⚡ electrical engineering

Diameter-Dependent Roughness Characterization and Cross-Standard Validation of Hydraulic Friction Loss in Flexible Fire Hoses

This study validates the necessity of using empirically determined, diameter-specific friction coefficients for flexible fire hoses by demonstrating through laboratory experiments and CFD simulations that their hydraulic friction losses significantly exceed smooth-pipe theoretical predictions due to structural and material irregularities.

Original authors: Rongxuan Zhao, Shuanghong Yang, Wantong Wang, Jin Qingsheng

Published 2026-07-08

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Rongxuan Zhao, Shuanghong Yang, Wantong Wang, Jin Qingsheng

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Big Picture: Why Fire Hoses Are Tricky

Imagine you are trying to water a garden using a long, flexible hose. If the hose is brand new, smooth, and rigid, the water flows easily. But fire hoses are different. They are made of a rubber lining wrapped in a woven fabric jacket. They are flexible, they can stretch a little under pressure, and their insides aren't perfectly smooth like a metal pipe.

This study asked a simple but critical question: How much does the water slow down and lose pressure as it travels through these specific types of fire hoses?

Getting this math right is like knowing exactly how much gas your car needs to drive up a hill. If you guess wrong:

Underestimate: You might not have enough water pressure at the nozzle to put out the fire.
Overestimate: You might use a pump that is way too big, making the equipment heavy and hard to carry.

The Experiment: The "Torture Test" for Hoses

The researchers from the China Fire and Rescue Institute set up a controlled laboratory "race track" to test two common sizes of fire hoses:

The "Small" Hose (D40): About 40mm wide (roughly the size of a large garden hose).
The "Big" Hose (D65): About 65mm wide (roughly the size of a large industrial hose).

How they did it:

They laid out a straight 20-meter (about 65 feet) section of hose.
They used a powerful fire truck pump to push water through at different speeds.
They measured the pressure at the start and the end to see how much "energy" the water lost just by rubbing against the inside of the hose.
They did this dozens of times to get a perfect average.

The Findings: The Numbers Check Out

The researchers compared their new, high-precision data against the official rules (the Chinese National Standard GB 50974-2014) that engineers currently use to design fire systems.

The Result: The official rules were spot on.

For the small hose, their new math matched the old rule with a tiny error of just 0.22%.
For the big hose, the error was only 2.73%.

The Analogy: It's like having a map that says a drive takes 30 minutes. You actually drive it 100 times with a stopwatch, and you find out it takes 29 minutes and 50 seconds. The map was accurate enough to trust.

The "Smooth Pipe" Myth

One of the most interesting parts of the study is what happens if you try to use standard physics formulas meant for smooth, rigid pipes (like the ones inside your house).

The Theory: Standard formulas assume the inside of the pipe is as smooth as glass.
The Reality: Fire hoses are rougher. The rubber lining and the woven fabric create tiny bumps and ridges inside.
The Discovery: When the researchers calculated the friction using standard "smooth pipe" math, they were two to three times too low.

The Analogy: Imagine running on a track.

Smooth Pipe Theory: You are running on a smooth, rubberized Olympic track. You can run very fast with little effort.
Fire Hose Reality: You are running on a track covered in sand and pebbles. You have to work much harder to go the same speed.
The Lesson: If you use the "Olympic track" math for a "pebble track," you will severely underestimate how much energy (pump power) you need.

The Computer Simulation: Seeing the Invisible

Since you can't see inside a hose while water is rushing through it at high speed, the researchers also built a 3D computer model (a digital twin) of the hoses.

They simulated the water flowing through the digital hoses.
The computer results matched their real-world experiments almost perfectly (within 1% error).
What they saw: The computer showed that the water swirls and tumbles violently near the walls of the hose (turbulence). This "churning" is what creates the friction. The model confirmed that the roughness of the rubber lining is the main culprit slowing the water down.

The "Stretch" Factor

The study also looked at how the hoses behave under pressure.

The Observation: As water pushes harder, the hoses stretch slightly, getting a tiny bit wider.
The Effect: For the larger hose, this stretching made the water flow slightly easier than a rigid pipe would, causing the friction to drop just a tiny bit more than a perfect square-law prediction.
The Takeaway: It's a small detail, but it proves that fire hoses are "alive" and flexible, not just static pipes.

The Bottom Line

This paper didn't invent a new type of hose or a new way to fight fires. Instead, it acted as a quality control check.

It confirmed that:

The current rules engineers use to calculate fire hose pressure are correct and reliable.
You cannot use standard "smooth pipe" formulas for fire hoses; you must use the specific numbers for these rough, flexible hoses, or your fire truck pump won't be strong enough.
The friction loss in these hoses follows a predictable "square" pattern (if you double the water speed, the pressure loss quadruples), which makes it easy for engineers to plan for emergencies.

