- Email: [email protected]
Seawater Flow Control
129
Chapter 9
Seawater Flow Control
9.1 Gravity flow Flow control means knowing what the distribution of seawater flow is to the various parts of the system and having sufficient control to adjust it to whatever flow is desired. It also means that these flows will be stable over time and reliable. This requires control over the fluid head or pressure within the system. In a gravity flow situation, this means control over either the water elevation in the head tank or the discharge elevations. Controlling the frictional head loss between the head-tank water elevation and the discharge is also critical in gravity systems. Fig. 9.1 shows a typical gravity flow situation from a head tank, which also serves as an emergency supply (see Section 5.15). The various priorities of use in emergencies can be reflected by the elevation of the taps into the head tank. Taps for large-flow low-priority or noncritical uses would be highest and taps for critical high-priority uses would be near the bottom. If the distribution system between the head tank and the point of application has low frictional losses (see Sections 6.4 and 6.5) relative to the driving head (H) and the water elevation in the head tank is constant, the flow rate can be well controlled, stable with time Inflow
,~
Over Flow
--Constant Elevation--
q---~ Head Tank
Driving Head H
Manifold/Header
]
/ TVariati~
Discharge..LL_31Lh in Discharge
Fig. 9.1. Gravity flow from head tank.
130 and reliable. I f the l o s s e s are an a p p r e c i a b l e f r a c t i o n o f H , the flow rates will c h a n g e e v e r y t i m e c o n d i t i o n s on any o f the b r a n c h e s o f that distribution s y s t e m are altered. T h e m a i n l i n e s should, t h e r e f o r e , be v e r y g e n e r o u s l y sized to v i r t u a l l y e l i m i n a t e frictional l o s s e s and in-line p r o c e s s i n g e q u i p m e n t r e m o v e d or m i n i m i z e d (see E x a m p l e 9.1). Since the l e n g t h s i n v o l v e d are o f t e n short, this is u s u a l l y not a hardship. E x a m p l e 9.1 s h o w s the interactive p r o p e r t i e s o f pipe v e l o c i t y and r e s i s t a n c e coefficient at l o w R e y n o l d s n u m b e r s . A g e n e r a l g u i d e is that if the v a l v e s are s i z e d to k e e p the pipe v e l o c i t y at 1 f t / s (0.3 m / s ) or less, that all the v a l v e s c a n be o p e r a t e d i n d e p e n d e n t l y . H o w e v e r , the r e d u c e d v e l o c i t y will i n c r e a s e the s e d i m e n t a t i o n and b i o f o u l i n g in t h e s e lines, r e q u i r i n g m o r e f r e q u e n t s e r v i c i n g to m a i n t a i n the l o w friction. H o w e v e r , a n o t h e r a d v a n t a g e o f l o w pipe v e l o c i t y is that the thrust b l o c k s at p i p e ends c a n u s u a l l y be o m i t t e d . T h r u s t b l o c k s are often r e q u i r e d to h o l d pipes in b e n d s due to m o m e n t u m effects o f c h a n g i n g flow directions (see S e c t i o n 6.7). T h e d i s c h a r g e e l e v a t i o n is often v e r y e a s y to c o n t r o l at the point o f application, since it
Example 9.1. Flow control with constant head tank and discharge elevations You have a laboratory distribution system similar to Fig. 9.1 with a large constantly overflowing head tank and a distribution system made with 'large' diameter piping and terminating immediately below a header pipe with distributed 'small' ball valves at a fixed elevation. The valve discharge is to the air and presumably over a tank. You wish to limit the amount of water that can be used at any specific point of application to 0.0005 m 3/s (about 8 gpm) for each user. The elevation difference between the water level in the head tank and the valve discharge is 4 m. (A) What size small valve should you use? If the piping is 'large', it can be assumed that the only frictional lose in the line is at the small valve. This also means that no matter what each user does with his valve he cannot substantially impact anyone else's flow rates. Using Bernoulli's equation, which is a more general form of Eq. 7.3 without a pump (TDH -- 0), with Point 1 on the water surface of the head tank and Point 2 being in the discharge plane of the valve, y~ hf is the sum of the piping losses between Points 1 and 2 as defined in Eq. 6.2 and y~ hi the sum of the fitting losses as defined in Eq. 6.6. The Zs are the elevations at the respective points.
