Goal
Estimate single-phase frictional pressure drop, Reynolds number, velocity, and head loss in a small tube from flow, fluid properties, length, diameter, and roughness.
Capillary-Tube Pressure-Drop Screening Calculator
Estimate single-phase frictional pressure drop, Reynolds number, velocity, and head loss in a small tube from flow, fluid properties, length, diameter, and roughness.
Key facts
- What it does
- Estimate single-phase frictional pressure drop, Reynolds number, velocity, and head loss in a small tube from flow, fluid properties, length, diameter, and roughness.
- Formula
Area = πD²/4; velocity = mass flow ÷ (density × area); Reynolds number = ρvD/μ; friction factor = 64/Re for laminar flow or a Swamee–Jain estimate otherwise; Darcy–Weisbach pressure drop = f(L/D)(ρv²/2).- You enter
- Mass flow rate · Fluid density · Dynamic viscosity · Tube length · Inner diameter · Absolute roughness · Gravitational acceleration
- Worked example
- The scenario gives about 1.159 m/s mean velocity, Reynolds number 6,374, and a frictional pressure drop of roughly 39 kPa using the stated single-phase approximation.
A clearer path to an answer
From your question to a useful result
This page keeps the calculation transparent: define the goal, enter the matching values, inspect the method, and decide what the result means in your situation.
Inputs
Mass flow rate · Fluid density · Dynamic viscosity · Tube length · Inner diameter · Absolute roughness · Gravitational acceleration
Method
Area = πD²/4; velocity = mass flow ÷ (density × area); Reynolds number = ρvD/μ; friction factor = 64/Re for laminar flow or a Swamee–Jain estimate otherwise; Darcy–Weisbach pressure drop = f(L/D)(ρv²/2).
Next step
Calculate, review the assumptions below, then compare a related tool when the decision needs more context.
Capillary-Tube Pressure-Drop Screening Calculator
Estimate single-phase frictional pressure drop, Reynolds number, velocity, and head loss in a small tube from flow, fluid properties, length, diameter, and roughness.
Open the Capillary-Tube Pressure-Drop Screening Calculator pageMore science tools
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Result
Enter your values above and choose Calculate to see the result here.
Calculation map
Follow the path from input to answer
01
Inputs (7)
- Mass flow rate Ready
- Fluid density Ready
- Dynamic viscosity Ready
- Tube length Ready
- +3 more inputs
02
Formula
Area = πD²/4; velocity = mass flow ÷ (density × area); Reynolds number = ρvD/μ; friction factor = 64/Re for laminar flow or a Swamee–Jain estimate otherwise; Darcy–Weisbach pressure drop = f(L/D)(ρv²/2).
Bounded, transparent calculation
03
Result
- Calculate to preview the result.
Recent runs
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Formula, assumptions, and example
Formula: Area = πD²/4; velocity = mass flow ÷ (density × area); Reynolds number = ρvD/μ; friction factor = 64/Re for laminar flow or a Swamee–Jain estimate otherwise; Darcy–Weisbach pressure drop = f(L/D)(ρv²/2).
A capillary tube can have strong frictional losses, but a real refrigerant device may enter two-phase flow. This page therefore labels itself a single-phase screening model: it calculates velocity, Reynolds number, an explicit friction-factor branch, Darcy–Weisbach pressure drop, and equivalent head loss without pretending to select a working refrigeration component.
- The fluid is single phase with constant density and dynamic viscosity along the tube.
- The tube is circular and the entered diameter is the internal diameter.
- The pressure drop is frictional and fully developed; fittings, inlet effects, elevation, and heat exchange are omitted.
- Laminar flow uses 64/Re; higher-Re flow uses a Swamee–Jain estimate with relative roughness.
- The transitional range is reported as uncertain rather than being hidden.
- Real refrigerant capillary sizing needs thermodynamic state, flashing, oil, safety, and validated design data.
Worked example: The scenario gives about 1.159 m/s mean velocity, Reynolds number 6,374, and a frictional pressure drop of roughly 39 kPa using the stated single-phase approximation.
Displayed input contract
- Mass flow rate · minimum 1.0E-9 · maximum 1000
- Fluid density · minimum 1.0E-6 · maximum 20000
- Dynamic viscosity · minimum 1.0E-12 · maximum 1000
- Tube length · minimum 1.0E-6 · maximum 1000000
- Inner diameter · minimum 1.0E-9 · maximum 100
- Absolute roughness · minimum 0 · maximum 1
- Gravitational acceleration · minimum 1.0E-6 · maximum 100
The displayed limits are checked before the handler runs. Model-specific domain checks may also reject impossible or non-finite inputs.
