{ CEE 410 Hydraulic Engineering 3- Minor Losses in Piping Michael D. Doran, P.E. DEE Professor of Practice Piping Systems System Head Calculations

Outcomes for today 1.Understand concepts of “K” and “L/D” for minor losses. 2.Understand basics of pressure and gravity piping system configuration. 3.Understand how to use H-W (pressure) and Manning’s (gravity) to preform system head calculations for water/wastewater.

Total Headloss Total H L = Pipe Friction H L + Minor H L

Total Headloss Total H L = Pipe Friction H L + Minor H L

Total Headloss Total H L = Pipe Friction H L + Minor H L + Analysis of Full Pipe Systems

Velocity Head is Lost

K-value Method Minor Head Loss: H L = K(V 2 /2g)

K-value for Entrance H L = K(V 2 /2g) K=0.78 r/DK Sharp

K-value for Exit H L = K(V 2 /2g) K=1.0

K-value for Elbow H L = K(V 2 /2g) 0.1 < K < 1.0+ Vary with dimensions and pipe diameter - Consult tables

K-value for Tee H L = K(V 2 /2g) 0.2 < K < 1.6 Vary with dimensions and pipe diameter - Consult tables ‘Thru’ or ‘Run’ ‘Branch’

K for Valve Vary with type of valve, dimensions and pipe diameter - Consult tables

K for Specialty Fittings Vary -Consult tables; Consult manufacturer

Example 1 (US) – What are the minor losses from a flush sharp-edged entrance, tee (run), swing check valve, standard 90° elbow, standard 45° elbow, an open gate valve, and an exit in a run of 12-inch piping with a velocity of 6.0 ft/s?

Looking up K values Condition/Fitting K Entrance (flush sharp-edge)0.50 Tee (run)0.26 Swing Check Valve deg Elbow deg Elbow0.21 Open Gate Valve0.10 Exit1.00 Total3.06

Computing ΣH L ΣH L = ΣK(V 2 /2g) = 3.06{6.0 2 /[2(32.2)]}ft 2 (s 2 ) s 2 (ft) = 1.7 ft

L/D Method Rather than using the “K(V 2 /2g)” approach, it may be useful in some cases to equate fittings to their “Equivalent Length” as a function of pipe diameter (L/D). A fitting with L/D = 30, for example, in a 12 inch pipe, is equivalent to 30 ft of pipe.

Common L/D Values Fitting/AppurtenanceL/D Standard 90 deg Elbow30 Standard 45 deg Elbow16 Long Rad 90 deg Elbow20 Tee (Run)20 Tee (Branch)60 Gate Valve(open)13 Swing Check Valve 135

Computing H L for L/D Example 2 (US) – For the situation of Example 1, how many feet of 12-inch pipe would need to be included in the analysis to represent the minor losses from the elbows, tee and valves?

Computing H L for L/D Condition/Fitting L/D Tee (run)20 Swing Check Valve deg Elbow30 45 deg Elbow16 Open Gate Valve13 Total 214 L = (L/D)D = 214(1.0 ft) = 214 ft

A Simple Pressure System EL = EL = G G G C

A Simple Pressure System EL = EL = G G G C 3,900 ft 10-in 3.50 ft 3 /s (cfs) (1,600 gpm) C=100

A Simple Pressure System EL = EL = G G G C Rounded Inlet r/d = 0.10

A Simple Pressure System EL = EL = G G G C (3) Open Gate Valves (1)Swing Check (2)45 deg Elbows (3)90 deg Elbows

1.Head due to elevation difference 2.Head due to pipe friction 3.Head due to minor losses 4.Total head = el + friction + minor

1.Head due to elevation difference Z out – Z in = – = ft

2. Head losses due to friction FittingL/D (3) Open Gate Valves39 (1)Swing Check 135 (2)45 deg Elbows32 (3)90 deg Elbows90 Total 296 L (appurtenances) = 296(10/12)ft = 247 ft L total = pipe + Equiv Lg = 3, = 4,147

H L = 1,043·Q 1.85 ·(C) ·(D )ft/100 ft pipe = 1,043(1, ) (10) = 2.4 ft/100 ft pipe H L = (2.4 ft/100 ft) (4,147 ft) = 100 ft 2. Head losses due to friction (cont’d)

