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/m3 (at 290°C). The angle of the elbow is 45°.
Calculate the force on the wall of a deflector elbow (i.e. calculate vector F3).
- 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: