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- 1. Southern Methodist University Bobby B. Lyle School of Engineering CEE 2342/ME 2342 Fluid Mechanics Roger O. Dickey, Ph.D., P.E. V. STEADY PIPE FLOW D. Pump Selection Reading Assignment: Chapter 12 Turbomachines Section 12.4 – The Centrifugal Pump, pp. 687-700 E. Pump Selection Pump Applications – Pumps are used in a wide array of engineering applications including: Low- -volume, low-head pumps used to elevate fluids, e.g., elevating water from a supply source to a water treatment plant or wastewater from a gravity sewer to a wastewater treatment plant. High- pressure throughout a distribution piping network, or through long transmission pipelines. ase fluid pressure at intermediate points along transmission pipelines, or within distribution piping networks.
- 2. one unit operation or process to another within an engineered system or facility. water supply purposes. at precisely controlled rates to chemical processes. gh pressures for firefighting. operation or process to another within an engineered system or facility. designed to collect precise sample volumes over precise time intervals within engineered systems or facilities. Pump Types - Pumps can be broadly classified as either, Dynamic Positive displacement Dynamic pumps deliver flow rates that vary as a function of the discharge head on the pump. Conversely, positive displacement pumps deliver flow rates that remain relatively constant, regardless of changes in the discharge head. Dynamic pumps can be further subdivided into classes, Centrifugal – axial flow, radial flow, mixed flow, and peripheral flow pumps
- 3. Special effect – including eductor (or jet), ejector, and air lift pumps 10 Positive displacement pumps can be further subdivided into classes, Reciprocating – piston (or plunger) and diaphragm pumps Rotary – including gear, lobe, screw, progressing cavity, vane, and peristaltic (or tubing) pumps 11 Centrifugal pumps are the most widely used type in engineering applications including: Low-lift – Vertical Turbine Axial Flow Archimedes Screw High-service – Split-case, double suction centrifugal Vertical-turbine Pump Axial Flow (Vertical Propeller) Pump
- 4. Archimedes Screw Pumps Split-case, Double-suction Centrifugal Pump Booster Recirculation and transfer Well – down-hole pumps Firefighting Figure 12.6 – Schematic of Basic Elements of Centrifugal Pumps
- 5. Centrifugal Pumps Submersible Vertical Sump Pump Horizontal Fire Pump System, Internal Combustion Driver Centrifugal Pumps Solids Handling, Enclosed Impeller Non-clog, Open Impeller Semi-open Impeller Enclosed Impeller Open Impeller Centrifugal Pump Impellers Down-hole Well Pumps
- 6. Special Effect Pumps Ejector Positive displacement pumps are commonly used for, Chemical metering – including diaphragm, gear, lobe, progressing cavity, and peristaltic pumps Diaphragm Metering Pump – for feeding chemical solutions Diaphragm Positive Displacement Metering Pumps Rotary Lobe Progressing Cavity Gear Sludge transfer – including piston, diaphragm, and progressing cavity pumps
- 7. Sampling – peristaltic pumps Progressing Cavity Sludge Pump Rubber Stator Steel Rotor Air-operated Diaphragm Sludge Pump Positive Displacement Sludge and Sampling Pumps Elastomer Diaphragms Peristaltic Tubing Sampling Pump Pump/Piping Systems - Pump Piping – Most pumps have isolation valves on both the suction pipe and the discharge pipe. Gate valves, plug valves, and ball valves are commonly used for this purpose. This allows the pump to be isolated from the piping system for maintenance or replacement.
