Calculation of Pressure Loss in Refrigeration System Liquid Supply Pipeline

The calculation of pressure loss in the refrigerant liquid pipeline is important for confirming the minimum subcooling required by the refrigeration system and the selection of the expansion valve. The pressure loss in the liquid pipe mainly consists of frictional pressure loss along the length and pressure loss caused by pipeline elevation.

Usually, we can use the Darcy-Weisbach equation to calculate the frictional loss along the length, which is a widely used method for calculating pressure loss of fluid in pipes. The following are the formulas and basic steps for calculating friction loss:

 

01. The Darcy-Weisbach equation is:

Where:

ΔP1 represents the pressure loss caused by friction along the length (Pa);

f is the friction factor, which is related to the Reynolds number (Re) and the relative roughness of the pipe;

L is the actual length of the pipe (m);

D is the inner diameter of the pipe (m);

ρ is the density of the fluid (kg/m³);

V is the average velocity of the fluid (m/s).

02. Friction factor

 

f can be determined through the Moody chart or empirical formulas, such as the Colebrook-White equation. For fully developed turbulent flow, the friction factor can be approximately calculated by the following formula: ϵ is the absolute roughness of the pipe inner wall (m);

Re is the Reynolds number.

This formula requires iterative solving. To simplify calculations, we can use an approximate formula, the Swamee-Jain equation, which is based on the Colebrook-White equation but provides a direct solution:

For smooth pipes, the Blasius formula provides a method to calculate the friction factor for turbulent flow, expressed as:

f is the friction factor;

04. Reynolds number (Re)

The Reynolds number is an important parameter to determine the flow state (laminar, transitional, turbulent), calculated as: Re=VDρ/μ, where:

ρ is the fluid density (kg/m³);

V is the fluid velocity (m/s);

For smooth pipes, the Blasius formula provides a method to calculate the friction factor for turbulent flow, expressed as:

 

D is the pipe diameter (m);

μ is the dynamic viscosity of the fluid (Pa·s).

Whether the refrigerant flow in the liquid pipe is laminar or turbulent mainly depends on the Reynolds number, a dimensionless parameter used to characterize the flow state of the fluid. According to general fluid mechanics guidelines:

When Reynolds number Re < 2300, the flow is generally considered laminar.

When Reynolds number Re > 4000, the flow is considered turbulent.

Between 2300 < Re < 4000, the flow may be transitional, exhibiting characteristics of both laminar and turbulent flow.

The refrigerant flow velocity in the supply liquid pipeline of refrigeration systems is usually between 0.3 m/s and 1.5 m/s.

Taking the example of R404A liquid at a condensing temperature of 40°C flowing at 1 m/s in a smooth copper pipe with a total length of 10 m, wall thickness of 0.7 mm, and diameter of 12.7 mm, the physical property parameters of R404A provided by Honeywell are:

R404A liquid density ρ = 964.65 kg/m³

Dynamic viscosity μ = 0.00010261 Pa·s

Flow velocity V = 1.0 m/s

Pipe diameter (D) = 0.0113 m

Absolute roughness of copper pipe ε = 0.0000015 m

First, we calculate the Reynolds number Re:

Re = ρ * V * D / μ = 964.65 × 1 × 0.0113 / 0.00010261 ≈ 106144

Since the Reynolds number is much greater than 4000, the flow state is turbulent. Then we solve the friction factor inside the pipe using the Colebrook-White formula or the Blasius formula respectively. Colebrook-White formula:

f = 0.25 / (-4.047)² ≈ 0.01526

Then the pressure drop inside the pipe: ΔP = f * L / D * ρ * V² / 2

= 0.01526 * 10 / 0.0113 * 964.65 * 1² / 2 = 6513.5 Pa

Calculate the friction factor inside the pipe using the Blasius formula

04. Reynolds number (Re)

f = 0.316 / Re^(1/4)

f = 0.316 / 106144^(1/4) ≈ 0.0175

Then the pressure drop inside the pipe: ΔP1 = f * L / D * ρ * V² / 2

P1 = f * L / D * ρ * V² / 2

= 0.0175 * 10 / 0.0113 * 964.65 * 1² / 2

= 0.0175 * 884.956 * 482.325

= 7469.6 Pa

The difference in pressure loss calculated by the two formulas for a 10 m pipeline is less than 1 kPa, which can basically be ignored for the high-pressure pipeline of the refrigeration system, and both are applicable when calculating the pressure drop in the supply liquid pipeline.

P1=f*L/D*ρV2/2

=0.0175*10/0.0113*964.65*12/2

=0.0175*884.956*482.325

=7469.6 Pa

The pressure loss difference value of a 10m pipeline calculated by the two formulas is less than 1kPa, which is basically negligible for the high - pressure pipeline of the refrigeration system. Both formulas are applicable when calculating the pressure drop of the liquid supply pipeline.

 

04. For refrigeration systems, the total length of piping = piping length + equivalent pipe length of intermediate components in the pipeline.

Equivalent pipe length refers to the elbows, valves, pipe joints, and other fittings present in the refrigeration piping. These fittings have certain resistance, and their pressure losses need to be included when calculating pipeline pressure loss. Generally, the resistance values of these fittings are expressed as the length of a pipe with the same diameter that has approximately the same resistance, hence called "equivalent pipe length."

If the valves and joints used cannot be confirmed during the design phase, the pipeline length can be calculated as the measured value from the plan multiplied by 1.2 to 1.3, taking the larger value if the length is significant.

Additionally, another important factor in liquid pipe pressure loss is the pressure loss caused by the elevation of the liquid pipe. It can be calculated using the formula ΔP3 = ρgh,

where ρ is the refrigerant density in kg/m³,

g is the acceleration due to gravity in m/s²,

h is the elevation height of the liquid pipe in meters.

 

Case Calculation Example

Let's do a case calculation:

For R404A liquid at a condensing temperature of 40°C flowing at 1 m/s inside a smooth copper pipe with a total length of 10 m, wall thickness of 0.7 mm, and diameter of 12.7 mm, with a pipeline elevation of 6 m, first calculate the friction factor using the Blasius formula:

= 0.0175 * 884.956 * 482.325

= 7469.6 Pa

The pressure drop caused by friction inside the pipe: ΔP = f * L / D * ρ * V² / 2,

Where:

= 0.0175 * 12 / 0.0113 * 964.65 * 12 / 2

= 0.0175 * 1061.947 * 482.325

= 8963.6 Pa

Pressure loss caused by pipeline elevation ΔP3 = ρgh

= 964.65 * 9.8 * 6

= 56721.42 Pa

Total pressure loss in the liquid pipe ΔP = ΔP1 + ΔP3

= 56721.42 + 8963.6

= 65685.02 Pa ≈ 0.66 bar

At this time, the pressure before the expansion valve is 16.62 bar, corresponding to a condensing temperature of 38.5°C. To ensure no flash gas appears before the expansion valve, the subcooling at the condenser outlet must be maintained above 1.5 K.

From the calculation, we can see that the pressure loss caused by the elevation of the liquid pipe is significant. When designing the pipeline, the pressure loss of each section should be controlled within 1°C of the refrigerant's saturation temperature. Generally, the recommended elevation for R404A liquid pipes should not exceed 5 m. If this height is exceeded, sufficient subcooling of the liquid pipe or appropriate liquid supply design measures must be ensured.

When selecting the expansion valve, this portion of the pressure loss before the valve should also be deducted accordingly. In this case, the pressure loss before the expansion valve is 0.66 bar.