## Example: The force acting on a deflector elbow

**An elbow** (let say of primary piping) is used to deflect water flow at a velocity of **17 m/s**. The piping diameter is equal to** 700 mm**. The gauge pressure inside the pipe is about **16 MPa** at the temperature of 290°C. Fluid is of constant density **⍴ ~ 720 kg/m ^{3}** (at 290°C). The angle of the elbow is

**45°**.

Calculate the **force on the wall** of a deflector elbow (i.e. calculate vector F_{3}).

**Assumptions:**

- The flow is steady.
- The frictional losses are negligible.
- The weight of the elbow is negligible.
- The weight of the water in the elbow is negligible.

We take the elbow as the **control volume**. The control volume is shown at the picture. The momentum equation is a vector equation so it has three components. We take the x- and z- coordinates as shown and we will solve the problem separately according to these coordinates.

First, let us consider the component in the **x-coordinate**. The conservation of linear momentum equation becomes:

Second, let us consider the component in the **y-coordinate**. The conservation of linear momentum equation becomes:

The final force acting on the wall of a deflector elbow will be:

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