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Chapter 8 Transportation and Metering of Fluids transporting fluids from one place to another measuring their rates of flow PIPE, FITTINGS, AND VALVES Pipe and tubing nominal diameter the actual outside diameter schedule number the wall thickness of pipe Selection of pipe sizes For turbulent flow of liquids in steel pipes larger than 1 in. (25 mm) in diameter, the optimum velocity is 0 .1 12 m Vopt 0.36 (8.1) where Vopt = optimum velocity, ft/s m = mass flow rate, lb/s = fluid density, lb/ft3 Joints and fittings to join pieces of tubing or pipe thick-walled tube connected by screw fittings flanges welding thin-walled tubing are joined by soldering compression flare fittings brittle materials (glass, carbon, cast iron) joined by flanges bell and spigot joints Screw fittings the ends of pipe are threaded the thread are tapered farthest from the end of the pipe are imperfect a tight joint is formed when the pipe is screwed into a fitting tape of polytetrafluoroethylene (teflon) is wrapped around the thread to ensure a good seal. screw fitting are more weak than the pipe (use higher schedule number) standardized for pipe size up to 12 in not usually larger than 3 in. Flanges matching disk or rings of metal bolted together compressing a gasket between their faces attached to the pipe by screwing them or by welding or by brazing blind flange or a blank flange a flange with no opening used to close a pipe Welding joining pieces of large steel pipe for high pressure service flanged and screw joints sources of emission of volatile matters welding leak proof Allowances for expansion pipe is subjected to varying temperatures and pressures cause the pipe to expand and contract fixed supports are not used (may tear loose, bend, or break) so the pipe rests loosely on rollers or is hung from above by chains or rods provision is made for taking up expansion by bends or loops in the pipe, by packed expansion joints by bellows or packless joints or by flexible metal hose Prevention of leakage around moving parts Common devices for minimizing leakage while permitting relative motion are: stuffing boxes mechanical seals Stuffing boxes - provide a seal around a rotation shaft that moves axially FIGURE 8.1 Stuffing boxes: (a) simple form; (b) with lantern gland. Mechanical seals the sliding contact is between a ring of graphite and a polish metal surface, usually of carbon steel require less maintenance than stuffing boxes FIGURE 8.2 Mechanical seal. VALVES to slow down or stop the flow of a fluid Gate valves diameter of the opening = dia. of the pipe direction of flow does not change small pressure drop not recommended for controlling flow fully open or fully closed Globe valves so called because in the earliest designs the valve body was spherical widely used for controlling flow the fluid passes through a restricted opening and changes direction several times pressure drop is large FIGURE 8.3 Common valves: (a) gate valve; (b) globe valve; (c) control valve with pneumatic valve activator. Plug cocks and ball valves plug cock as in a lab stopcock fully open to fully closed pressure drop is minimal when it is fully open ball valve sealing element is spherical occasionally applied in flow control Check valves permits flow in one direction only opened by the pressure of the fluid when the flow stops, the valve automatically closes by gravity or by a spring pressing against the disk FIGURE 8.4 Check valves: (a) lift check; (b) ball check.; (c) swing check. Pumps transportation of liquids through pipes and channels increase the mechanical energy of the liquid velocity pressure elevation positive-displacement pumps and centrifugal pumps Positive-displacement apply pressure directly to the liquid by reciprocating piston rotating members Centrifugal pump generate high rotational velocities convert kinetic energy of the liquid to pressure energy Developed head FIGURE 8.5 Pump flow system. Eq. (4.65) can be written p 2 p b Vb a a Va 2 Wp b gZb gZa (8.2a) 2 2 or in fps units, p gZ V 2 p gZ V a 2 Wp b b b b a a a (8.2b) gc 2g c gc 2g c The quantities in the parentheses are total heads, H 2 p V H gZ (8.3a) 2 and 2 gZ V p H (8.3b) gc 2 gc Ha = total suction head dimension work per unit mass Hb = total discharge head H b H a H Wp (8.4) 2 H p V Z (8.5a) g g 2g 2 Hg c