Hydraulic Engineering - PDHonline.com
Transcript of Hydraulic Engineering - PDHonline.com
PDHonline Course H146 (4 PDH)
Hydraulic Engineering
Instructor: Mohamed Elsanabary, Ph.D., Prov. Lic. Engineering.
2013
PDH Online | PDH Center
5272 Meadow Estates Drive Fairfax, VA 22030-6658
Phone & Fax: 703-988-0088 www.PDHonline.org www.PDHcenter.com
An Approved Continuing Education Provider
Hydraulic EngineeringHydraulic Engineering
Session 3Session 3
By
Dr. Mohamed Helmy Elsanabary
www.PDHcenter.com PDHonline Course H146 www.PDHonline.org
© Mohamed Elsanabary, Ph.D. Page 2 of 21
Session Goals
• Understand the gradually varied flow (GVF);Understand the gradually varied flow (GVF);
• Understand the surface slope;
d d h b d l• Understand the bed slope;
• Understand the water surface profiles;
• Calculate the water surface curve length.
© Dr. Mohamed Elsanabary
www.PDHcenter.com PDHonline Course H146 www.PDHonline.org
© Mohamed Elsanabary, Ph.D. Page 3 of 21
Gradually Varied Flow (GVF)Gradually Varied Flow (GVF)
© Dr. Mohamed Elsanabary
www.PDHcenter.com PDHonline Course H146 www.PDHonline.org
© Mohamed Elsanabary, Ph.D. Page 4 of 21
Gradually Varied Flow (GVF)Gradually Varied Flow (GVF)
Energy equation for nonuniform, steady flow with basic assumption that the change in energy with distance is equal to the friction loses
T=dA/dyT dA/dy
© Dr. Mohamed Elsanabary
www.PDHcenter.com PDHonline Course H146 www.PDHonline.org
© Mohamed Elsanabary, Ph.D. Page 5 of 21
Gradually Varied Flow (GVF)Gradually Varied Flow (GVF)
By dividing the equation by dx:
© Dr. Mohamed Elsanabary
www.PDHcenter.com PDHonline Course H146 www.PDHonline.org
© Mohamed Elsanabary, Ph.D. Page 6 of 21
Gradually Varied Flow (GVF)Gradually Varied Flow (GVF)
Therefore, the governing equation for gradually varied flow:
Where the variation of depth y with the channel distance x is shown to be a function of bed slope S0, Friction Slope , Sf and the flow Froude number F
© Dr. Mohamed Elsanabary
flow Froude number Fr .
www.PDHcenter.com PDHonline Course H146 www.PDHonline.org
© Mohamed Elsanabary, Ph.D. Page 7 of 21
Gradually Varied Flow (GVF)Gradually Varied Flow (GVF)
Gi h f d h i h di lGives change of water depth with distance along channelFor GVF calculation please note:For GVF calculation please note:• So and Sf are positive when sloping down in direction
of flow• y is measured from channel bottom• dy/dx =0means water depth is constant
• y = yn is when So=Sf
© Dr. Mohamed Elsanabary
www.PDHcenter.com PDHonline Course H146 www.PDHonline.org
© Mohamed Elsanabary, Ph.D. Page 8 of 21
Water Surface ProfilesWater Surface Profiles
© Dr. Mohamed Elsanabary
www.PDHcenter.com PDHonline Course H146 www.PDHonline.org
© Mohamed Elsanabary, Ph.D. Page 9 of 21
Water Surface ProfilesWater Surface ProfilesWhen there is a change in cross section or slope or anobstruction to the flow the qualitative analysis of the flowobstruction to the flow, the qualitative analysis of the flowprofile depends on locating the control points, determiningthe type of water surface profile upstream anddownstream of the control points, and then sketchingthese profiles. It must be remembered that when flow issupercritical (Fr > 1), the control depth is upstream and thep ( r ), p pwater surface profile analysis proceeds in the downstreamdirection. When flow is subcritical (Fr < 1), the controldepth is downstream and the computations must proceeddepth is downstream and the computations must proceedupstream. Water surface profiles that result from a changein slope of the bed are shown in the next slide:
© Dr. Mohamed Elsanabary
www.PDHcenter.com PDHonline Course H146 www.PDHonline.org
© Mohamed Elsanabary, Ph.D. Page 10 of 21
Water Surface ProfilesWater Surface Profiles
© Dr. Mohamed Elsanabary
www.PDHcenter.com PDHonline Course H146 www.PDHonline.org
© Mohamed Elsanabary, Ph.D. Page 11 of 21
Water Surface ProfilesWater Surface ProfilesExample:A 16 ft wide, rectangular channel goes from a very steep grade to amild slope The design discharge is 875 ft3/s and the normal depth andmild slope. The design discharge is 875 ft3/s and the normal depth andvelocity on the steep slope were calculated to be 1.0 ft and 49 ft/s,respectively. On the mild slope, the normal depth and velocity werecalculated to be 9 71 ft and 5 51 ft/s respectively Determine the typecalculated to be 9.71 ft and 5.51 ft/s, respectively. Determine the typeof flow occurring in both channels. If a hydraulic jump occurs, evaluatethe depth downstream of the hydraulic jump, the location of the jump,and the water surface profile classification.p
© Dr. Mohamed Elsanabary
www.PDHcenter.com PDHonline Course H146 www.PDHonline.org
© Mohamed Elsanabary, Ph.D. Page 12 of 21
Water Surface ProfilesWater Surface Profiles
© Dr. Mohamed Elsanabary
www.PDHcenter.com PDHonline Course H146 www.PDHonline.org
© Mohamed Elsanabary, Ph.D. Page 13 of 21
Water Surface ProfilesWater Surface Profiles
© Dr. Mohamed Elsanabary
www.PDHcenter.com PDHonline Course H146 www.PDHonline.org
© Mohamed Elsanabary, Ph.D. Page 14 of 21
Water Surface ProfilesWater Surface Profiles
© Dr. Mohamed Elsanabary
www.PDHcenter.com PDHonline Course H146 www.PDHonline.org
© Mohamed Elsanabary, Ph.D. Page 15 of 21
Computation of GVFComputation of GVF
© Dr. Mohamed Elsanabary
www.PDHcenter.com PDHonline Course H146 www.PDHonline.org
© Mohamed Elsanabary, Ph.D. Page 16 of 21
Computation of GVFComputation of GVF
© Dr. Mohamed Elsanabary
www.PDHcenter.com PDHonline Course H146 www.PDHonline.org
© Mohamed Elsanabary, Ph.D. Page 17 of 21
Computation of GVFComputation of GVF
© Dr. Mohamed Elsanabary
www.PDHcenter.com PDHonline Course H146 www.PDHonline.org
© Mohamed Elsanabary, Ph.D. Page 18 of 21
Computation of GVFComputation of GVF
© Dr. Mohamed Elsanabary
www.PDHcenter.com PDHonline Course H146 www.PDHonline.org
© Mohamed Elsanabary, Ph.D. Page 19 of 21
AssignmentAssignment
© Dr. Mohamed Elsanabary
www.PDHcenter.com PDHonline Course H146 www.PDHonline.org
© Mohamed Elsanabary, Ph.D. Page 20 of 21
AssignmentAssignment
© Dr. Mohamed Elsanabary
www.PDHcenter.com PDHonline Course H146 www.PDHonline.org
© Mohamed Elsanabary, Ph.D. Page 21 of 21