vZ/2g + P1/Y -k- Z 1
-"
vZ/2g + P2/Y -k- Z 2 -'[-Y~ he + ~_, hi
The pressure at Points 1 and 2 are both atmospheric or zero gage pressure. Assuming a 'large' head tank, the velocity at the head-tank water surface is also zero. The seawater velocity at Point 2 depends on the 'size' of the valve. Putting in the zeros and replacing ~ hi with Eq. 6.6 produces the following: Z1 -
Z2 --
4 m = vZ/Zg + KvVZ/Zg = (1 + Kv)VZ/Zg = (1 + 0.2)V2/2(9.81)
We get the 'small' ball valve loss coefficient (Kv) from Table 6.4. We now have one equation and one unknown. Solving for V2 = 8.09 m/s. Now solving for the cross-sectional diameter that will produce the maximum stated flow at this velocity: Velocity = flow rate/cross • area = 8.09 m/s = O.O005/(rcd2/4) Solving for the diameter d: d = 0.0089 m = 0.89 cm (about 1/2 inch valve) Now valves come only in discrete sizes and the nominal size may not correspond to the actual flow diameter, so some adjustments have to be made in valve selection.
131
Example 9.1. (continued) (B) What is the minimum size of the 'large' pipe that will make the pipe losses 2% of the previous total frictional losses with the valve fully open? Let us assume an 'equivalent pipe' length of 25 m. We will neglect losses from fittings and transitions or include them in the specified 'equivalent' length (see Section 6.5 for discussion). We will also estimate from experience a fairly clean plastic 'smooth' pipe with a resistance coefficient = 0.03. Total losses before = elevation head - velocity head -- 4 - v2/2g = 4 - (8.09)2/2(9.81) = 0.66 m 2% of 0.66 = 0.0132 m, so pipe losses = f l V 2 / 2 g d
(Eq. 6.2) = O.03(25)V2/2(9.81)d = 0.0132 m
In this equation the velocity is that in the pipe. This appears to be one equation with two unknowns, but V and d are not independent, substituting in: V -- flow rate/(rcd2/4) and solving for d = 0.065 m = 6.5 cm (about 2.5 inches) We now can solve for the pipe velocity (0.15 m/s) and the Reynolds number (1 x 104) and can check the assumed resistance coefficient using Fig. 6.3. The estimate was good. (C) If there are 10 users, what is the minimum pipe diameter for the main distribution lines to still to be 'large'? We have to tenfold the flow rate, estimate a new resistance coefficient (which will be checked later) for a smooth pipe equal to 0.02 and keep the pipe frictional losses at the same 2% (0.0132 m). Recalculating the equations above: d' = 0.0899 m -- 8.99 cm (about 3.5 inches) v' -- 0.79 m/s, Reynolds number = 7
x 10 4
Check Fig. 6.3 for resistance coefficient, 0.02 was a good estimate Main seawater distribution pipes of about this size should assure the independence of each system user's flow rate from the actions of the other users.
u s u a l l y i n v o l v e s m u c h s m a l l e r flow rates than t h o s e at h e a d tanks. T h i s can be d o n e w i t h flexible t u b i n g on the d i s c h a r g e spigot and a vertical s u p p o r t stand. T h e a m o u n t o f c o n t r o l this will p r o v i d e o v e r the flow rate is p r o p o r t i o n a l to the m a g n i t u d e o f the p o s s i b l e e l e v a t i o n v a r i a t i o n at the p o i n t o f a p p l i c a t i o n relative to the total driving h e a d at that point. I f h is a substantial f r a c t i o n o f H (see Fig. 9.1), t h e r e will be a c o n s i d e r a b l e r a n g e for flow rate control.