V = Q/A = 3.50 ft 3 = 6.4 ft/s (s) π (5/12)2 ft 2 3. Head losses due to entrance and exit H L = ΣKV 2 /2g = ( )6.4 2 ft 2 (s 2 ) ~ 1 ft s 2 (2)(32.2) ft

1.Head due to elevation difference140 ft 2.Head due to pipe friction100 ft 3.Head due to minor losses 1 ft 4.Total head = el + friction + minor241 ft System Head

Gravity pipe H L concepts Q1Q1 Q3Q3 Q2Q2

Pipe Friction Losses Q1Q1 Q3Q3 Q2Q2

Gravity pipe H L concepts Pipe Friction Losses Q1Q1 Q3Q3 Q2Q2 Minor Losses

Pipe Friction Losses Q = 1.486·A · R 0.67 ·S 0.50 n Manning’s Equation

Gravity Flow Minor H L Flow through MH: Straight alignment No diameter change Constant Q Well benched Benches K=0.2

Gravity Flow Minor H L Flow through MH: Algular alignment No diameter change Constant Q Well benched AngleK

Gravity Flow Minor H L Flow through MH: Junctions Well benched K=0.8 K=1.0

H L through Surcharged MH HGL K=1.5 (conservative)

Example 3 (US) – Determine appropriate sewer diameters and invert elevations for this condition at MHs 2 and 3. Size Yellow Pipes and determine S downstream MH3. IE = cfs 12-in San MH1 MH2 MH cfs 8-in San IE at MH2 300 LF 250 LF n=0.015

What diameter pipes should we use? Want to maintain 2 ft/s V to maintain solids in suspension. Pipes (US) generally come in 8, 12, 18, 24, 48, 54, 60, 66, 72 inch diameters Grade is usually precious (to minimize pumping downstream). So, generally we will choose a pipe that would have a velocity of 2 ft/s or a little more when flowing full.

Choose Pipe Diameters For Q = 1.56 cfs: V = Q/A 8”IDV=1.56/(π )=4.6 ft/s 12”IDV=1.56/π )=2.0 ft/s 18”IDV=1.56/π )=0.9 ft/s

Choose Pipe Diameters For Q = 1.56 cfs: V = Q/A 8”IDV=1.56/(π )=4.6 ft/s 12”IDV=1.56/π )=2.0 ft/s 18”IDV=1.56/π )=0.9 ft/s 12-in fits situation well.

Choose Pipe Diameters For Q = = 2.23 cfs: V = Q/A 12”IDV=2.23/π )=2.8 ft/s 18”IDV=2.23/π )=1.3 ft/s

Choose Pipe Diameters For Q = = 2.23 cfs: V = Q/A 12”IDV=2.23/π )=2.8 ft/s 18”IDV=2.23/π )=1.3 ft/s 12-in fits, or could install 18-in at slope sufficient to maintain 2 ft/s flowing partially full. Let’s chose 12-in for prob.

S = n·Q 1.486(A)R MH1 to MH2 S = 0.015(1.56) 1.486(π )(1.0/4) = ft/ft MH2 to MH3 S = 0.015(2.23) 1.486(π )(1.0/4) = ft/ft

Minor Losses: MH 1) KV 2 /2g = 0.3(1.56/π ) 2 ft 2 (s 2 ) = 0.02 ft (s 2 )(2)(32.2)ft Set IE at outlet at = MH 2) KV 2 /2g = 0.8(2.23/π ) 2 ft 2 (s 2 ) = 0.10 ft (s 2 )(2)(32.2)ft MH 3) KV 2 /2g = 0.6(2.23/π ) 2 ft 2 (s 2 ) = 0.08 ft (s 2 )(2)(32.2)ft

MH2 Inverts Inlet = MH1 Out IE - 300(0.0026) = – 0.78 = Outlet = – Minor Loss = – 0.10 = MH3 Inverts Inlet = MH2 Out IE - 250(0.0053) = – 1.32 = Outlet = – Minor Loss = – 0.08 = Slope Downstream of MH3 = (same as for MH2 to MH3)

IE = cfs 12-in San MH1 MH2 MH cfs 8-in San IE at MH2 300 LF 250 LF IE = IE = IE = IE = IE = S = S =

Outcomes for today 1.Understand concepts of “K” and “L/D” for minor losses. 2.Understand basics of pressure and gravity piping system configuration. 3.Understand how to use H-W (pressure) and Manning’s (gravity) to preform system head calculations for water/wastewater.