- 8. Most pumps have a check valve on the discharge line between the pump outlet connection and the discharge isolation valve to prevent backward flow through the pump when the pump is not operating. A sketch of a common pump piping arrangement follows, Gate Valve Check Valve Suction Piping Gate Valve Eccentric Reducer Concentric Reducer Discharge Piping Pump The suction pipe for any pump should never be of smaller
- 9. diameter than the pump inlet connection. If possible, the suction pipe should be 2 or more pipe sizes larger than the pump inlet connection to minimize friction losses. Recommended, economical velocities for pump suction and discharge piping may be summarized graphically as: Recommended Velocities System Head-Discharge Curve Consider the energy equation around a CS between Sections 1 and 2 that encloses a pump, Solve this equation for the pump energy input, hP, or “Total Head” required, Change in Velocity Head , Static Head Change in Pressure Head, Total Head Loss, hL = hf + hm
- 10. A plot of the input Total Head, hP , as a function of flow rate, Q, is called the System Head-Discharge Curve for a given pump/piping system. Consider a typical pump/piping system for transferring water from one tank into a second tank having a higher water surface elevation,
- 11. GV CV Pump GV Write the energy equation between the surface of the two tanks, (i) p1 = p2 = pATM = 0 (ii) V1 = V2 = 0 Simplifying yields,
- 12. The total head loss varies with V 2, hence with Q2, such that the System Head-Discharge Curve has the following general appearance, Total Head, hP [L] Discharge, Q [L3/T] hL , Total Head Loss System Head-Discharge Curve Reconsider the head loss equation for a piping system with a single pipe size: There are usually multiple pipe sizes, having differing fluid velocities, each with different appurtenances in pump/piping systems. The total head loss for a pump/piping system is obtained by summing the head losses for the different pipe sizes: where, hL = total head loss for all system pipe sizes [L] hfi = friction loss for pipe size i [L]
- 13. sum of the energy losses for all individual minor loss components j, for pipe size i [L] Expanding the summation over all pipe sizes: Minor Losses Pipe Size 1 Friction Loss Pipe Size 1 Minor Losses Pipe Size 2 Friction Loss Pipe Size 2 Pump Head-Discharge Curve The discharge delivered by a centrifugal pump typically declines as the Total Head on the pump increases. The Total Head at which the pump discharge is reduced to zero is called the Shut-off Head. A hypothetical centrifugal Pump Head- Discharge Curve, for a single operating speed follows:
- 14. Total Head, hP [L] Discharge, Q [L3/T] Pump Head-Discharge Curve Shut-off Head Other examples of hypothetical centrifugal Pump Head- Discharge Curves are shown in Figures 12.11 p. 693, and 12.12 p. 694 in the textbook. Example manufacturer’s Pump Head-Discharge Curves taken from the Goulds Pump Catalog are contained in the class handout. Legend: Goulds Pump Head-Discharge Curves Efficiency (U-shaped) Curves Additional information often contained on manufacturer’s Pump Head-Discharge Curves includes, Pump efficiency Brake horsepower (i.e., power that must be supplied to the pump input shaft by a drive motor) Net Positive Suction Head (NPSH) required to prevent cavitation Head-discharge characteristics as a function of pump operating speed Head-discharge characteristics as a function of impeller
- 15. diameter (a given pump casing can often accommodate a range of impeller diameters) Superimposing Pump Head-Discharge Curves over a System Head-Discharge Curve allows the operating point for a pump/piping system to be established graphically, as the intersection of the curves: Total Head, hP [L] Discharge, Q [L3/T] Pump Operating Point QPump hPump Pump Head-Discharge Curve System Head-Discharge Curve This graphical approach is commonly used to select a suitable centrifugal pump for a given piping system and desired flow rate, Qdesign . A trial-and-error procedure is used. Several different Pump Head-Discharge Curves may be superimposed over the System Head-Discharge Curve until a pump is found with suitable operating characteristics — discharge, head, efficiency, NPSH, etc.
