Module 3d: Flow in Pipes Manning s Equation

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Dulcie Norman
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1 Module d: Flow i Pipes Maig's Equatio for velocity ad flow applicable to both pipe (closed-coduit) flow ad ope chael flow. Robert Pitt Uiversity of Alabama ad hirley Clark Pe tate - Harrisburg It is typically applied oly i ope-chael flow (fluid i cotact with atmosphere). For Fluid Velocity i U.. Customary Uits: For Fluid Velocity i I Uits: V 1.86R R V / Where V velocity (ft/sec) R hydraulic radius (ft) slope of the eergy grade lie Maig s roughess coefficiet Where V velocity (m/sec) R hydraulic radius (m) slope of the eergy grade lie Maig s roughess coefficiet 1

2 urface Ucoated cast-iro pipe Coated cast-iro pipe Commercial wrought-iro pipe, galvaized mooth brass ad glass pipe Vitrified sewer pipe Commo clay draiage tile Glazed brickwork : Values Commercial wrought-iro pipe, black mooth lockbar ad welded O pipe Brick i cemet mortar; brick sewers Best / Good I: Metcalf & Eddy, Ic. (George Tchobaoglous). Wastewater Egieerig: Collectio ad Pumpig of Wastewater. McGraw-Hill, Ic (Table -1) Bad urface Neat cemet surfaces Cemet mortar surfaces Cocrete pipe Wood stave pipe Plak flumes Plaed Uplaed With battes Cocrete-lied chaels Cemet-rubble surface ry-rubble surface ressed-ashlar surface : Values Best Good I: Metcalf & Eddy, Ic. (George Tchobaoglous). Wastewater Egieerig: Collectio ad Pumpig of Wastewater. McGraw-Hill, Ic (Table -1) : Values : Values urface Best Good Bad urface Best Good Bad emicircular metal flumes, smooth emicircular metal flumes, corrugated Caals ad ditches Earth, straight ad uiform Rock cuts, smooth ad uiform Rock cuts, jagged ad irregular redged-earth chaels Caals, rough stoy beds, weeds o earth baks Earth bottom, rubble sides Natural-stream chaels Clea, straight bak, full stage, o rifts/deep pools Clea, straight bak, full stage, o rifts deep pools, but some weeds/stoe Widig, some pools ad shoals, clea Widig, some pools/shoals, clea, lower stages, more ieffective slope/sectios Widig, some pools/shoals, some weeds/stoes Widig, some pools/shoals, clea, lower stages, more ieffective slope/sectios, stoy sectios luggish river reaches, weedy or very deep pools Very weedy reaches I: Metcalf & Eddy, Ic. (George Tchobaoglous). Wastewater Egieerig: Collectio ad Pumpig of Wastewater. McGraw-Hill, Ic (Table -1) I: Metcalf & Eddy, Ic. (George Tchobaoglous). Wastewater Egieerig: Collectio ad Pumpig of Wastewater. McGraw-Hill, Ic (Table -1)

3 Nature of urface Cocrete Pipe Corrugated Metal Pipe Vitrified Clay Pipe teel Pipe Moolithic Cocrete Cemet Rubble Brick Lamiated Treated Wood Ope Chaels Lied with Cocrete : Values Earth, clea, after weatherig Maig s Rage I: Viessma ad Hammer. Water upply ad Pollutio Cotrol, ixth Editio (Table 6.1) Adapted from: esig Charts for Ope-Chael Flow. U.. epartmet of Trasportatio, Federal Highway Admiistratio, Hydraulic esig eries No., U.. Govermet Pritig Office, Washigto,.C Nature of urface Ope Chaels Excavated i rock, smooth Natural tream Chaels No boulders or brush ese growth of weeds Excavated i rock, smooth : Values Earth, with grass ad some weeds Excavated i rock, jagged ad irregular Bottom of cobbles with large boulders Earth, with grass ad some weeds Excavated i rock, jagged ad irregular Maig s Rage I: Viessma ad Hammer. Water upply ad Pollutio Cotrol, ixth Editio (Table 6.1) Adapted from: esig Charts for Ope-Chael Flow. U.. epartmet of Trasportatio, Federal Highway Admiistratio, Hydraulic esig eries No., U.. Govermet Pritig Office, Washigto,.C Example: What is the velocity of water i a 1-ich diameter cocrete pipe that has a slope of %, assumig that the pipe is flowig full? The roughess coefficiet for cocrete. % 0.0 Calculate hydraulic radius, R. R (pipe full) / [(1 ich)/(1 i/ft)]/ 0.01 ft ubstitutig ito :.9 V (0.01 ft) (0.0) V 11.6(0.076)(0.11) 1 V 1. ft/sec iameter of a Pipe Flowig Full Usig Maig s Equatio for Velocity 1.9 V R π A P π R π A P π

4 iameter of a Pipe Flowig Full Usig Maig s Equatio for Velocity 1.9 V V 1.9 V 1.9 V 1.9 / / For Fluid Flow i U.. Customary Uits: Where 1.86AR Q Q flow (ft /sec) A cross-sectioal area of flow (ft ) R hydraulic radius (ft) slope of the eergy grade lie Maig s roughess coefficiet For Fluid Flow i I Uits: Example: etermie the discharge of a trapezoidal chael havig a brick bottom ad grassy sides, with the followig dimesios: depth 6 ft, bottom width 1 ft, top width 18 ft. Assume Q AR Where Q flow (m /sec) A cross-sectioal area of flow (m ) R hydraulic radius (m) slope of the eergy grade lie Maig s roughess coefficiet For the rectagular area with the brick bottom: To use Maig s, eed A ad R: A (epth of Flow)(Bottom Width of Chael) A (6 ft)(1 ft) 7 ft P wetted perimeter 1 ft R A/P 7 ft /1 ft 6 ft

