How is pressure loss in a hose calculated?

The pressure loss in a flexible hose is typically determined by establishing an equivalent length multiplier relative to a clean carbon steel pipe (with a baseline roughness of 0.05 mm), and then solving the standard Darcy-Weisbach or Fanning friction equation for that total equivalent pipe length.

What is the equivalent length factor for a corrugated metal hose?

A corrugated metal hose has a high equivalent length multiplier relative to 0.05 mm roughness steel pipe, typically ranging between 2.3 and 2.5 times the physical hose length, due to severe internal turbulence.

Pressure losses in hoses : how to calculate

Follow us on Twitter
Question, remark ? Contact us at contact@myengineeringtools.com

Introduction
What is a Hose?
Different Types of Hoses
How to Calculate Pressure Loss in a Hose
Interactive Online Hose Pressure Drop Calculator
Conclusion

1. Introduction

Understanding pressure losses in hoses is crucial for engineers in designing and optimizing fluid transport systems. This article aims to provide a comprehensive understanding of hoses, their types, and how to calculate pressure losses in them.

2. What is a Hose?

A hose is a flexible conduit designed to transport fluids from one location to another. Hoses are used in a myriad of applications, from garden watering to high-pressure industrial processes. The functionality of a hose is largely dependent on its ability to withstand the operating pressure and temperature while minimizing pressure losses.

3. Different Types of Hoses

Hoses can be categorized based on their material construction, diameter, length, and the type of connectors used. Common materials include rubber, PVC, stainless steel, and Teflon, each with unique properties affecting flexibility, durability, pressure handling, and, consequently, pressure loss.

For instance, rubber hoses are flexible and resistant to wear, making them suitable for high-pressure applications. On the other hand, stainless steel hoses, while less flexible, offer high temperature and chemical resistance.

Hoses come in a wide array of types, categorized based on the materials they are constructed from and their design:

3.1 Classification Based on Material

a. Rubber Hoses: Known for their excellent flexibility, resistance to abrasion, and compatibility with a wide range of fluids. They are often used for applications involving water, air, and hydraulic fluids.

b. PVC Hoses: PVC (polyvinyl chloride) hoses are lightweight and cost-effective. They are commonly used for the transfer of non-corrosive fluids, such as water and some chemicals.

c. Thermoplastic Hoses: These hoses are lightweight, durable, and suitable for applications where resistance to chemical attack and high pressure is required.

3.2 Classification Based on Construction

a. Reinforced Hoses: These hoses have an inner tube for fluid transfer and additional layers of reinforcement, such as textile, steel wire, or fiber, to provide strength and prevent kinking or collapsing under pressure.

b. Non-Reinforced Hoses: Non-reinforced hoses are suitable for low-pressure applications and may consist of a single layer of material. They are generally used for light-duty tasks.

The choice of hose type depends on factors like the nature of the fluid being transported, the working environment, and the required flexibility and strength.

4. How to Calculate Pressure Loss in a Hose

Pressure loss in a hose, often referred to as head loss, is a decrease in fluid pressure as the fluid moves through the hose. It's primarily caused by frictional forces between the fluid and the inner surface of the hose.

Several factors contribute to pressure loss in a hose:

Length of the Hose : Longer hoses result in higher pressure losses due to the increased contact between the fluid and hose material.
Diameter of the Hose : Smaller diameters lead to higher pressure losses as they create more resistance to fluid flow.
Flow Rate : Higher flow rates increase the velocity of the fluid, leading to greater pressure losses.
Fluid Viscosity: More viscous fluids experience higher frictional forces, resulting in increased pressure losses.

The method found in the literature to calculate the pressure loss in a hose is to calculate the equivalent length considering a steel pipe with a roughness of 0.05 mm and then apply an equivalence to the length of the hose according to the following references [1] :

Hose Type	Equivalent length multiplier vs steel pipe (0.05 mm roughness)
Rubber hose, smooth	0.6 - 0.9
Rubber hose, with wire reinforcement	0.7 - 1.3
Metal hose corrugated	2.3 - 2.5

Step 1 : Calculate the hose length in the circuit considered

Determine the physical hose length of the circuit under evaluation.