9.2 Water level control T h e r e are a n u m b e r o f w a y s to c o n t r o l w a t e r levels in h e a d tanks, or any o t h e r t y p e o f tank. T h e s e are s h o w n in Fig. 9.2. T h e y w i l l all e f f e c t i v e l y c o n t r o l the w a t e r elevation, p r o v i d i n g that the flow into the tank is g r e a t e r than any flow d e m a n d s on the t a n k (not s h o w n ) . T h e first is the s i m p l e overflow. S i n c e this is built into the tank, it has the least c a p a b i l i t y to alter the w a t e r elevation. T h e o n l y p o s s i b i l i t y is to c h a n g e the e l e v a t i o n o f the entire tank, w h i c h for s m a l l h e a d tanks m a y not be too difficult. T h e r e m o v a b l e s t a n d p i p e can be s w i t c h e d for
132
Overflow
Removable Stand Pipe with "0" Ring Socketor Threaded Joints ~
I
"11
Removable Stand Pipe
Stand Pipe
Special Drain
(;
Internal , Stand Pipe V~
"0" Ring Socket or Threaded Joint
~ ormal Drain Drain
Auxiliary M~ Box I
l Syphon
Fig. 9.2. Water level control approaches. Least flexible to most flexible.
a longer or shorter one (within limits) to change water elevations. A related alternative is an external standpipe. This allows unrestricted access to the tank and easier drainage. As with the internal standpipe, water elevation in the tank can be controlled by selecting the length of the standpipe and both provide easier tank cleaning than the other options due to the inherent bottom drain capability. The siphon is the most flexible as the small auxiliary box can be readily moved up or down. It does not require any modifications to the main tank. The only constraints are that the siphon must be sufficiently large so as to have negligible frictional losses and must be secured at both ends. The small tank should contain at least 15 seconds of flow to keep the velocity effects negligible. It is helpful if the siphon is flexible and transparent. There are a number of other possible variations on the use of siphons in level and flow control and more detailed design information is presented by Garrett (1991). Under normal operating conditions all four approaches can accurately control the water level. During periods of water stoppage, critical flow needs supplied from the tank or even small leaks in the tank or standpipe may allow complete or partial tank drainage. This may be more important for siphon systems, as the siphon effect is broken when the water level drops below the siphon intake hose and it will not restart by itself when the water is restored. Also, all four approaches can fail by flooding, if overflow pipes or screens become clogged with debris.
133 If water levels become too high or to low, it is important to find out about it as soon as possible. Changes in water level are often the first noticeable sign of a failure. For these reasons, water levels are often instrumented to set off alarms or trigger other actions at predetermined high or low water elevations. As an example, if a pump is drawing from a tank that loses water and the pump is not automatically shut off, it will run dry and self destruct. There is a wide variety of programmable water level switches available, many made with synthetic materials. In addition, one can easily be made with a small float, a vertical rod, two brackets, two rod guides and two contact switches. The rod is connected to the float and is allowed, by the two guides, to go up and down with the water level. The brackets are fastened to the rod at the correct elevations and activate the contact switches as the rod moves up and down with the float.
9.3 Control of flow rate The desired flow can be controlled with a valve at the point of application. This is commonly done and in many cases is a satisfactory solution, if the rest of the distribution system has negligible frictional losses. More precise control of flow rate may be required under some conditions. Fig. 9.3 shows the discharge of an orifice to air. This can provide flow rates that are consistent for long periods of time to within a few percent, even for wide seasonal water-property variations and with raw seawater. However, the hole diameter (D) must be larger than the biggest particles to be encountered to avoid clogging. H can be the driving head directly from the head tank, if the distribution system to the point of use has negligible losses, or it can be the head of a small auxiliary head box at the point of application. For accuracy it is important that the flow velocity just upstream of the orifice be negligible. A large pipe is adequate if the flow velocity in the pipe is very low. It is also important that the edges of
n
Constant Water Elevation
Fig. 9.3. Discharge of circular orifice to air. O = C(rcD2/4)(2gn) ~
where Q = discharge flow (ft3/s or m3/s); C -- nondimensional coefficient -- 0.6-0.7; D = orifice diameter (ft or m); g --- gravitational constant (32.2 ft/s 2 or 9.81 m/s2).
134
Example 9.2. Submerged orifice flow control A submerged orifice discharging to air with a diameter of 1 cm is connected to an overflow head box in a manner similar to that shown in Fig. 9.3. This head box has an adjustable overflow pipe. At what elevation H above the center line of the orifice should the overflow pipe be set to get a desired flow rate of 0.1 l/s?