5 ubstitutig ito Maig s: 1.9 Q (7 ft )(6 ft) Q ft /sec Q 91ft /sec (0.00) For the two triagular areas with grass-lied sides: To use Maig s, eed A ad R for oe side: A (0.5)(epth of Flow)(Width of Oe ide) A 0.5(6 ft)( ft) 9 ft To use Maig s, eed A ad R for oe side: P hypoteuse of right triagle P (epth of Flow) + (Width of Oe ide) P (6 ft) + ( ft) P 6 ft + 9 ft 5 ft P 6.71 ft R A/P 9 ft/6.71 ft) 1.5 ft ubstitutig ito Maig s for oe side of the chael: 1.9 Q (9 ft )(1.5 ft) Q 9. ft /sec (0.00) Total Flow Flow from Rectagular ectio + (Flow from Oe Triagular ectio) iameter of a Pipe Flowig Full Usig Maig s Equatio for Flow 1.9 Q AR Total Flow 91 cfs + (9. cfs) cfs π A P π R π A P π 5

1998. Also ca use omographs to get solutio. Also ca use omographs to get solutio. From: Metcalf ad Eddy, Ic. ad George Tchobaoglous.

6 iameter of a Pipe Flowig Full Usig Maig s Equatio for Flow 1.9 π Q Q 1.9 Q 1.9π Q 1/ 1.9π 5 / Q 1/ 1.9π π 5 / Q 1.9π / 8 8 / 8 / Also ca use omographs to get solutio. From: Warre Viessma, Jr. ad Mark Hammer. Water upply ad Pollutio Cotrol ixth Editio. Addiso-Wesley Also ca use omographs to get solutio. Also ca use omographs to get solutio. From: Metcalf ad Eddy, Ic. ad George Tchobaoglous. Wastewater Egieerig: Collectio ad Pumpig of Wastewater. McGraw-Hill, Ic From: Metcalf ad Eddy, Ic. ad George Tchobaoglous. Wastewater Egieerig: Collectio ad Pumpig of Wastewater. McGraw-Hill, Ic

Also ca use omographs to get solutio. Also ca use omographs to get solutio. From: Metcalf ad Eddy, Ic. ad George Tchobaoglous. Wastewater Egieerig: Collectio ad Pumpig of Wastewater. McGraw-Hill, Ic.

Example: Give a 0-ich cocrete coduit with a roughess coefficiet of, 0.005 ad a discharge capacity of 9.85 cfs, what diameter pipe is required to quadruple the capacity.

7 Also ca use omographs to get solutio. Also ca use omographs to get solutio. From: Metcalf ad Eddy, Ic. ad George Tchobaoglous. Wastewater Egieerig: Collectio ad Pumpig of Wastewater. McGraw-Hill, Ic From: Metcalf ad Eddy, Ic. ad George Tchobaoglous. Wastewater Egieerig: Collectio ad Pumpig of Wastewater. McGraw-Hill, Ic Example: Give a 0-ich cocrete coduit with a roughess coefficiet of, ad a discharge capacity of 9.85 cfs, what diameter pipe is required to quadruple the capacity. Use Maig s equatio to solve for pipe diameter: 5 / Q 1.9π / 8 To quadruple capacity, Q 9. ft /sec. ubstitutig: 5 / ()(9. ft /sec) 1.9 (0.005) π.8 ft.6i Wat smallest commercial pipe size whose I is greater tha or equal to.6 i. Use a 6-i. pipe. Or ca be solved by usig the omograms. To use I uit omograms, eed to covert flow rate to I uits: Q 9. ft /sec(0.08 m/ft) m /sec 1.1 m /sec / 8 7

8 From omogram, should be slightly greater tha 1050 mm ( iches). Based o the omogram, use a 8-i. diameter pipe. X Example: etermie the head loss i a 6-cm cocrete pipe with a average velocity of 1.0 m/sec ad a legth of 0 m. For a pipe flowig full: 0.6m R m By defiitio: lope of eergy lie Head Loss/Legth of Pipe Or: Head Loss h L (lope)(pipe Legth) Let (cocrete pipe) 1 olve Maig s for lope: V R V R V R ubstitutig: (1m /sec) Head Loss lope(pipe Legth) h L (0 m) 0.05 m Also ca use omogram to get the slope. For 60 mm ad V 1 m/sec. lope Head Loss lope(pipe Legth) h L 0.008(0 m) 0.08 m Both solutio methods show that the head loss is less tha 0.10 m. For 60 mm (18 i.) ad V 1 m/sec (. fps). lope Head Loss lope(pipe Legth) h L 0.008(0 m) 0.08 m X X X 8

UNIFORM FLOW. U x. U t

UNIFORM FLOW. U x. U t UNIFORM FLOW if : 1) there are o appreciable variatios i the chael geometry (width, slope, roughess/grai size), for a certai legth of a river reach ) flow discharge does ot vary the, UNIFORM FLOW coditios