Understanding Pressure Calculation in Heat Exchangers: A Technical Deep Dive

Pressure calculation in heat exchangers determines fluid dynamics and system efficiency. It involves analyzing pressure drops and flow resistance.

This article explores detailed formulas, variable explanations, and real-world applications for precise pressure calculations in heat exchangers.

• Calculate pressure drop for a shell-and-tube heat exchanger with water at 60°C.
• Determine pressure loss in a plate heat exchanger handling oil at 120°C.
• Estimate pressure drop for steam flowing through a double-pipe heat exchanger.
• Analyze pressure changes in a heat exchanger with refrigerant R134a at varying flow rates.

Common Parameters and Values in Pressure Calculation for Heat Exchangers

Fundamental Formulas for Pressure Calculation in Heat Exchangers

Pressure drop in heat exchangers is primarily caused by frictional losses and changes in momentum. The calculation involves fluid mechanics principles and empirical correlations.

Darcy-Weisbach Equation for Pressure Drop

The Darcy-Weisbach equation is the cornerstone for calculating pressure drop due to friction in pipes and tubes:

• ΔP: Pressure drop (Pa or N/m²)
• f: Darcy friction factor (dimensionless)
• L: Length of the pipe or flow path (m)
• D: Hydraulic diameter of the pipe or tube (m)
• ρ: Fluid density (kg/m³)
• v: Fluid velocity (m/s)

The friction factor f depends on the flow regime and pipe roughness. It is calculated differently for laminar and turbulent flows.

Calculating Reynolds Number (Re)

Reynolds number determines the flow regime:

• Re: Reynolds number (dimensionless)
• μ: Dynamic viscosity of the fluid (Pa·s)

Flow regimes based on Reynolds number:

• Laminar flow: Re < 2300
• Transitional flow: 2300 < Re < 4000
• Turbulent flow: Re > 4000

Friction Factor (f) Determination

For laminar flow, friction factor is calculated as:

For turbulent flow, the Colebrook-White equation is used (implicit):

Alternatively, the Swamee-Jain explicit approximation is often used for turbulent flow:

• ε: Pipe roughness (m)

Pressure Drop Due to Sudden Expansion or Contraction

In heat exchangers, pressure losses also occur due to changes in cross-sectional area:

• K: Loss coefficient (dimensionless), depends on geometry

Total Pressure Drop in Heat Exchanger

The total pressure drop is the sum of frictional losses and minor losses:

Minor losses include bends, valves, expansions, contractions, and fittings.

Detailed Explanation of Variables and Typical Values

• Fluid Velocity (v): Typically ranges from 0.5 to 5 m/s in heat exchangers to balance pressure drop and heat transfer efficiency.
• Density (ρ): Varies widely; water at room temperature is approximately 998 kg/m³, steam can be as low as 0.6 kg/m³.
• Dynamic Viscosity (μ): Water at 20°C has about 0.001 Pa·s; oils and other fluids can have higher viscosities, increasing pressure drop.
• Pipe Diameter (D): Tube diameters in shell-and-tube exchangers typically range from 12 mm to 25 mm; shell diameters vary more widely.
• Length (L): Length of tubes or flow path can be several meters, directly proportional to pressure drop.
• Roughness (ε): New steel pipes have roughness around 0.045 mm; older or corroded pipes can be rougher, increasing friction.
• Friction Factor (f): Depends on flow regime and roughness; lower for smooth pipes and laminar flow, higher for turbulent flow and rough pipes.

Real-World Application Examples

Example 1: Pressure Drop Calculation in a Shell-and-Tube Heat Exchanger with Water

A shell-and-tube heat exchanger has tubes of 20 mm diameter and 5 m length. Water at 60°C flows inside the tubes at 2 m/s. Calculate the pressure drop due to friction.

• Given data:
  • Diameter, D = 0.02 m
  • Length, L = 5 m
  • Velocity, v = 2 m/s
  • Density of water at 60°C, ρ ≈ 983 kg/m³
  • Dynamic viscosity of water at 60°C, μ ≈ 0.00047 Pa·s
  • Pipe roughness, ε = 0.000045 m (new steel)

Step 1: Calculate Reynolds number

Since Re > 4000, flow is turbulent.

Step 2: Calculate friction factor using Swamee-Jain equation

Calculate inside the log:

Logarithm:

Friction factor:

Step 3: Calculate pressure drop

The pressure drop due to friction in the tubes is approximately 13 kPa.

Example 2: Pressure Drop in a Plate Heat Exchanger Handling Oil

Consider a plate heat exchanger where oil flows at 1.5 m/s through channels of hydraulic diameter 0.01 m and length 3 m. Oil properties at 120°C are:

• Density, ρ = 850 kg/m³
• Dynamic viscosity, μ = 0.005 Pa·s
• Surface roughness, ε = 0.0001 m

Calculate the pressure drop due to friction.

Step 1: Calculate Reynolds number

Flow is transitional (2300 < Re < 4000), so friction factor can be approximated by interpolation or conservative turbulent flow assumption.

Step 2: Calculate friction factor using Swamee-Jain (turbulent assumption)

Step 3: Calculate pressure drop

The pressure drop in the plate heat exchanger channels is approximately 15.8 kPa.

Additional Considerations in Pressure Drop Calculations

• Temperature Effects: Fluid properties such as density and viscosity vary with temperature, significantly affecting pressure drop.
• Two-Phase Flow: In cases where phase change occurs (e.g., boiling or condensation), pressure drop calculations become more complex and require specialized correlations.
• Fouling and Scaling: Deposits on heat exchanger surfaces increase roughness and reduce flow area, increasing pressure drop over time.
• Flow Distribution: Maldistribution in multi-pass heat exchangers can cause uneven pressure drops and reduced performance.
• Minor Losses: Include bends, valves, expansions, and contractions; often estimated using loss coefficients from standards such as Crane Technical Paper No. 410.

Standards and References for Pressure Drop Calculations

• ASME Boiler and Pressure Vessel Code (BPVC) – Guidelines for pressure vessel and heat exchanger design.
• Colebrook Equation Explanation – TWI
• Engineering Toolbox – Pressure Loss in Pipes
• Crane Technical Paper No. 410 – Flow of fluids through valves, fittings, and pipe.

Summary of Key Steps for Pressure Calculation in Heat Exchangers

• Identify fluid properties at operating temperature (density, viscosity).
• Determine flow velocity and hydraulic diameter.
• Calculate Reynolds number to establish flow regime.
• Compute friction factor using appropriate correlations.
• Calculate frictional pressure drop using Darcy-Weisbach equation.
• Include minor losses from fittings and geometry changes.
• Sum all losses for total pressure drop estimation.

Accurate pressure drop calculations are essential for selecting pumps, designing heat exchanger components, and ensuring efficient thermal performance. Understanding the interplay of fluid mechanics and heat exchanger geometry enables engineers to optimize system design and operation.