Q : C(:rDZ/4)(2gH) ~ Q -- 0.1 1/s : 0.0001 m3/s C = 0.65 D=
lcm--0.01m
g -- 9.81 m / s 2 Jr = 3.14 0.0001 = 0.65(3.14 x 0.012/4)(2 x 9.81 • H ) ~ H--0.196m
=20cm
This H value should get you close to the required flow rate. Fine adjustments should be made by checking the flow with a graduate tube and stopwatch.
the orifice be sharp, to prevent variations in flow separation and resulting changes in flow rate. This approach has been used successfully with orifices cut into threaded PVC caps on 4 and 6 in. lines with flows over 50 gpm (3.1 l/s) and down to flows as low as 0.25 gpm (0.0016 l/s) with raw seawater and auxiliary head boxes (see Example 9.2). A similar water flow control device for use inside tanks, but with its discharge underwater, has been demonstrated to be precise, inexpensive and reliable (Kinghorn, 1982a). Discharging to air above the water surface has the distinct advantage that the proper operation of the device can be easily checked visually and by sound. With a little experience, even small changes in flow due to partial clogging or loss of head are readily observed. The amount of servicing required depends on prior processing of the water (filtering, sterilization, sedimentation, etc.). With a little care, even under the worst conditions, such devices can often be left unattended for long periods. Another variation for very low flow rates in the order of 0.08 gpm (0.005 l/s) involves the use of nonwetting micropipette tips. These can be cut with a razor blade and fine flow adjustments accomplished by varying the discharge elevation above the water surface (see Fig. 16.1). With filtered water the tips will not clog, but with water containing high concentrations of phytoplankton daily attention is required. This approach provides very precise flow control and is an alternative to very expensive metering pumps. 9.4 Flow measurement
It is sometimes necessary to monitor flow rates in pipes and there are several approaches to this requirement. There are a number of industrially available induction or ultrasonic flow meters that can precisely monitor most flows from outside the pipe. Other types of flow meters have rotors or other appendages exposed to the flow but are generally undesirable for extended marine uses due to biofouling and seawater corrosion problems. However, remote reading propeller flow meters have been successfully used in freshwater hatcheries. Orifices or venturi
135
Example 9.3. A venturi flow measurement A 1-cm-diameter venturi is in a 2-cm-diameter pipe with an air-seawater manometer attached as shown in Fig. 9.4. The manometer deflection is 50 cm, what is the flow rate and average velocity of seawater in the pipe?
Q - - K(rrdZ/4)(2gh) o.5 d D
=lcm =2cm
-0.01m =0.02m
d/D = 0.5 h
--50cm
g
-- 9.81 m / s 2
=0.5m
K
= 1.0 (to be confirmed)
Q --- (3.14)(1.0)(0.01)2/4[(2)(9.81)(0.5)] 0.5 -- 0.000246 m3/s = 0.25 1/s V = Q / p i p e area = 0.78 m / s At this point, it is not known if the assumed K value is reasonable and within the specified conditions.
Re = V d / v v
= 1.0459 x 10 -6 mZ/s, from Table A-3 for 20~
and 35 g / k g salinity
Re = (0.78)(0.01)/1.0459 x 10 -6 = 7.5 x 103 which is greater than minimum of 5 x 103 Reynolds number is within the specified range and flow rate estimate should be close. Actual calibration of flow rates versus manometer deflections would be more accurate than such calculations.
combined with a simple manometer or differential pressure gauge provide a cheap and reliable alternative to expensive industrial equipment (see Fig. 9.4). The manometer is an air-seawater type and may require a vertical height of around 6 ft (2 m). It has a captive air bubble and the measurement is the difference in the elevation of the two sides (see Example 9.3). It is helpful if the tubing from the devices to the manometer's glass or clear plastic tubing is flexible and transparent. If any bubbles are in the lines, other than the big one at the top of the manometer, the accuracy of the measurement can be greatly degraded. The venturi has much lower frictional losses than the orifice and this may be an important consideration for some applications. The manometer deflection, h, happens to be the actual frictional head loss for the orifice, but this is not true for the venturi. The orifice ports should be a few pipe diameters on either side of the orifice. The orifice edge should be sharp to get consistent flow separation. The loss coefficient K is dependent on the diameter ratio d/D (higher ratios higher values) and somewhat on the Reynolds number (Re), especially with Re below 5 x 103. More precise values for K can be found in fluid mechanics texts (Roberson and Crowe, 1990). More recent fluid mechanics texts tend to eliminate coverage of manometers. If a differential pressure gauge is to be used in place of a manometer in Fig. 9.4 or Example 9.3, the manometer deflection (head of manometer fluid) can be converted to a pressure reading. The maximum and minimum manometer deflections can likewise be converted to maximum and minimum pressure readings needed to specify the pressure gauge.
