An elbow (let say of primary piping) is used to deflect water flow at a velocity of 17 m/s. Calculate the force on the wall of a deflector elbow. Thermal Engineering
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).
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:
References:
Reactor Physics and Thermal Hydraulics:
J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading, MA (1983).
J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.
W. M. Stacey, Nuclear Reactor Physics, John Wiley & Sons, 2001, ISBN: 0- 471-39127-1.
Todreas Neil E., Kazimi Mujid S. Nuclear Systems Volume I: Thermal Hydraulic Fundamentals, Second Edition. CRC Press; 2 edition, 2012, ISBN: 978-0415802871
Zohuri B., McDaniel P. Thermodynamics in Nuclear Power Plant Systems. Springer; 2015, ISBN: 978-3-319-13419-2
Moran Michal J., Shapiro Howard N. Fundamentals of Engineering Thermodynamics, Fifth Edition, John Wiley & Sons, 2006, ISBN: 978-0-470-03037-0
Kleinstreuer C. Modern Fluid Dynamics. Springer, 2010, ISBN 978-1-4020-8670-0.
U.S. Department of Energy, THERMODYNAMICS, HEAT TRANSFER, AND FLUID FLOW. DOE Fundamentals Handbook, Volume 1, 2 and 3. June 1992.
White Frank M., Fluid Mechanics, McGraw-Hill Education, 7th edition, February, 2010, ISBN: 978-0077422417
See also:
Conservation of Momentum
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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°.