pgc V Z (8.5b) g g 2g In Eqs (8.5a) and (8.5b) each term has the dimension of length Power requirement The power supplied to the pump, PB m H PB m Wp (8.6) where m is the mass flow rate define: Pf m H (8.7) The power delivered to the fluid, Pf Pf From Eqs (8.6) and (8.7) PB (8.8) For fans, use average density, = (a+b)/2 for Suction lift and cavitation If the suction pressure is only slightly greater than the vapor pressure, some liquid may flash to vapor inside the pump, a process called cavitation. greatly reduces the pump capacity causes severe erosion. If the suction pressure is actually less than the vapor pressure, there will be vaporization in the suction line, and no liquid can be drawn into the pump. To avoid cavitation the pressure at the pump inlet must exceed the vapor pressure by a certain value called the net positive suction head (NPSH) NPSH = 2-3 m (5 to 10 ft) for small centrifugal pumps = up to 15 m (50 ft) for very large pumps. For a pump taking suction from a reservoir 1 p a p v NPSH h fs Za (8.9a) g or in fps units, g c pa p v NPSH h fs Za (8.9b) g where pa' = absolute pressure at surface of reservoir pv = vapor pressure hfs = friction in suction line NPSHR = Minimum required NPSH specified by manufacturers EXAMPLE 8.1. Benzene at 100F (37.8C) is pumped through the system of Fig. 8.5 at the rate of 40 gal/min (9.09 m3/h). The reservoir is at atmospheric pressure. The gauge pressure at the end of the discharge line is 50 lbf/in.2 (345 kN/m2). The discharge is 10 ft, and the pump suction is 4 ft above the level in the reservoir. The discharge line is 1½-in. Schedule 40 pipe. The friction in the suction line is known to be 0.5 lbf/in.2 (3.45 kN/m2), and that in the discharge line is 5.5 lbf/in.2 (37.9 kN/m2). The mechanical efficiency of the pump is 0.60 (60 percent). The density of benzene is 54 lb/ft3 (865 kg/m3), and its vapor pressure at 100F (37.8C) is 3.8 lbf/in.2 (26.2 kN/m2). Calculate (a) the developed head of the pump and (b) the total power input. (c) If the pump manufacturer specifies a required NPSHR of 10 ft (305 m), will the pump be suitable for this service? Solution. (a) The pump work Wp is found by using Eq. (4.65). The upstream station a is at the level of liquid in the reservoir, and the downstream station b is at the end of the discharge line, as shown in Fig 8.5. When the level in the tank is chosen as the datum of heights and it is noted that Va = 0, Eq. (4.65) gives 2 p b gZb b V b p a Wp hf gc 2gc The exit velocity Vb is found by using data from App. 3. For a 1½-in. Schedule 40 pipe, a velocity of 1 ft/s corresponds to a flow rate of 6.34 gal/min, and 40 V b 6.31 ft s 6.34 With b = 1.0, Eq. (4.65) gives W 14.7 50144 g 10 6.312 5.5 0.5144 14.7 144 2 32.17 p 54 gc 54 54 = 159.9 ftlbf/lb By Eq. (8.4) Wp is also the developed head, and H = Hb – Ha = 159.9 ftlbf/lb (477.9 J/kg) (b) The mass flow rate is 40 54 m 4.81 lb s 2.18 kg s 7.48 60 The power input is, from Eq. (8.6), 4.81 159.9 P B 2.33 hp 1.74 kW 550 0.60 (c) Use Eq. (8.9), pa/ = 14.7144/54 = 39.2 ftlbf/lb. The vapor pressure corresponds to a head of 3.8 144 10.1 ft lb f / lb 30.2 J kg 54 The friction in the suction line is 0.5 144 hf 1.33 ft lb f lb 3.98 J kg 54 The value of the available NPSH from Eq. (8.9), assuming g/gc = 1, is NPSH = 39.2 - 10.1 - 1.33 – 4 = 23.77 ft (7.25 m) The available NPSH is considerably larger than the minimum required value of 10 ft, so the pump should be suitable for the proposed service. *Positive-Displacement Pumps* Reciprocating pumps - the chamber is a stationary cylinder that contains a piston or plunger e.g. piston pumps, plunger pumps, and diaphragm pump Rotary pumps - the chamber moves from inlet to discharge and back to the inlet. 