Pipe roughness $\epsilon$ calculator

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Pipe Roughness Calculator

Absolute Roughness of Pipe Materials

Student Information

StudentCABALLERO MEDRANO

App Creation DateSeptember 10, 2026

What Is Absolute Roughness?

Absolute roughness ($\varepsilon$) is the average height of the microscopic irregularities (peaks and valleys) found on the internal surface of a pipe wall. It is an intrinsic property of the pipe material and its manufacturing process. Absolute roughness is a key input for calculating the friction factor in pipe-flow problems (e.g., using the Colebrook equation or the Moody diagram), since the ratio $\varepsilon / D$ (relative roughness) directly affects the pressure drop caused by fluid friction against the pipe wall.

How to Use This App

1. Select a pipe material from the dropdown menu below.
2. The application automatically displays the absolute roughness of the selected material.
3. Compare the resulting value in millimeters (mm), meters (m), feet (ft), and inches (in).

Select Pipe Material

-- Select a pipe material --

Absolute Roughness

Material	ε (mm)	ε (m)	ε (ft)	ε (in)
—	—	—	—	—

Mathematical Relations (Unit Conversions)

All roughness values are stored internally in millimeters (the most common unit reported by fluid-mechanics references) and converted automatically using the following relations:

$$ \varepsilon(\text{m}) = \dfrac{\varepsilon(\text{mm})}{1000} $$

$$ \varepsilon(\text{mm}) = \varepsilon(\text{m}) \times 1000 $$

$$ \varepsilon(\text{ft}) = \dfrac{\varepsilon(\text{m})}{0.3048} $$

$$ \varepsilon(\text{in}) = \dfrac{\varepsilon(\text{m})}{0.0254} $$

Base conversion factors used: 1 m = 1000 mm, 1 ft = 0.3048 m, 1 in = 0.0254 m.

Pipe Roughness Concept

The absolute roughness ε represents the average peak-to-valley height of surface irregularities on the pipe's internal wall — not the pipe's overall wall thickness.

References

• Darby, R., Chemical Engineering Fluid Mechanics, 2nd ed., Marcel Dekker, New York, 2001 (roughness table, Chapter 6, "Pipe Flow"). This textbook is the primary reference indicated for this activity.
• Transparency note on data verification: the roughness values used in this app were cross-checked against the classic pipe-roughness data set originally compiled by L. F. Moody (1944), which Darby's textbook — like most modern fluid mechanics texts — reproduces for these same materials. Because this app's author could not directly access a page scan of Darby's book to confirm exact printed digits, the values below were verified instead against multiple independent, reputable technical sources that report the same figures, listed here:
• Munson, B.R., Young, D.F., Okiishi, T.H., Fundamentals of Fluid Mechanics, 6th ed. — "Equivalent Roughness for New Pipes" table.
• White, F.M., Fluid Mechanics, 7th ed., McGraw-Hill — pipe roughness data table.
• Perry's Chemical Engineers' Handbook — pipe roughness reference values.
• Engineers Edge, "Pipe Roughness Coefficients," engineersedge.com/fluid_flow/pipe-roughness.htm — consulted for cross-verification.
• Where a source reports a range (e.g., concrete, riveted steel, wood stave) instead of a single value, this app displays the full range and uses the midpoint of that range for the numeric calculation, clearly marked as such below the results table.

Pipe Roughness Calculator — Developed by CABALLERO MEDRANO for the course Transport of Fluids. Self-contained HTML/CSS/JavaScript application. No installation required.

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Continuity Equation Calculator

Volumetric Flow Rate, Fluid Velocity, and Flow Area

Created by: Dilan Abel Acevedo Hernández | Date: September 10, 2026

How to Use This Tool

1. Select the variable you want to calculate: flow rate (Q), velocity (V), or flow area (A).
2. Enter the two known quantities using MKS units: m³/s, m/s, or m².
3. The result is calculated automatically as you enter valid data. You may also press the Calculate button.
4. The calculated value is displayed in MKS, CGS, and British (Imperial) units.
5. Negative values are not permitted, and division by zero is prevented.

Governing Equation

\[ Q = V \times A \]

\(Q\) = volumetric flow rate, \(V\) = average fluid velocity, and \(A\) = cross-sectional flow area.

Equation for selected calculation: \(Q = V \times A\)

Calculator

Variable to Calculate Volumetric Flow Rate (Q) Fluid Velocity (V) Flow Area (A)

Volumetric Flow Rate, Q (m³/s)

Fluid Velocity, V (m/s)

Flow Area, A (m²)

Enter the two known quantities in MKS units.

Results and Unit Conversions

Volumetric Flow Rate (Q)

— m³/s

Unit System	Value	Unit
MKS (SI)	—	m³/s
CGS	—	cm³/s
British (Imperial)	—	ft³/s

Conversion factors: 1 m³/s = 10⁶ cm³/s = 35.3146667 ft³/s; 1 m/s = 100 cm/s = 3.2808399 ft/s; 1 m² = 10⁴ cm² = 10.7639104 ft².

Differential distillation calculator

✨ Differential (Rayleigh) Distillation ✨

👨‍🎓 Author: ORTIZ RIOS RICARDO 📅 Date: September 10, 2026

🔬 Process Explanation & Equipment

This application solves the differential (batch) distillation of a Benzene-Toluene mixture at 101.32 kPa (1 atm). In this process, a liquid mixture is boiled in a closed still. As boiling proceeds, the generated vapor is continuously removed and condensed into a receiver.

