GENERAL FORMULA TO DETERMINE BEND LENGTH \( \frac{\text { Angle of Bend }}{360^{\circ}} \times \begin{array}{l}2 \pi r=\text { minimum length of those to make bend } \\ r=\text { given bend radius of hose }\end{array} \) Example: To make a \( 90^{\circ} \) bend with a hose with a 2 " I.D. Given \( r=4.5 \) inches \[ \frac{90^{\circ}}{360^{\circ}} \quad[2 \times 3.14 \times 4.5] \quad .25 \times 2 \times 3.14 \times 4.5=7 \text { " } \]

To determine the **bend length** of a hose (or any flexible tubular component), you can use the following general formula: \[ \text{Bend Length} = \left( \frac{\text{Angle of Bend}}{360^\circ} \right) \times 2\pi r \] Where: - **Angle of Bend** is the total angle through which you want to bend the hose (in degrees). - \( r \) is the **bend radius**, which is the distance from the centerline of the hose to the center of the bend. - \( \pi \) (Pi) is approximately 3.1416. ### **Understanding the Formula** 1. **Circumference Calculation**: - The term \( 2\pi r \) calculates the circumference of a full circle with radius \( r \). This represents the total length around the bend if it were a complete 360-degree circle. 2. **Proportion of Bend**: - By multiplying the circumference by the fraction \( \frac{\text{Angle of Bend}}{360^\circ} \), you determine the length corresponding to the specific bend angle you're creating. ### **Step-by-Step Example** **Given:** - **Angle of Bend** = \( 90^\circ \) - **Inner Diameter (I.D.)** of Hose = 2 inches - **Bend Radius (\( r \))** = 4.5 inches **Calculation:** 1. **Plug the values into the formula:** \[ \text{Bend Length} = \left( \frac{90^\circ}{360^\circ} \right) \times 2\pi \times 4.5 \text{ inches} \] 2. **Simplify the fraction:** \[ \frac{90^\circ}{360^\circ} = 0.25 \] 3. **Calculate the circumference part:** \[ 2\pi r = 2 \times 3.14 \times 4.5 = 28.26 \text{ inches} \quad (\text{Using } \pi \approx 3.14) \] 4. **Determine the bend length:** \[ \text{Bend Length} = 0.25 \times 28.26 = 7.065 \text{ inches} \] **Rounded Off:** \[ \text{Bend Length} \approx 7 \text{ inches} \] ### **Visual Representation** Imagine the hose forming a quarter-circle (since \( 90^\circ \) is a quarter of \( 360^\circ \)). The **bend length** is essentially the length of the hose along that quarter-circle. ### **Key Points to Consider** - **Bend Radius Selection**: The bend radius \( r \) should typically be larger than the hose's inner diameter to prevent kinking and ensure smooth flow. In your example, with an I.D. of 2 inches, a bend radius of 4.5 inches provides a sufficient curvature. - **Material Flexibility**: Ensure that the hose material can accommodate the calculated bend without sustaining damage or compromising performance. - **Applications**: This formula is widely applicable in plumbing, automotive hoses, pneumatic systems, and any scenario where hoses or tubing need to be routed through bends. ### **Final Formula Recap** \[ \boxed{\text{Bend Length} = \left( \frac{\text{Angle of Bend}}{360^\circ} \right) \times 2\pi r} \] This formula provides a straightforward method to calculate the necessary length of hose required to achieve a desired bend, ensuring both functionality and longevity of the hose system.