1. Piston - max. discharge pressure is about 50 atm liquid is drawn through an inlet check valve into the cylinder by the withdrawal of a piston then is forced out through a discharge check valve on the return stroke 2. Plunger - containing a close-fitting reciprocating plunger in a heavy-walled cylinder of small diameter 1 the plunger fills nearly all the space in the cylinder discharge pressure 1,500 atm or higher 3. Diaphragm - the reciprocating member is a flexible diaphragm of metal, plastic, or rubber. handling toxic or corrosive liquids amount up to 100 gal/min. pressure up to 100 atm FIGURE 8.6 Diaphragm pump. Volumetric efficiency - ratio of the volume of fluid discharge to the volume swept by the piston. Plunger and Diaphragm - used as “metering pumps” because the volume flow is constant, controllable, and adjustable. Rotary pumps e.g. gear pump, lobe pumps, screw pumps, cam pumps, and vane pumps contain no check valves close tolerances between the moving and stationary parts operate best on clean, moderately viscous fluid discharge pressures up to 200 atm or more FIGURE 8.6 Gear pumps: (a) spur-gear pump; (b) internal-gear pump. *Centrifugal pumps* the liquid enters through a suction connection concentric with the axis of a high-speed rotary element called the impeller, which carries radial vanes integrally cast in it. the liquid leaving the outer periphery of the impeller is collected in a spiral casing called the volute and leaves the pump through a tangential discharge connection. FIGURE 8.8 Single-suction centrifugal pump. Centrifugal pump theory the liquid enters axially at the suction, station a in the rotating eye of the impeller, the liquid spreads out radially and enters the channels between the vanes at station 1. it flows through the impeller, leaves the periphery of the impeller at station 2. collected in the volute, and leaves the discharge at b FIGURE 8.8 Centrifugal pump FIGURE 8.10 Characteristic curves of a centrifugal pump operating at various speeds. Comparison of Devices for Moving Fluids considering the flow capacity, power requirements, mechanical efficiency, reliability, and ease of maintenance Positive-displacement machines - handle smaller quantities of fluids at higher discharge pressures than do centrifugal machines. - no air binding and usually self-priming. - used for controlling and metering flow - require considerable maintenance - produce the highest pressure - cannot be used with slurries. - discharge line cannot be closed without stalling or breaking the pump, so that a bypass line with a pressure relief valve is required Centrifugal machines - deliver fluid at a uniform pressure without shocks or pulsations. - run at higher speeds than positive-displacement machines - the discharge line can be completely closed without damage. - can handle corrosive liquids and slurries - require less maintenance Vacuum pumps - a compressor that takes suction at a pressure below atmospheric and discharges at atmospheric pressure Measurement of Flowing Fluids Full-Bore Meters - venturi and orifice meters, rotameters Selection installed cost and costs of operation the range of flow rates it can accommodate its inherent accuracy Venturi meter FIGURE 8.17 Venturi meter. most commonly used with liquids requires less power than other types angle of discharge cone is 5o-15o to minimize boundary layer separation For incompressible fluid with no friction Eq. (4.65) becomes 2 2p a p b 2 b V a V b a (8.22) 2 Db Vb 2 Vb Va (8.23) Da where Da = diameter of pipe Db = diameter of throat of meter = diameter of ratio Db/Da 1 2p a pb Vb (8.24) b a4 Venturi coefficient (Cv ) - for the small friction loss between locations a and b Cv 2p a pb Vb (8.25) 1 4 Cv = the venturi coefficient (determined experimentally) = 0.98 for pipe diameters of 2 to 8 in. = 0.99 for larger sizes Volumetric and mass flow rates Cv Sb 2p a pb q Vb Sb (8.26) 1 4 where q = volumetric flow rate Sb = area of throat Cv Sb m q 2p a pb (8.27) 4 1 where m = mass flow rate Orifice meter Venturi meter Orifice meter expensive can change to meet the requirement occupies considerable space larger power consumption ratio of throat diameter to pipe diameter cannot be changed the principle is identical C0 2p a pb u0 (8.28) 1 4 where u0 = velocity through orifice (determined experimentally) = ratio of orifice diameter to pipe diameter pa, pb = pressures at stations a and b C0 = the orifice coefficient = 0.61 for flange taps and vena contracta taps and when Re > 30,000 D0 u 0 4m Re0 (8.29) D. where D0 = orifice diameter EXAMPLE 8.4. An orifice meter with flange taps is to be installed in a 100-mm line to measure the flow of water. The maximum flow rate is expected to be 50 m3/h at 15C. The manometer used to measure the differential pressure is to be filled with mercury, and water is to fill the leads above the surfaces of the mercury. The water temperature will be 15C throughout. (a) If the maximum manometer reading is to be 1.25 m, what