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Date of download: 12/16/2017 Copyright © ASME. All rights reserved.

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1 Date of download: 12/16/2017 Copyright © ASME. All rights reserved. From: Unsteady Velocity Profiles in Laminar and Turbulent Water Hammer Flows J. Fluids Eng. 2009;131(12): doi: / Figure Legend: Positive and negative characteristics for water hammer problem

2 Date of download: 12/16/2017 Copyright © ASME. All rights reserved. From: Unsteady Velocity Profiles in Laminar and Turbulent Water Hammer Flows J. Fluids Eng. 2009;131(12): doi: / Figure Legend: Introduction of variables in a part of pipe for implicit characteristics method

3 Date of download: 12/16/2017 Copyright © ASME. All rights reserved. From: Unsteady Velocity Profiles in Laminar and Turbulent Water Hammer Flows J. Fluids Eng. 2009;131(12): doi: / Figure Legend: Velocity profile in steady turbulent pipe flow: (a) Re=40,000 and (b) Re=58,650

4 Date of download: 12/16/2017 Copyright © ASME. All rights reserved. From: Unsteady Velocity Profiles in Laminar and Turbulent Water Hammer Flows J. Fluids Eng. 2009;131(12): doi: / Figure Legend: Experimental apparatus with copper pipe line

5 Date of download: 12/16/2017 Copyright © ASME. All rights reserved. From: Unsteady Velocity Profiles in Laminar and Turbulent Water Hammer Flows J. Fluids Eng. 2009;131(12): doi: / Figure Legend: Pressure-time history at the pipe-midpoint: (a) laminar water hammer, Re=82 and (b) turbulent water hammer, Re=6166

6 Date of download: 12/16/2017 Copyright © ASME. All rights reserved. From: Unsteady Velocity Profiles in Laminar and Turbulent Water Hammer Flows J. Fluids Eng. 2009;131(12): doi: / Figure Legend: Velocity profiles at the pipe-midpoint for the turbulent water hammer: (a) test no. 2, P=40 and (b) test no. 3, P=2

7 Date of download: 12/16/2017 Copyright © ASME. All rights reserved. From: Unsteady Velocity Profiles in Laminar and Turbulent Water Hammer Flows J. Fluids Eng. 2009;131(12): doi: / Figure Legend: Velocity contours along the pipe length for test no. 2 (the velocity values are normalized as a percentage of initial bulk velocity)

8 Date of download: 12/16/2017 Copyright © ASME. All rights reserved. From: Unsteady Velocity Profiles in Laminar and Turbulent Water Hammer Flows J. Fluids Eng. 2009;131(12): doi: / Figure Legend: Velocity profiles at the pipe-midpoint for the laminar water hammer, test no. 1

9 Date of download: 12/16/2017 Copyright © ASME. All rights reserved. From: Unsteady Velocity Profiles in Laminar and Turbulent Water Hammer Flows J. Fluids Eng. 2009;131(12): doi: / Figure Legend: Shear stress profiles at the pipe-midpoint for the turbulent water hammer, test no 2: (a) in the whole cross section of the pipe and (b) in the pipe near wall


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