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Unformatted text preview: Lecture 10 Minor Losses & Pressure Requirements I. Minor Losses • Minor (or “fitting”, or “local”) hydraulic losses along pipes can often be estimated as a function of the velocity head of the water within the particular pipe section: hml V2 = Kr 2g (208) where hml is the minor loss (m or ft); V is the mean flow velocity, Q/A (m/s or fps); g is the ratio of weight to mass (9.81 m/s2 or 32.2 ft/s2); and Kr is a coefficient, dependent on the type of fitting (valve, bend, transition, constriction, etc.) • • • • • • • Minor losses include head losses through/past hydrants, couplers, valves, pipe elbows, “tees” and other fittings (see Tables 11.1 and 11.2) For example, there is some loss when water flows through a hydrant, but also some loss when water flows in a pipe past the location of a closed hydrant Kr = 0.3 to 0.6 for flow in a pipeline going past a closed hydrant, whereby the velocity in the pipeline is used to compute hml Kr = 0.4 to 0.8 for flow in a pipeline going past an open hydrant; again, the velocity in the pipeline is used to compute hml Kr = 6.0 to 8.0 for flow from a pipeline through a completely open hydrant. In this case, compute hml using the velocity of the flow through the lateral fitting on the hydrant, not the flow in the source pipeline. For flow through a partially open hydrant, Kr increases beyond the 6.0 to 8.0 magnitude, and the flow rate decreases correspondingly (but not linearly) • In using Tables 11.1 and 11.2 for hydrants, the nominal diameter (3, 4, 5, and 6 inches) is the diameter of the hydrant and riser pipe, not the diameter of the source pipeline Use the diameter of the hydrant for Kr and for computing Vr. However, for line flow past a hydrant, use the velocity in the source pipeline, as indicated above. Always use the largest velocity along the path which the water travels – this may be either upstream or downstream of the fitting Do not consider velocities along paths through which the water does not flow • In Table 11.2, for a sudden contraction, Kr should be defined as: • • Sprinkle & Trickle Irrigation Lectures Page 111 Merkley & Allen ( 2 Kr = 0.7 1 − Dr • ) 2 (209) where Dr is the ratio of the small to large inside diameters (Dsmall/Dlarge) Allen (1991) proposed a regression equation for gradual contractions and expansions using data from the Handbook of Hydraulics (Brater & King 1976): ( 2 Kr = K f 1 − Dr ) 2 (210) where Kf is defined as: K f = 0.7 − cos( f ) ⎡cos( f ) ( 3.2 cos( f ) − 3.3 ) + 0.77 ⎤ ⎣ ⎦ (211) and f is the angle of the expansion or contraction in the pipe walls (degrees or radians), where f ≥ 0 • • • • For straight sides (no expansion or contraction), f = 0° (whereby Kf = 0.03) For an abrupt change in pipe diameter (no transition), f = 90° (whereby Kf = 0.7) The above regression equation for Kf gives approximate values for approximate measured data, some of which has been disputed In any case, the true minor head loss depends on more than just the angle of the transition Expansion Contraction • For a sudden (abrupt) expansion, the head loss can also be approximated as a function of the difference of the mean flow velocities upstream and downstream: Merkley & Allen Page 112 Sprinkle & Trickle Irrigation Lectures hml • • ( Vus − Vds )2 = 2g (212) An extreme (albeit unrealistic) case is for Vds = 0 and hml = Vus2/2g (total conversion of velocity head) Various other equations (besides those given above) for estimating head loss in pipe expansions and contractions have been proposed and used by researchers and engineers Minor Loss Example • • • • A mainline with an open lateral hydrant valve has a diameter of 200 mm ID upstream of the hydrant, and 150 mm downstream of the hydrant The diameter of the hydrant opening to the lateral is 75 mm Qupstream = 70 lps and Qlateral = 16 lps The pressure in the mainline upstream of the hydrant is 300 kPa • The mean flow velocities are: V200 = V150 0.070 m3 / s ⎛ π(0.200 m)2 ⎞ ⎜ ⎟ ⎜ ⎟ 4 ⎝ ⎠ = 2.23 m / s 0.070 − 0.016 m3 / s = = 3.06 m / s ⎛ π(0.150 m)2 ⎞ ⎜ ⎟ ⎜ ⎟ 4 ⎝ ⎠ Vhydrant = Sprinkle & Trickle Irrigation Lectures 0.016 m3 / s ⎛ π(0.075 m)2 ⎞ ⎜ ⎟ ⎜ ⎟ 4 ⎝ ⎠ = 3.62 m / s Page 113 (213) (214) (215) Merkley & Allen • • • Note that V200 and V150 are both above the normal design limit of about 2 m/s The head loss past the open hydrant is based on the higher of the upstream and