Step 2 : Determine Equivalent Carbon Steel Pipe Length

Convert this length to equivalent length with the hose. For example, if the hose length (without singularities) of a metal corrugated hose is 10 m, the equivalent length in carbon steel (roughness 0.05 mm) will be \(10 \times 2.5 \text{ m} = 25 \text{ m}\).

Step 3 : Add Singularities/Fittings

Add the equivalent length of singularities (fittings, valves, elbows) to the equivalent straight pipe length calculated before.

Step 4 : Apply Darcy-Weisbach Equation

Calculate the pressure loss in the circuit thanks to the Darcy-Weisbach equation, considering the total equivalent length applied to a steel pipe with roughness \(\epsilon = 0.05 \text{ mm}\).

The formula to calculate pressure loss in a hose is given by the Darcy-Weisbach equation:

\[ \frac{f}{2} = \frac{D_H}{4 \cdot \rho \cdot u_m^2} \frac{\Delta P_f}{L} \] \[ \Rightarrow \Delta P_f = 4 \cdot \rho \cdot u_m^2 \cdot \frac{f/2}{D_H} \cdot L \]

\(f/2\) = Fanning friction factor (dimensionless)
\(D_H\) = Hydraulic diameter in m
\(u_m\) = Mean fluid velocity in m/s
\(\Delta P_f\) = Pressure drop due to friction in Pa
\(L\) = Length of pipe in m
\(\rho\) = Fluid density in \(kg/m^3\)
* Note: \(f\) in the formula image acts as the Fanning friction factor. The Darcy friction factor \(f_D = 4 \cdot (f/2) = 2f\).

💡 PLANT ENGINEERING RULES OF THUMB & SAFETY LIMITS

Liquid Velocity Limits: Keep continuous liquid suction velocity under 1.2 m/s (4 ft/s) and discharge velocity under 3.0 m/s (10 ft/s) for optimal hose lifespan. Higher velocities cause rapid erosion of internal lining.
Corrugated Hoses: Expect severe pressure drops (2.3x - 2.5x of steel pipe) in corrugated metal hoses due to continuous turbulence generation.
Bending Factor: Dynamic installations with bends sharper than the manufacturer's Minimum Bend Radius (MBR) can increase local pressure losses by over 50% and drastically accelerate mechanical failure.
Roughness Standard: Always use \(\epsilon = 0.05\text{ mm}\) (carbon steel baseline) when applying the hose equivalence method.

⚠️ ENGINEERING NOTICE & EDUCATIONAL DISCLAIMER: This interactive calculator is provided exclusively for preliminary estimation and educational purposes. It is not intended for detailed design or equipment procurement without certified vendor rating. No warranty, expressed or implied, is provided, and no liability is assumed.

🧮 Hose Pressure Drop Sizing Calculator

Hose Material/Type

Equivalent Length Multiplier

Hose Physical Length (m)

Hose Internal Diameter (mm)

Volumetric Flow Rate (m³/h)

Fluid Density (kg/m³)

Fluid Viscosity (cP)

Fittings Equivalent Length (m)

Calculation Results

Equivalent Hose Straight Length: -

Total Circuit Equivalent Length: -

Fluid Velocity: -

Reynolds Number (Re): -

Fanning Friction Factor (f): -

Darcy Friction Factor (f_D): -

TOTAL PRESSURE LOSS: -

5. Conclusion

Accurately calculating pressure loss in hoses is vital for system efficiency and safety. Understanding the types of hoses and their impact on pressure loss allows engineers to make informed decisions when designing fluid transport systems. As engineers, we must continue to refine our calculations and understandings to optimize our designs and operations.

Source References

[1] Neutrium.net