- 16. Total Head, hP [L] Discharge, Q [L3/T] Operating Point for Pump #2 Operating Point for Pump #1 Qdesign Pump #2 Selected * Important Point Uncertainty exists in estimating pipe friction and minor losses. Pipe roughness, hence friction losses, may also increase over time due to pipe corrosion or scaling. It is highly recommended that two System Head-Discharge Curves be developed, one for pump capacity selection, and the other for motor selection as follows: (1) For ensuring adequate pump capacity, Qdesign , estimate the maximum friction loss assuming old, rough pipe using the Hazen-Williams Equation with C = 100. Furthermore, use conservatively high estimates of minor losses by employing minor loss coefficients, i.e., KL values, from the upper-end of typical design ranges for each type of piping appurtenance.
- 17. (2) Determine the maximum possible discharge and associated head, (Qmax , hp,Qmax) for the selected pump/piping system. This operating point typically requires the maximum motor power output. Estimate the friction loss assuming new, clean pipe using the Darcy-Weisbach Equation. Furthermore, use low estimates of minor losses by employing minor loss coefficients, i.e., KL values, from the lower-end of typical design ranges for each type of piping appurtenance. Plot both System Head-Discharge Curves (i.e., one curve for lowest likely head loss values, and another for highest likely head loss values), and the Pump Head-Discharge Curve for the selected pump on the same graph. Read the design operating point (Qdesign , hp,Qdesign), and the maximum power input operating point (Qmax , hp,Qmax) from the graph as follows: Total Head, hP [L] Discharge, Q [L3/T] Operating Point (Qdesign , hp,Qdesign) Operating Point (Qmax , hp,Qmax) Maximum Friction and Minor Losses Minimum Friction and Minor Losses
- 18. Common Pump Piping Arrangements (1) Horizontal Dry Pit – Flooded Suction GV CV Pump GV
- 19. Wet Well Dry Well Suction Head (2) Horizontal Dry Pit – Suction Lift GV CV Pump GV Wet Well
- 20. Suction Lift (3) Vertical Wet Pit Wet Well
- 21. CV GV Ground Surface (4) Submersible Wet Well CV GV
- 29. 1 1 Southern Methodist University Bobby B. Lyle School of Engineering CEE 2342/ME 2342 Fluid Mechanics Roger O. Dickey, Ph.D., P.E. V. STEADY PIPE FLOW Multiple Pipe Systems – Series, Parallel, and Branching Pipes and Pipe Networks Reading Assignment: Chapter 8 Viscous Flow in Pipes Section 8.5.2 – Multiple Pipe Systems, pp. 456-460 C. Multiple Pipe Systems Pipes in Series – Consider pipes in series as illustrated in Figure 8.34 (a), p. 456 where every fluid particle that passes through the CV, entering at Section A and exiting at Section B, passes through each of the pipes in sequence:
- 30. Figure 8.34 (a) Series Pipe System, p. 456 – Modified Q CS In this scenario Q is the same in each pipe, but V varies from one pipe to the next because pipe sizes differ. Total head loss, hLA-B , from Section A to Section B is simply the sum of the head losses through each of the pipes of differing size. Governing equations for any arbitrary number of pipes in series, numbered 1 through n, located between Sections A and B are: The head loss for any given pipe size i, hLi , is comprised of both the pipe friction loss and minor losses. Thus, the total head loss for a series piping system between any two Sections A and B, hLA-B , is obtained by summing both the pipe friction losses and the minor losses for all n pipe sizes: where, hLA-B =total head loss across the n
- 31. pipe sizes between A and B [L] hfi = friction loss for pipe size i [L] sum of the energy losses for all individual minor loss components j, for pipe size i [L] Expanding the summation over all pipe sizes: Minor Losses Pipe Size 1 Friction Loss Pipe Size 1 Minor Losses Pipe Size 2 Friction Loss Pipe Size 2 Friction factors, fi , will generally differ for the various pipes because the Reynolds number, Rei , and relative roughness, εi /Di , tend to vary from one pipe size to the next. Series pipe problems of Types I, II, and III are solved in exactly the same manner as the corresponding type of simple pipe problem, but with multiple fi and Vi values.
