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 $$ \frac{90^{\circ}}{360^{\circ}} \quad[2 \times 3.14 \times 4.5] \quad .25 \times 2 \times 3.14 \times 4.5=7 \text { " } $$

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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.
To find the bend length, use the formula: $$ \text{Bend Length} = \left( \frac{\text{Angle of Bend}}{360^\circ} \right) \times 2\pi r $$ **Example:** For a $$ 90^\circ $$ bend with a 4.5-inch radius: $$ \text{Bend Length} = \left( \frac{90}{360} \right) \times 2 \times 3.14 \times 4.5 = 7 \text{ inches} $$ So, the bend length is 7 inches.

GENERAL FORMULA TO DETERMINE BEND LENGTH

Example: To make a bend with a hose with a 2 " I.D. Given inches

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GENERAL FORMULA TO DETERMINE BEND LENGTH Example: To make a bend with a hose with a 2 " I.D. Given inches