Methodology: This calculator follows the WorldCalculate input, formula, precision, and boundary policy. Read the official methodology.
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Answer-first guide
How to use the Capillary-Tube Pressure-Drop Screening Calculator for a real question
Estimate single-phase frictional pressure drop, Reynolds number, velocity, and head loss in a small tube from flow, fluid properties, length, diameter, and roughness. Start with one clearly defined goal, enter values in the units shown, and keep the result attached to the assumptions below.
What this answers
This tool is useful when your question includes refrigerant capillary tube calculator, capillary pressure drop, Darcy Weisbach capillary. It returns the outputs declared in the calculator contract rather than a live quote, approval, diagnosis, or professional sign-off.
What you enter
Mass flow rate · Fluid density · Dynamic viscosity · Tube length · Inner diameter · Absolute roughness · Gravitational acceleration. Keep the same time period, unit system, and currency wherever the form requires comparable values.
How to check it
Run the worked example first, compare its output with the page's example, then change one input at a time. This makes an unexpected result easier to trace to a unit, boundary, or assumption.
Three checks before you rely on the answer
- Match the question. Confirm that the result means the quantity you need, not a similar-sounding percentage, balance, rate, or estimate.
- Match the inputs. Use the requested units and period, and read each hint before replacing the example values with your own.
- Read the boundary. Review the assumptions and limits. The fluid is single phase with constant density and dynamic viscosity along the tube.
Need a wider view? Browse Science Calculators or compare the related tools below. The WorldCalculate methodology explains how formulas, examples, limits, and revisions are reviewed.
How to use the Capillary-Tube Pressure-Drop Screening Calculator
- Enter Mass flow rate (kg/s).
- Enter Fluid density (kg/m³).
- Enter Dynamic viscosity (Pa·s).
- Enter Tube length (m).
- Enter Inner diameter (m).
- Enter Absolute roughness (m).
- Enter Gravitational acceleration (m/s²).
- Choose Calculate and read the result panel.
- Use Download PDF or Download Word to save a result sheet.
Formula
Area = πD²/4; velocity = mass flow ÷ (density × area); Reynolds number = ρvD/μ; friction factor = 64/Re for laminar flow or a Swamee–Jain estimate otherwise; Darcy–Weisbach pressure drop = f(L/D)(ρv²/2).
A capillary tube can have strong frictional losses, but a real refrigerant device may enter two-phase flow. This page therefore labels itself a single-phase screening model: it calculates velocity, Reynolds number, an explicit friction-factor branch, Darcy–Weisbach pressure drop, and equivalent head loss without pretending to select a working refrigeration component.
Worked example
The scenario gives about 1.159 m/s mean velocity, Reynolds number 6,374, and a frictional pressure drop of roughly 39 kPa using the stated single-phase approximation.
Assumptions and limits
- The fluid is single phase with constant density and dynamic viscosity along the tube.
- The tube is circular and the entered diameter is the internal diameter.
- The pressure drop is frictional and fully developed; fittings, inlet effects, elevation, and heat exchange are omitted.
- Laminar flow uses 64/Re; higher-Re flow uses a Swamee–Jain estimate with relative roughness.
- The transitional range is reported as uncertain rather than being hidden.
- Real refrigerant capillary sizing needs thermodynamic state, flashing, oil, safety, and validated design data.
Who uses this calculator?
- Fluid-mechanics students checking pipe-loss equations
- HVAC learners comparing flow-property sensitivity
- Engineers using an early single-phase screening worksheet
When is it useful?
- Estimate frictional pressure loss in a small circular tube.
- Inspect how diameter and mass flow affect Reynolds number.
- Compare laminar and turbulent friction-factor branches without sizing equipment.
Context and background
The model-first approach to science
Science calculators define a system, choose an equation, apply units and constants, and show the substitution. Effects outside that model remain outside the result.
Introductory science problem solving builds from measured quantities and idealized relationships. Those models are valuable for learning and first-pass estimates, while experiments and engineering decisions need additional evidence.
Research and review
How this guide was researched
Researched by Hassan ALRowaie, Founder and editorial researcher at WorldCalculate.
This guide follows the live calculator's declared inputs, formula, worked example, assumptions, validation boundaries, and source-backed methodology. The review date describes editorial review of the calculator explanation; it is not a promise that external facts or rates remain current.
Small tubes are sensitive to diameter, flow, and fluid properties. This calculator provides a deliberately bounded pressure-drop screen using single-phase Darcy–Weisbach arithmetic, then explains why a real refrigerant capillary tube may need a two-phase thermodynamic model.
What the screen calculates
The page calculates the mean velocity in a circular tube, the Reynolds number, a friction factor, a frictional pressure drop, and an equivalent head loss. These are linked outputs rather than separate guesses, so a visitor can see how mass flow and tube geometry enter the result.