downstream velocities, which in this example is 3.06 m/s From Table 11.1, the Kr for flow past the open hydrant (line flow; 6” mainline) is 0.5; thus, (hml )past • • (3.06)2 = 0.5 = 0.24 m 2(9.81) (216) The head loss due to the contraction from 200 mm to 150 mm diameter (at the hydrant) depends on the transition If it were an abrupt transition, then: 2 ⎡ ⎛ 150 ⎞2 ⎤ Kr = 0.7 ⎢1 − ⎜ ⎟ ⎥ = 0.13 200 ⎠ ⎥ ⎢⎝ ⎣ ⎦ • • (217) And, if it were a 45° transition, Kf = 0.67, also giving a Kr of 0.13 Then, the head loss is: (hml )contraction (3.06)2 = 0.13 = 0.06 m 2 (9.81) (218) • Thus, the total minor loss in the mainline in the vicinity of the open hydrant is about 0.24 + 0.06 = 0.30 m (0.43 psi). • The loss through the hydrant is determined by taking Kr = 8.0 (Table 11.1; 3” hydrant): (hml )through • • (3.62)2 = 8.0 = 5.3 m 2 (9.81) (219) This is a high loss through the hydrant (about 7.6 psi), so it may be advisable to use a larger diameter hydrant. The pressure in the mainline downstream of the hydrant is (9.81 kPa/m): P150 = P200 − γ (hml )past 2 2 ⎛ V200 − V150 ⎞ + γ⎜ ⎟ ⎜ ⎟ 2g ⎝ ⎠ ⎛ (2.23) − (3.06) P150 = 300 − (9.81)(0.24) + 9.81⎜ ⎜ 2(9.81) ⎝ 2 Merkley & Allen Page 114 2 ⎞ ⎟ = 295 kPa ⎟ ⎠ (220) Sprinkle & Trickle Irrigation Lectures II. Total Dynamic Head • • • • The Total Dynamic Head (TDH) is the head that the pump “feels” or “sees” while working, and is calculated to determine the pump requirements It includes the elevation that the water must be lifted from the source (not necessarily from the pump elevation itself) to the outlet, the losses due to “friction”, the pressure requirement at the outlet, and possibly the velocity head in the pipeline For a sprinkler system, the value of TDH depends on the positions of the laterals, so that it can change with each set. Pump selection is usually made for the “critical” or extreme lateral positions, that is, for the “worst case scenario”. Keller & Bliesner recommend the addition of a “miscellaneous” loss term, equal to 20% of the sum of all “friction” losses. This accounts for: 1. 2. 3. 4. • • • Uncertainty in the Kr values (minor losses) Uncertainty in the Hazen-Williams C values Aging of pipes (increase in losses) Wear of pump impellers and casings Losses in connectors or hoses from the mainline to laterals, if present, must also be taken into account when determining the TDH See Example Calculation 11.2 in the textbook The next two lectures will provide more information about TDH and pumps III. The System Curve • • • • • • • The system curve determines the relationship between TDH and flow rate This curve is approximately parabolic, but can take more complex shapes Note that head losses in pipe systems are approximately proportional to the square of the flow rate (Q2 or V2) For the Hazen-Williams equation, these losses are actually proportional to Q1.852 or V1.852 For standard, non-FCN, sprinkler nozzles, the head at the sprinkler is also proportional to Q2 Sprinkler systems can have a different system curve for each position of the lateral(s) Defining the system curve, or the “critical” system curve, is important for pump selection because it determines, in part, the operating point (TDH and Q) for the system Sprinkle & Trickle Irrigation Lectures Page 115 Merkley & Allen IV. Valving a Pump • A throttle valve may be required at a pump: (a) Filling of the system’s pipes • • • • • The head is low, and the flow rate is high Pump efficiency is low and power requirements may be higher Water hammer damage can result as the system fills Air vents and other appurtenances can be “blown off” For the above reasons, it is advisable to fill the system slowly (b) To avoid cavitation, which damages the pump, pipes and appurtenances (c) To control the TDH as the sprinklers are moved to different sets • Throttle valves can be automatic or manual Pressure Requirements & Pumps I. Types of Pumps 1. Positive Displacement • • • Piston pumps Rotary (gear) pumps Extruding (flexible tube) pumps 2. Variable Displacement • • • • • Centrifugal pumps Injector pumps Jet pumps The above lists of pump types are not exhaustive Positive displacement pumps have a discharge that is nearly independent of the downstream (resistive) pressure. That is, they produce a flow rate that is relatively independent of the total dynamic head, TDH Merkley & Allen Page 116 Sprinkle & Trickle Irrigation Lectures Positive Displacement Pumps Axial-Flow Impeller