136
Closed ,~ve
s
~6~__~d ~; I
/ ~
Clear'"'"-~Flexible
Water
Tubn ig
IIhManometer Deflection I
Venturi
|
To ...... Manometer
Orifice \
J
Air-Water Manometer Fig. 9.4. Flow rate measurement in pipes using venturi and orifices. Re = Reynolds number = Vd/v
Q = K(rcd2/4)(2gh) ~
where V -- average pipe velocity (ft/s or m/s); d = throat diameter of venturi or orifice (ft or m); v -- kinematic viscosity of fluid, see Table A-3 (ft2/s or mZ/s); D = pipe inside diameter (ft or m)" Q -- flow rate (ft3/s or m3); h - manometer deflection (ft or m); g -- gravitational constant (32.2 ft/s 2 or 9.81 m/s2); K = nondimensional flow coefficient; K = for venturi -- 0.95-1.05 for Re greater than 5 x 103 and d/D of 0.4-0.6 - - the higher the d/D the higher the K" K = for orifice --- 0.60-0.75 for Re greater than 5 x 103 and d/D of 0 . 1 - 0 . 6 - - the higher the d/D the higher the K, much higher values are possible at lower Re and higher d/D.
Occasionally, flow might have to be measured in open channels. Some of the available open channel flow measurement devices can be used down to relatively low flow rates of about 0.5 gpm (0.028 l/s), even though such equipment is usually associated with very high rates. Open-channel flow measurement devices include V-notch, rectangular, and trapezoidal weirs and Parshall flumes. They all involve the prediction of flow rate based on the backing up of water upstream of the device. For more information see Davis and Sorensen (1969) and Leupold and Stevens (1975). All the flow measurement and control devices mentioned have to be checked and calibrated with various versions of 'graduate tube (bucket) and stopwatch'. Calibrating with actual measurements can result in excellent subsequent flow measurement and control.
Chapter 9
Seawater Flow Control
9.1 Gravity flow Flow control means knowing what the distribution of seawater flow is to the various parts of the system and having sufficient control to adjust it to whatever flow is desired. It also means that these flows will be stable over time and reliable. This requires control over the fluid head or pressure within the system. In a gravity flow situation, this means control over either the water elevation in the head tank or the discharge elevations. Controlling the frictional head loss between the head-tank water elevation and the discharge is also critical in gravity systems. Fig. 9.1 shows a typical gravity flow situation from a head tank, which also serves as an emergency supply (see Section 5.15). The various priorities of use in emergencies can be reflected by the elevation of the taps into the head tank. Taps for large-flow low-priority or noncritical uses would be highest and taps for critical high-priority uses would be near the bottom. If the distribution system between the head tank and the point of application has low frictional losses (see Sections 6.4 and 6.5) relative to the driving head (H) and the water elevation in the head tank is constant, the flow rate can be well controlled, stable with time Inflow
,~
Over Flow
--Constant Elevation--
q---~ Head Tank
Driving Head H
Manifold/Header
]
/ TVariati~
Discharge..LL_31Lh in Discharge
Fig. 9.1. Gravity flow from head tank.