- 32. Refer to handout V.C.1. Series Pipes Example for piping systems having multiple pipes in series. Pipes in Parallel – Consider parallel pipes as illustrated in Figure 8.34 (b), p. 456 where fluid particles passing through the CV, beginning at Section A along the free surface of the left tank and ending at Section B along the free surface of the right tank, may take any of the available parallel paths, with the total flow rate equaling the sum of the flow rates through the individual pipes: Figure 8.34 (b) Parallel Pipe System, p. 456 – Modified CS
- 33. In this scenario Qi may differ in each pipe i, but the head loss across each pipe is the same, hLA-B , as can be seen by writing the energy equation along a path through any pipe between Sections A and B. Governing equations for any arbitrary number of pipes in parallel, numbered 1 through n, located between Sections A and B are: Head loss across a given pipe i, hLi , is comprised of both the pipe friction loss and minor losses and it must equal the total head loss across the overall parallel piping system between the two Sections A and B, hLA-B : where, hLA-B =total head loss across all parallel pipes between Sections A and B [L] hfi = friction loss for pipe i [L] sum of the energy losses for all individual minor loss components j, for pipe i [L]
- 34. Refer to handout V.C.2. Parallel Pipes Example for piping systems having multiple pipes in parallel. Branching Pipes and Pipe Networks – Multiple pipe systems may also involve branching pipes as illustrated in Figure 8.35, p. 457: In this scenario, continuity at Node N requires that: Application of the energy equation reveals that the head loss across parallel Pipes (2) and (3) between Node N and Section B are equal, although the pipe sizes and flow rates may differ. Similarly, the head losses across series Pipes (1) and (2) equals the head loss across series Pipes (1) and (3) because these two sets of series pipes operate in parallel. Branching pipe systems may be quite complex like the common 3-reservoir problem, illustrated in Figure 8.36, p. 458, where the direction of flow in Pipe (2) may not be known a priori: Q1 Q2 Q3
- 35. In other words, water flowing out of the highest Reservoir A may flow into both of the lower Reservoirs B and C. However, it is entirely possible that water flows out of both higher Reservoirs A and B into the lowest Reservoir C. Refer to handout V.C.3. Three Reservoir Problem Example. Branching pipe systems may also involve loops forming complex distribution networks as illustrated in Figure 8.37, p. 460: Pipe network problems are solved by using node and loop equations analogous to those used for electrical circuits— specific variable analogs are pressure-voltage, flow rate- current, and pipe friction-resistance. Net flow rate into a node must be zero (Continuity Principle), and the net pressure difference must be zero when following a path around a given loop that returns to the starting point. Combining these concepts with head loss equations allows determination of flows and pressures throughout the network. Computer models are usually used to solve the resulting set of simultaneous equations to determine the direction and magnitude of the flow rate through each pipe, and the pressure at each node in the network. n Q Q Q =
- 43. Southern Methodist University Bobby B. Lyle School of Engineering CEE 2342/ME 2342 Fluid Mechanics Roger O. Dickey, Ph.D., P.E. V. STEADY PIPE FLOW A. Pipe Friction Formulas B. Hydraulic and Energy Grade Lines Reading Assignment: Chapter 3 Elementary Fluid Dynamics … Section 3.7 - The Energy Line and the Hydraulic Grade Line, pp. 131-133 A. Pipe Friction Formulas Empirical pipe friction formulas have been developed for specific fluids flowing through a selected range of pipe sizes and materials. This simplifies friction loss calculations by eliminating the need to determine Darcy-Weisbach friction factors. In the U.S., the Hazen-Williams Formula is commonly used for the turbulent flow of water at normal environmental temperatures through circular pipes with diameters in the range of 2 inches to 6 ft. This formula is extensively used for design and evaluation of water distribution piping networks. In USC units, the Hazen-Williams Formula is, This equation holds only for the following units, Velocity, V (ft/sec) Hydraulic Radius, Rh (ft)