Closed Centrifugal Pump Impeller Jet Pump Sprinkle & Trickle Irrigation Lectures Page 117 Merkley & Allen • • • • • But, with positive displacement pumps, the required pumping energy is a linear function of the pressure Positive displacement pumps can be used with thick, viscous liquids. They are not commonly used in irrigation and drainage, except for the injection of chemicals into pipes and for sprayers Piston-type pumps can develop high heads at low flow rates Air injection, or jet pumps are typically used in some types of well drilling operations. The air bubbles effectively reduce the liquid density and this assists in bringing the drillings up out of the well. Needs a large capacity air compressor. Homologous pumps are geometrically similar pumps, but of different sizes II. Centrifugal Pumps 1. Volute Case This is the most common type of irrigation and drainage pump (excluding deep well pumps). Produce relatively high flow rates at low pressures. 2. Diffuser (Turbine) The most common type for deep wells. Designed to lift water to high heads, typically using multiple identical “stages” in series, stacked up on top of each other. 3. Mixed Flow Uses a combination of centrifugal and axial flow action. For high capacity at low heads. 4. Axial Flow Water flows along the axis of impeller rotation, like a boat propeller. Appropriate for high discharge under very low lift (head). An example is the pumping plant on the west side of the Great Salt Lake. 5. Regenerative The characteristics of these pumps are those of a combination of centrifugal and rotary, or gear, pumps. Shut-off head is well-defined, but efficiency is relatively low. Not used in irrigation and drainage. • • • In general, larger pumps have higher maximum efficiencies (they are more expensive, and more effort is given toward making them more efficient) Impellers can be open, semi-open, or closed. Open impellers are usually better at passing solids in the pumped liquid, but they are not as strong as closed impellers Double suction inlet pumps take water in from both sides and can operate without axial thrust Merkley & Allen Page 118 Sprinkle & Trickle Irrigation Lectures Closed Impeller Semi-Open Impeller Open Impeller Characteristic Curve • • • • Total Dynamic Head, TDH • The pump “characteristic curve” defines the relationship between total dynamic head, TDH, and discharge, Q The characteristic curve is unique for a given pump design, impeller diameter, and pump speed The characteristic curve has nothing to do with the “system” in which the pump operates The “shut-off” head is the TDH value when Q is zero (but the pump is still operating) The shut-off head can exceed the recommended operating pressure, or even the bursting pressure, especially with some thin-wall plastic pipes 0 Efficiency cte Shut-Off Head Cha ra risi cC urv e Power 0 Sprinkle & Trickle Irrigation Lectures Flow Rate, Q Page 119 Merkley & Allen III. Centrifugal Pumps in Parallel • • p • Pumps in PARALLEL means that the total flow is divided into two or more pumps Typical installations are Two On in P for a single inlet pipe, e aral Pu lel branched into two m pumps, with the outlets from the pumps converging to a single discharge pipe If only one of the pumps operates, some 0 Flow Rate, Q 0 type of valve may be required so that flow does not flow backwards through the idle pump Flow rate is additive in this case Total Dynamic Head, TDH • pump 1 pump 2 Two Pumps in Parallel IV. Centrifugal Pumps in Series • • • Pumps in SERIES means that the total flow passes through each of two or more pumps in line Typical installations are for increasing pressure, such as with a booster pump Head is additive in this case Merkley & Allen Page 120 Sprinkle & Trickle Irrigation Lectures Total Dynamic Head, TDH Two in Se rie s One P ump 0 Flow Rate, Q 0 • • • • It is common for turbine (well) pumps to operate in series For centrifugal pumps, it is necessary to exercise caution when installing in series because the efficiency can be adversely affected May need straightening vanes between pumps to reduce swirling Note that the downstream pump could cause negative pressure at the outlet of the US pump, which can be a problem pump 1 pump 2 Two Pumps in Series Sprinkle & Trickle Irrigation Lectures Page 121 Merkley & Allen Merkley & Allen Page 122 Sprinkle & Trickle Irrigation Lectures ...
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