In short: The math we are using today works, but it relies on the specific, rough nature of fire hoses, not the smooth nature of regular pipes.

Technical Summary: Diameter-Dependent Roughness Characterization and Cross-Standard Validation of Hydraulic Friction Loss in Flexible Fire Hoses

Problem Statement
Accurate characterization of friction loss is critical for the design and safety of fire protection water supply systems. While classical pipe flow theories (e.g., Darcy-Weisbach, Colebrook-White) and smooth-pipe correlations are well-established for rigid conduits, they are inadequate for flexible fire hoses. These hoses possess unique hydraulic environments characterized by rubber lining roughness, woven jacket structural irregularities, and wall compliance under pressure.

In China, the national standard GB 50974-2014 prescribes reference resistance coefficients for D40 (40 mm) and D65 (65 mm) hoses. However, these values were derived from limited historical data and have not been systematically validated against contemporary hose products manufactured with modern rubber compounding and textile weaving technologies. Furthermore, existing literature often focuses on U.S. hose specifications or specific deformation behaviors without directly measuring friction loss coefficients for the specific hose types universally deployed in Chinese fire services. This gap creates a risk of underestimating or overestimating pressure drops, potentially compromising firefighting effectiveness or leading to unnecessarily conservative system designs.

Methodology
The study employed a dual approach combining controlled laboratory experiments and Computational Fluid Dynamics (CFD) simulations to investigate D40 and D65 rubber-lined woven fire hoses.

Experimental Setup: A 20-meter straight hose lay was tested using a fire truck pump capable of delivering up to 25 L/s. High-precision instrumentation, including an electromagnetic flowmeter (±0.5% accuracy) and a calibrated differential pressure transmitter (±0.25% accuracy), measured pressure drops across the test section.
Test Conditions: Experiments were conducted at ambient temperatures (~20°C). For the D40 hose, 15 data points were collected across six test groups (flow rates 4.0–5.8 L/s). For the D65 hose, 42 data points were collected across seven groups (flow rates 7.8–12.5 L/s).
Data Processing: Resistance coefficients ( $S$ ) were calculated using the relationship derived from the Darcy-Weisbach equation ( $S = \Delta P / (9.81 \times Q^2 \times L)$ ). Linear regression and power-law fitting were used to verify the quadratic relationship between pressure drop and flow rate and to determine flow regime exponents.
CFD Simulation: Three-dimensional RANS simulations using the SST $k-\omega$ turbulence model were conducted to validate experimental results and visualize internal flow structures. The hose internal surfaces were modeled with equivalent sand-grain roughness heights (0.13 mm for D40, 0.10 mm for D65) derived from experimental friction factors. Mesh independence studies confirmed grid-converged solutions.

Key Results

Resistance Coefficients: The experimentally determined mean resistance coefficients were 0.0449 s²/L²·m for the D40 hose and 0.00226 s²/L²·m for the D65 hose. These values show excellent agreement with the GB 50974-2014 standard references (0.045 and 0.0022, respectively), yielding relative errors of 0.22% and 2.73%.
Flow Regime Validation: Power-law analysis yielded exponents of 1.987 for D40 and 1.974 for D65. These values are close to the theoretical value of 2.0, confirming that the flow operates in a fully turbulent regime and validating the quadratic friction loss model for engineering calculations.
Friction Factor Discrepancy: The Darcy friction factors derived from the experiments were found to be two to three times higher than predictions made by the Blasius equation for smooth pipes. This highlights the significant impact of the hose's internal roughness and structural irregularities.
CFD Validation: The CFD model demonstrated excellent agreement with experimental data, with mean absolute relative errors of 1.0% (D40) and 1.1% (D65). The simulations confirmed that the entrance region accounts for less than 2% of total pressure drop and provided detailed insights into wall shear stress and turbulence kinetic energy distributions, which peak in the near-wall buffer layer.

Significance and Claims
The authors claim that this study provides robust experimental validation for the current resistance coefficients specified in Chinese national standards, confirming their applicability to modern hose manufacturing. The research emphasizes that theoretical estimates based on smooth-pipe assumptions are insufficient for flexible fire hoses due to the coupled effects of rubber lining roughness, woven jacket irregularities, and wall compliance.

By confirming the validity of the quadratic friction loss model and quantifying the specific resistance coefficients, the study supports the continued use of established design values in engineering practice while underscoring the critical necessity of relying on empirically determined coefficients rather than theoretical smooth-pipe estimates for accurate hydraulic network analysis and system safety optimization. The validated CFD model further offers a reliable tool for investigating internal flow physics and extrapolating friction loss predictions beyond tested ranges.