diameter, to the nearest millimeter, should be specified for the orifice? (b) What will be the power to operate the meter at full load? Solution (a) Equation (8.29) is used to calculate the orifice diameter. The quantities to be substituted are 50 q 0.0139 m3 s 3,600 62.37 16.018 999 kg m3 (App. 6) C0 0.61 g 9.80665 m s2 From Eq. (2.10), p a pb 9.80665 1.25 13.6 1.0 999 2 154 ,300 N m Substituting these values in Eq. (8.38) gives 0.61S0 2 154,300 0.0139 1 4 999 From which 2 S0 3 D 1.296 10 0 1 4 4 1 4 As a first approximation, call 1 4 =1.0. Then 40.6 D0 40.6 mm 0.406 100 And 1 4 1 0.4064 0.986 The effect of this term is negligible in view of the desired precision of the final result. Check the Reynolds number. The viscosity of water at 15C, from App. 6. is 1.147 cP or 0.001147 kg/ms 2 D 0.041 2 S0 0 0.00132 m2 4 4 q 0.0139 uo 10.53 m s S0 0.00132 The Reynolds number, from Eq. (8.40), is 0.041 10.53 999 Re0 376,000 0.001147 The Reynolds number is large enough to justify the value of 0.61 for C0. b) From Fig. 8.18, for = 0.406, the permanent loss in pressure is 81% of the differential. Since the maximum volumetric flow rate is 0.0139 m3/s, the power required to operate the orifice meter at full flow is 0.81 0.0139 154,300 P 0.81qp a p b 1,000 1.737 kW Area meters: Rotameters - in the orifice, nozzle, or venturi the variation of flow rate through a constant area generates a variable pressure drop, which is related to the flow rate - area meters pressure drop is constant, the area through which the fluid flows varies with the flow rate. the area is related to the flow rate. Rotameter consists of a gradually tapered glass tube mounted vertically in a frame with the large end up. fluid flows upward through the tapered tube and suspends freely a float the greater the flow rate, the higher the float rides in the tube can be used for either liquid or gas flow measurement. FIGURE 8.21 Principle of a rotameter. Insertion Meters sensing element is inserted into the flow stream measure the average flow velocity or local velocity at one point only. the position of the sensing element is important. Pitot tube measure local velocity along a streamline consists of two tubes connected to a manometer static tube measures the static pressure P0 (no velocity component perpendicular to its opening) the impact tube measures the stagnation pressure of the fluid FIGURE 8.26 Principle of pitot tube. For incompressible fluids 2 ps po uo (8.35) EXAMPLE 8.5. Air at 200F (93.3C) is forced through a long, circular flue 36 in. (914 mm) in diameter. A pitot tube reading is taken at the center of the flue at a sufficient distance from flow disturbances to ensure normal velocity distribution. The pitot reading is 0.54 in. (13.7 mm) H2O, and the static pressure at the point of measurement is 15.25 in. (387 mm) H2O. The coefficient of the pitot tube is 0.98. Calculate the flow of air, in cubic feet per minute, measured at 60F (15.6C) and a barometric pressure of 29.92 in. (760 mm) Hg. Solution Assume the Mach number correction is negligible. The velocity at the center of the flue, which is that measured by the pitot tube, is calculated by Eq. (8.35) using fps units and a coefficient of 0.98. Equation (8.46) becomes 2gc p s pb uo 0.98 (8.47) The necessary quantities are as follows. The absolute pressure at the instrument is 15.25 p 29.92 31.04 in. Hg 13.6 Since 1 lb mole occupies 359 ft3 at 32F and 1 atm, the density of the air is 29 492 31.04 0.0625 lb ft 3 359 460 200 29.92 From the manometer reading ps pb 0.54 62.37( g ) 2.81(32.174) lb f ft2 12 By Eq. (8.47), the maximum velocity is 2 x(2.81 x32 .174 ) um ax 0.98 52 .7 ft s 0.0625 This is sufficiently low for the Mach number correction to be negligible. To obtain the average velocity from the maximum velocity, Fig. 5.8 is used. The Reynolds number, based on the maximum velocity, is calculated as follows. From App. 8, the viscosity of air at 200F is 0.022 cP, and Remax 36 12 52.70.0625 670 ,000 0.022 0.000672 The ratio V/umax, from Fig. 5.8, is a little greater than 0.86. Using 0.86 as an estimated value gives V 0.86 52.7 45.3 ft s The Reynolds number Re is 670,0000.86 = 576,000, and V/umax is exactly 0.86 as estimated. The volumetric flow rate is 520 31.04 2 36 q 45.3 60 12 4 660 29.92 15,704 ft 3 min 7.41 m s 3

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