The word screening is important. The tool does not select a capillary tube, certify a pressure rating, or predict the operating point of an appliance.
From mass flow to velocity
Mass flow rate becomes volume flow after division by density. Dividing that volumetric flow by the circular cross-sectional area gives mean velocity. The area depends on diameter squared, so a small diameter change can produce a large velocity change.
Use the internal diameter rather than an outside dimension. Keep the flow unit in kilograms per second and the properties in SI units so the returned velocity is in metres per second.
Reynolds number and regime
Reynolds number compares inertial effects with viscous effects using density, velocity, diameter, and dynamic viscosity. The calculator reports it as a dimensionless indicator and labels the low, high, and transitional ranges.
The thresholds used here are a practical educational branch, not a guarantee that every rough or developing flow behaves exactly at a boundary. A transitional result should be treated as uncertain rather than displayed with false confidence.
Friction factor choices
For laminar flow, the Darcy friction factor is 64 divided by Reynolds number. Above the laminar range, the page uses an explicit Swamee–Jain approximation involving relative roughness and Reynolds number. Showing the branch makes it possible to reproduce the result.
Other correlations and Moody-chart methods can be appropriate for different flow conditions. The user should keep the chosen correlation with the result when comparing scenarios.
Darcy–Weisbach pressure loss
The pressure loss is f times L/D times the dynamic-pressure term rho v squared over two. Length increases loss linearly in this model. Diameter affects both velocity and the length-to-diameter ratio, which is why narrow tubes can become very restrictive.
The pressure result is frictional only. It does not include fittings, entrance losses, elevation, acceleration, or heat transfer. A real system pressure balance must add the terms that apply to its geometry.
Why refrigerant flow needs caution
A refrigerant can flash from liquid toward two-phase flow in a capillary tube. Density and viscosity then vary, and momentum changes can contribute to the pressure drop. A constant-property single-phase equation cannot capture that behavior.
This page is useful for learning the pipe-loss structure or screening a clearly single-phase fluid. It must not be used as a substitute for thermodynamic property data, equipment specifications, or professional refrigeration design.
Sensitivity checks
Try changing only diameter, length, mass flow, or viscosity. Diameter usually produces a strong response because it changes area, velocity, and L/D simultaneously. Flow increases the dynamic-pressure term and can also move the regime branch.
Sensitivity results are mathematical comparisons, not an approval to change a working system. Preserve the base case and the property source so a reviewer knows which assumptions moved.
A safe reporting format
Report the fluid phase assumption, property values and temperature, geometry, correlation, regime, and excluded losses. Include the pressure unit and whether the result is a frictional drop or a complete system pressure difference.
If the task is actual capillary selection or service, stop at this screen and use validated design procedures with appropriate review. A transparent limitation is part of a correct engineering calculation.
Frequently asked questions
What is the Capillary-Tube Pressure-Drop Screening Calculator?
Estimate single-phase frictional pressure drop, Reynolds number, velocity, and head loss in a small tube from flow, fluid properties, length, diameter, and roughness.
What is the formula for the Capillary-Tube Pressure-Drop Screening Calculator?
Area = πD²/4; velocity = mass flow ÷ (density × area); Reynolds number = ρvD/μ; friction factor = 64/Re for laminar flow or a Swamee–Jain estimate otherwise; Darcy–Weisbach pressure drop = f(L/D)(ρv²/2). A capillary tube can have strong frictional losses, but a real refrigerant device may enter two-phase flow. This page therefore labels itself a single-phase screening model: it calculates velocity, Reynolds number, an explicit friction-factor branch, Darcy–Weisbach pressure drop, and equivalent head loss without pretending to select a working refrigeration component.
What do I need to use this calculator?
Enter Mass flow rate, Fluid density, Dynamic viscosity, Tube length, Inner diameter, Absolute roughness, Gravitational acceleration, then choose Calculate.
What are the limits of this calculator?
The fluid is single phase with constant density and dynamic viscosity along the tube. The tube is circular and the entered diameter is the internal diameter. The pressure drop is frictional and fully developed; fittings, inlet effects, elevation, and heat exchange are omitted. Laminar flow uses 64/Re; higher-Re flow uses a Swamee–Jain estimate with relative roughness. The transitional range is reported as uncertain rather than being hidden. Real refrigerant capillary sizing needs thermodynamic state, flashing, oil, safety, and validated design data.
Methodology
This calculator is part of the WorldCalculate library. Its formula, example, assumptions, input bounds, and output formatting follow the official methodology.
Use this calculator as part of a bigger plan
These WorldCalculate collections connect this tool with related questions while keeping each calculation separate and transparent.