Integral Mass Balance (Rayleigh Equation):
$$ \ln\left(\frac{L_1}{L_2}\right) = \int_{x_W}^{x_F} \frac{dx}{y - x} $$

This equation calculates the area under the curve of \( 1/(y-x) \) vs \( x \) to relate the total moles evaporated to the changing liquid composition.

📊 Data Input

📌 How to Use:

1. Select Mode: Choose whether to calculate the final Residue (\(x_W\)) or the required Vapor amount (\(V\)).
2. Input Feed Data: Enter your initial mixture composition (\(x_F\)) and total moles (\(L_1\)).
3. Set Target: Provide the known Vapor (\(V\)) or Target Residue (\(x_W\)) based on your mode.
4. Calculate: Click the button below to run the numerical integration.

Select Calculation Mode: Mode 1: Known Vapor (V) ➔ Calculate Residue (x_W) Mode 2: Known Residue (x_W) ➔ Calculate Vapor (V)

Feed Composition (\(x_F\)):

Initial Feed Amount (\(L_1\), moles):

Amount Vaporized (\(V\), moles):

Target Residue Composition (\(x_W\)):

✅ Final Results

Amount Vaporized (\(V\)):

Remaining Liquid (\(L_2\)):

Integral Value \(\ln(L_1/L_2)\):

Residue (\(x_W\)):

Average Distillate (\(y_{avg}\)):

Ethanol concentration estimator based on relative density

Ethanol Concentration Estimator

Author: Sarai J. Carrasco Miranda

Creation Date: September 2026

Operating Condition: Measurement temperature must be at 20 °C (68 °F) relative to water at 20 °C.

Description and Instructions

This web application calculates the weight percentage concentration of ethanol in aqueous solutions using specific gravity measurements at 20 °C.

How to use:

1. Measure the specific gravity of the ethanol-water solution at 20 °C.
2. Enter the measured specific gravity value in the text field below (valid range: 0.7893 to 0.9982).
3. Click "Calculate Concentration" to perform the automated calculation and visualize your point on the reference curve.

Mathematical Model

Experimental data are numerically interpolated from standard ethanol-water thermodynamic tables (CRC Handbook / Perry's):

$$C(d) = C_i + \frac{C_{i+1} - C_i}{d_{i+1} - d_i} (d - d_i)$$

Where d_i and C_i are the adjacent data points for specific gravity (SG_20/20) and concentration (% w/w) respectively.

Estimation Calculator

Specific Gravity (SG 20/20):

Fitted Curve and Data Validation

Ethanol-Water VLE Calculator

Student: Enriquez Palma

Creation date: September 8, 2026

System: Ethanol (component 1) + Water (component 2)

Total pressure: 1 atm = 101.325 kPa = 760 mmHg

Purpose

This app calculates the missing two equilibrium variables when one of the following is supplied: liquid ethanol mole fraction x, vapor ethanol mole fraction y, or temperature T.

The equilibrium data are represented with a dense table using a step of 0.001 in x, obtained by linear interpolation between the tabulated ethanol-water VLE data at 1 atm.

How to use

1. Select whether the known variable is x, y, or T.
2. Enter its value in the corresponding field.
3. Press Calculate.
4. The program reports the missing equilibrium variables.

Mole fractions are dimensionless. Temperature must be entered in °C.

Calculation

Known variable Liquid mole fraction x Vapor mole fraction y Temperature T (°C)

x

Mathematical basis

The app uses the VLE relationship represented by the experimental ethanol-water equilibrium data:

\(T=f(x),\qquad y=g(x)\)

For a supplied x, interpolation directly provides y and T. For a supplied y, the program searches the dense table for the corresponding x and T. For a supplied T, the program searches for all crossings of the temperature curve and reports every equilibrium solution when the ethanol-water azeotrope produces more than one composition at the same temperature.

Reference data

The base data correspond to ethanol-water VLE at 1 atm, with x and y as mole fractions of ethanol. The original tabulated points are shown below; the calculator internally uses a 0.001 x-step interpolation.

x ethanol	y ethanol	T (°C)

Reference: Wankat, Separation Process Engineering, ethanol-water VLE data at 1 atm (Table 2-1), as reproduced in public technical sources.

VLE Data Calculator: n-Heptane / n-Octane System

Author: Duran Flores Sandra Date: September 5, 2026

Instructions

This application automates Vapor-Liquid Equilibrium (VLE) calculations for a binary mixture of n-heptane (B) and n-octane (A) using high-density interpolated experimental data.

Total System Pressure: $P_{\text{total}} = 760 \text{ mmHg}$

Select any known parameter ($T$, $x_b$, or $y_b$), enter its value within the valid range, and click Calculate to evaluate the remaining equilibrium properties.

Mathematical Foundations

The equilibrium mole fractions are computed from vapor pressure data via Raoult's Law:

$$x_b = \frac{P_{\text{total}} - P_A^{\text{sat}}}{P_B^{\text{sat}} - P_A^{\text{sat}}}$$

$$y_b = \frac{x_b \cdot P_B^{\text{sat}}}{P_{\text{total}}}$$

Interpolation over fine sub-intervals ($\Delta T = 0.01 \text{ °C}$) guarantees numerical consistency and bi-directional accuracy across all state variables.

Select Known Parameter: Temperature, $T$ (°C) Liquid mole fraction of n-heptane, $x_b$ Vapor mole fraction of n-heptane, $y_b$

Enter Value (°C):

Equilibrium State Results

System Temperature ($T$)

-

°C

Liquid Mole Fraction ($x_b$)

-

mol n-heptane / mol

Vapor Mole Fraction ($y_b$)

-

mol n-heptane / mol