equation or other empirical formulas to calculate friction losses in the straight sections of ducts
  2. Consider Fittings and Accessories: Determine pressure losses associated with fittings, bends, elbows, transitions, dampers, filters, grilles, etc. These pressure losses are often provided by manufacturers or can be obtained from engineering handbooks
  3. Sum Up Pressure Drops: Sum up all the pressure drops along the duct system to find the total pressure drop
  4. Compare with System Requirements: Compare the total pressure drop with the system requirements and ensure that the selected fan or blower can provide sufficient pressure to overcome the resistance in the duct system.

Note: 

  • It’s worth noting that there are software programs and spreadsheets available that can streamline these calculations, especially for complex duct systems.
  • Refer to ASHRAE or API 560 handbooks for accurate calculations for specific applications.

Friction Pressure Drop using the Darcy-Weisbach Equation

  • This is one of the most widely used equations for calculating pressure drop in pipe fittings.
  • This is given on the web page for pressure drop through pipe based on Reynolds number
  • The equation is given by:
Darcy Weeisbach Equation for Pressure Drop Determination
Darcy Weeisbach Equation for Pressure Drop Determination

Where:

  • ΔP is the pressure drop across the fitting (Pa or psi )
  • f is the Darcy friction factor (dimensionless)
  • L is the length of the fitting (m or ft)
  • D is the diameter of the fitting (m or ft)
  • ρ is the density of the fluid (kg/m³ or lb/ft3)
  • V is the velocity of the fluid (m/s or ft/s)
  • The Darcy friction factor (f) depends on the Reynolds number and the roughness of the pipe walls. You need to refer  the Moody’s factor
  • This equation is suitable for both laminar and turbulent flow.

Coefficient (C)-value Method

  • This method involves using C-values (also known as resistance coefficients) to represent the pressure drop caused by various types of fittings.
  • Each type of fitting has an associated K-value that is determined experimentally. The pressure drop across the fitting is then calculated using the equation:

        ΔP= C*K*V^2

Where:

      • ΔP is the pressure drop across the fitting (Pa or mm of Water column )
      • C is the pressure loss coefficient (dimensionless)
      • K is the correction factor (the unit conversion factor), roughness factor, temperature change factor
      • V is the velocity of the fluid (m/s)
    • This method is simpler to use compared to the Darcy-Weisbach equation, but it may not be as accurate in all situations
    • Remember that these equations provide approximations and are based on certain assumptions. They might not account for all complexities such as turbulence, heat transfer, and specific flow characteristics.
    • For accurate results, it’s recommended to consult engineering handbooks, and software tools, or seek guidance from experts in fluid dynamics and piping systems.

Dynamic Pressure Drop:

    • This accounts for pressure changes due to elevation changes.
    • It is calculated using the hydrostatic pressure equation:

ΔP for dynamic =⋅

where:

          • ΔP is the dynamic pressure drop,
          • is the fluid (air) density,
          • is the acceleration due to gravity,
          • Δℎ is the elevation change.

Calculation of Pressure Drop in Fitting 

  • The method of Coefficient (C)-value used to determine this loss
  • Enter the input value from your pipe fitting
    • V is the average inlet velocity  (m/s)
    • ρ is the Density of fluid (kg/m3)
    • C  is the pressure Loss coefficient (dimensionless)
  • Note the pressure Loss coefficient from the following tables

 

 

Pressure Loss Coefficient Factor for Piping As per API 560

  • Various types of pipe fitting are given as standard geometry. You can refer ASHRAE handbook or API 560 for more details on loss coefficient
  • Fittings and Bends:
    • Pressure drops occur at fittings, bends, and other obstructions in the duct. Manufacturers often provide data on pressure drop for various fittings.
    • The equivalent length method is commonly used to account for pressure drops due to fittings. The total equivalent length is added to the actual duct length in the frictional pressure drop calculation.
  • Expansion and Contraction:
    • Changes in duct cross-sectional area can cause pressure drops. The pressure drop can be calculated using the velocity change across the expansion or contraction.
  • Entrance and Exit Losses:
    • Pressure drops occur at the entrance and exit of the duct. Empirical coefficients are often used to estimate these losses.

Pressure Loss coefficient for internal flow with 90 Degree pipe

  • Pressure loss coefficient for Internal flow with obstacles

Pressure Loss coefficient for internal flow with obstacle in duct

  • Pressure Loss coefficient for internal flow

Pressure Loss coefficient for internal flow

 

References

  1. Pressure Drop in Pipes and Duct by ASHRAE Ducting,
  2. ASHRAE Chapter 34, Duct Design based on pressure Drop