PRESSURE DROP AND OSSES IN PIPE When water (luid) lows in a pipe, or example rom point A to point B, pressure drop will occur due to the energy losses (major and minor losses). A B Bernoulli equation: PA A PB B + + za + + zb + h ρg g ρg g I pipe diameter is the same, the velocity remain constant along the pipe. A B I the height is the same, the potential energy can be neglected. za zb z
Pressure drop could be determine as: + g g D h g P P B A ρ where is a riction actor, and need to be determine.for laminar low, Re 64 For turbulent low, need to be determined using Moody chart The relative pipe roughness, D ε need to be measured.
COEBROO-WHITE EUATION This is an equation to ind the value o riction actor,, or turbulent low. log 0 ε.5 + 3.7D Re D ε Re Darcy riction actor, dimensionless Inside diameter o pipe in meter Pipe surace roughness in meter Reynolds number, dimensionless From this equation, Moody chart was developed. Moody chart consist three (3) major parts;. aminar region. Transition region 3. Turbulent region
aminar region The value o riction actor is proportional with Reynolds number. 64 Re A straight line could be plotted on the Moody chart. Transition region Friction will be aected with Reynolds number and internal pipe roughness. Complete turbulent region log 0 ε.5 + 3.7D Re From equation above, high Reynolds number could lead to a very small value. It is means that only internal pipe surace roughness would inluence the riction value. In Moody chart, the graph line would become a horizontal straight line.
Example Water lows through 406.4 mm pipeline. It has 4.55 mm wall thickness. Flowrate is.36 m 3 /min. Assuming a pipe roughness o 0.0508 mm, calculate the riction actor and head loss due to riction in 305 m o pipe length. Flowrate,.36 m 3 /min 0.89 m 3 /s Inner diameter 406.4 (9.55) 387.35 mm 0.38735 mm ρd 5 Re 5.5 0 μ ε 0.0000508 0.0003 0.000 D 0.38735 From Moody chart, 0.05 PA PB ρg D g.54 (m) P A P B 5. kpa
Example A concrete pipe, m inside diameter, is used to transport water rom a pumping acility to a storage tank 5km away. Neglecting any dierence in elevations, calculate the riction actor and pressure loss due to riction at a low rate o 34,000m 3 /h. Assume a pipe roughness o 0.05mm. I a delivery pressure o 4kPa must be maintained at the delivery point and the storage tank is at an elevation o 00m above that o the pumping acility, calculate the pressure required at the pumping acility at the given low rate, using the Moody chart.
HAZEN-WIIAMS EUATION A more popular approach to the calculation o head loss in water piping systems is the use o the Hazen-Williams equation. In this method a coeicient C known as the Hazen-Williams C actor is used to account or the internal pipe roughness o eiciency. Unlike the Moody chart or the Colebrook-White equation, the Hazen-Williams equation does not require use o the Reynolds number or viscosity o water to calculate the head loss due to riction. The Hazen-Williams equation or head loss is expressed as ollows: For SI unit: h 0.67 4.87 D C.85 h Frictional head loss in m ength o pipe in m D Inside diameter o pipe in m Flow rate in m 3 /s C Hazen-Williams C actor or roughness coeicient, dimensionless.
For British unit: h 4.73 4.87 D C.85 h Frictional head loss in t ength o pipe in t D Inside diameter o pipe in t Flow rate in t 3 /s C Hazen-Williams C actor or roughness coeicient, dimensionless. Note: Above equation can be rearrange a ollows: S h where S is the hydraulic slope
Commonly used values o the Hazen-Williams C actor or various applications. Pipe material C actor Smooth pipes (all metal) 30 40 Cast iron (old) 00 Iron (worn/pitted) 60 80 Polyvinyl chloride (PC) 50 Brick 00 Smooth wood 0 Smooth masonry 0 itriied clay 0
MANNING EUATION The Manning equation was originally developed or use in open channel low o water. It is also sometimes used in pipe low. The Manning equation uses the Manning index, n or roughness coeicient. For SI unit: AR n 3 h Flow rate, m 3 /s A cross sectional area o pipe, m R hydraulic radius (D/4 or circular pipes lowing ull) n Manning index, or roughness coeicient, dimensionless D Inside diameter o pipe, m h Friction loss, m ength o pipe, m
For British unit:.486 AR n 3 h Flow rate, t 3 /s A cross sectional area o pipe, t R hydraulic radius (D/4 or circular pipes lowing ull) n Manning index, or roughness coeicient, dimensionless D Inside diameter o pipe, t h Friction loss, t ength o pipe, t Example o Manning index Pipe material Resistance actor PC 0.009 ery smooth 0.00 Cement-lined ductile iron 0.0 New cast iron, welded steel 0.04 Old cast iron, brick 0.00 Badly corroded cast iron 0.035 Wood, concrete 0.06 Clay, new riveted steel 0.07 Canals cut through rock 0.040 Earth canals average condition 0.03 Rivers in good conditions 0.030
MINOR OSSES Minor losses in a water pipeline are classiied as those pressure drops that are associated with piping components such as valves and itting. There are included: Elbow and tees Pipe diameter enlargement / reduction Nozzle Entrance / exit losses They are relatively small compared to riction loss in a straight length o pipe. Minor loss g Where is a resistance actor. It must be noted that this way calculating the minor losses is valid only in turbulent low. No data are available or laminar low. Some engineers use the equivalent length to determine minor losses.
SIMPIFICATION OF MAJOR OSS CACUATION Head loss due to riction; g D h From continuity equation, D A 4 π 4 D π 4 6 D π Head loss equation can be written as: 5 6 g D g D h π h Usually, or turbulent low, h
Major losses in series pipe Flow rate is constant A B C Major losses keep increasing h h A + h B + h C ( + + ) A B c
Major losses in parallel pipe Flow rate is constant at inlet and outlet (only) A B However, low rate or pipe, and 3 are dierent. A B + + 3 Major losses are constant or pipe, and 3. h h h h3
h h 3 B A + + 3 h h h h + + 3 + +