- 44. Friction Slope, Sf (ft/ft) In SI units, the Hazen-Williams Formula is, This equation holds only for the following units, Velocity, V (m/sec) Hydraulic Radius, Rh (m) Friction Slope, Sf (m/m) Multiply both sides of the equation by cross-sectional area, A, and substitute discharge, Q, for (VA) on the left-hand side. Also, for circular conduits flowing full, the hydraulic radius is Rh=D/4. Substituting D/4 for Rh , inserting appropriate conversion factors, and simplifying yields the Hazen-Williams Equation in terms of discharge as a function of pipe diameter: In USC units, the Hazen-Williams Formula in terms of discharge is, This equation holds only for the following units, Discharge, Q (gpm) Pipe Diameter, D (in) Friction Slope, Sf (ft/ft) In SI units, the Hazen-Williams Formula in terms of discharge
- 45. is, This equation holds only for the following units, Q (m3/sec) D (m) Sf (m/m) The Hazen-Williams Coefficient, C , depends on the roughness of the pipe. The higher the C value the smoother the pipe, C = 100 typical design value Tables of C values are widely available for the common materials used for commercial pipe, as shown in the following table: Typical Values of C Pipe Material C FE Supplied-Reference Handbook, 8th Ed., 2011 – p. 161 The Hazen-Williams Formula can be rearranged to determine the friction slope, Sf , i.e., pipe friction loss per unit length of pipe:
- 46. Only for USC Units Only for SI Units The friction loss, hf , for a given length of pipe, L, is then computed by rearranging the definition of friction slope Sf , Multiply the previous friction slope equations by L, use C = 100 as a reference value, and simplify to yield convenient equations for friction loss, hf : This equation holds only for the following units, Friction Loss, hf (ft) Pipe Length, L (ft) Discharge, Q (gpm) Pipe Diameter, D (in) Only for USC Units Only for
- 47. SI Units This equation holds only for the following units, Friction Loss, hf (m) Pipe Length, L (m) Discharge, Q (m3/sec) Pipe Diameter, D (m) Refer to Handouts – V.A. Hazen-Williams Examples for applications of the Hazen-Williams Equation. B. Hydraulic and Energy Grade Lines The Hydraulic Grade Line (HGL) and Energy Grade Line (EGL) are useful concepts for visualizing pipe flow problems. The HGL is a plot of the piezometric head as the ordinate, against length along the pipe as the abscissa. Each point along the HGL is the elevation to which the fluid would rise in a piezometer, located at that point along the pipe. The EGL is a plot of the total available mechanical energy as the ordinate, against length along the pipe as the abscissa. By definition, the EGL is always above the HGL by an amount .
- 48. The slope of the EGL is the friction slope, Sf , i.e., the friction loss per unit length along a pipe, Elevation Datum Distance Energy
- 52. Pump Energy Input, hP 54 . 0 63 . 0 318 . 1 f h S CR V = 54 . 0 63 . 0 849 . 0 f
- 58. ÷ ø ö ç ç è æ g V 2 2 L h S f f º Page 1 of 2 HOMEWORK NO. 13 SOLUTION Problem Statement Compare results from the implicit Colebrook equation to the following explicit equation sometimes used in spreadsheet models as a good approximation: It is valid for 10
- 59. –6 < ε/D < 10 –2 and 5000 < Re <10 +8 . An advantage of the equation is that given Re and ε/D it does not require an iteration procedure to obtain f, i.e., it is explicit in f. Plot a graph of the percent difference in f as given by this equation and the original Colebrook equation for Re values in the range of validity of the approximate equation, specifically for ε/D = 10 –4 . Spreadsheet software is mandatory for completing the required repetitive calculations and plotting the required graph of percent difference in friction factor f between the two formulas, 325.1 D f
- 61. app app ff PUMP AND PIPING SYSTEM SKETCH Gate Valve Gate Valve Check Valve Pump 50 ft 476 ft 24 ft Suction Piping