130 and reliable. I f the l o s s e s are an a p p r e c i a b l e f r a c t i o n o f H , the flow rates will c h a n g e e v e r y t i m e c o n d i t i o n s on any o f the b r a n c h e s o f that distribution s y s t e m are altered. T h e m a i n l i n e s should, t h e r e f o r e , be v e r y g e n e r o u s l y sized to v i r t u a l l y e l i m i n a t e frictional l o s s e s and in-line p r o c e s s i n g e q u i p m e n t r e m o v e d or m i n i m i z e d (see E x a m p l e 9.1). Since the l e n g t h s i n v o l v e d are o f t e n short, this is u s u a l l y not a hardship. E x a m p l e 9.1 s h o w s the interactive p r o p e r t i e s o f pipe v e l o c i t y and r e s i s t a n c e coefficient at l o w R e y n o l d s n u m b e r s . A g e n e r a l g u i d e is that if the v a l v e s are s i z e d to k e e p the pipe v e l o c i t y at 1 f t / s (0.3 m / s ) or less, that all the v a l v e s c a n be o p e r a t e d i n d e p e n d e n t l y . H o w e v e r , the r e d u c e d v e l o c i t y will i n c r e a s e the s e d i m e n t a t i o n and b i o f o u l i n g in t h e s e lines, r e q u i r i n g m o r e f r e q u e n t s e r v i c i n g to m a i n t a i n the l o w friction. H o w e v e r , a n o t h e r a d v a n t a g e o f l o w pipe v e l o c i t y is that the thrust b l o c k s at p i p e ends c a n u s u a l l y be o m i t t e d . T h r u s t b l o c k s are often r e q u i r e d to h o l d pipes in b e n d s due to m o m e n t u m effects o f c h a n g i n g flow directions (see S e c t i o n 6.7). T h e d i s c h a r g e e l e v a t i o n is often v e r y e a s y to c o n t r o l at the point o f application, since it
Example 9.1. Flow control with constant head tank and discharge elevations You have a laboratory distribution system similar to Fig. 9.1 with a large constantly overflowing head tank and a distribution system made with 'large' diameter piping and terminating immediately below a header pipe with distributed 'small' ball valves at a fixed elevation. The valve discharge is to the air and presumably over a tank. You wish to limit the amount of water that can be used at any specific point of application to 0.0005 m 3/s (about 8 gpm) for each user. The elevation difference between the water level in the head tank and the valve discharge is 4 m. (A) What size small valve should you use? If the piping is 'large', it can be assumed that the only frictional lose in the line is at the small valve. This also means that no matter what each user does with his valve he cannot substantially impact anyone else's flow rates. Using Bernoulli's equation, which is a more general form of Eq. 7.3 without a pump (TDH -- 0), with Point 1 on the water surface of the head tank and Point 2 being in the discharge plane of the valve, y~ hf is the sum of the piping losses between Points 1 and 2 as defined in Eq. 6.2 and y~ hi the sum of the fitting losses as defined in Eq. 6.6. The Zs are the elevations at the respective points.
vZ/2g + P1/Y -k- Z 1
-"
vZ/2g + P2/Y -k- Z 2 -'[-Y~ he + ~_, hi
The pressure at Points 1 and 2 are both atmospheric or zero gage pressure. Assuming a 'large' head tank, the velocity at the head-tank water surface is also zero. The seawater velocity at Point 2 depends on the 'size' of the valve. Putting in the zeros and replacing ~ hi with Eq. 6.6 produces the following: Z1 -
Z2 --
4 m = vZ/Zg + KvVZ/Zg = (1 + Kv)VZ/Zg = (1 + 0.2)V2/2(9.81)
We get the 'small' ball valve loss coefficient (Kv) from Table 6.4. We now have one equation and one unknown. Solving for V2 = 8.09 m/s. Now solving for the cross-sectional diameter that will produce the maximum stated flow at this velocity: Velocity = flow rate/cross • area = 8.09 m/s = O.O005/(rcd2/4) Solving for the diameter d: d = 0.0089 m = 0.89 cm (about 1/2 inch valve) Now valves come only in discrete sizes and the nominal size may not correspond to the actual flow diameter, so some adjustments have to be made in valve selection.
131
Example 9.1. (continued) (B) What is the minimum size of the 'large' pipe that will make the pipe losses 2% of the previous total frictional losses with the valve fully open? Let us assume an 'equivalent pipe' length of 25 m. We will neglect losses from fittings and transitions or include them in the specified 'equivalent' length (see Section 6.5 for discussion). We will also estimate from experience a fairly clean plastic 'smooth' pipe with a resistance coefficient = 0.03. Total losses before = elevation head - velocity head -- 4 - v2/2g = 4 - (8.09)2/2(9.81) = 0.66 m 2% of 0.66 = 0.0132 m, so pipe losses = f l V 2 / 2 g d
(Eq. 6.2) = O.03(25)V2/2(9.81)d = 0.0132 m
In this equation the velocity is that in the pipe. This appears to be one equation with two unknowns, but V and d are not independent, substituting in: V -- flow rate/(rcd2/4) and solving for d = 0.065 m = 6.5 cm (about 2.5 inches) We now can solve for the pipe velocity (0.15 m/s) and the Reynolds number (1 x 104) and can check the assumed resistance coefficient using Fig. 6.3. The estimate was good. (C) If there are 10 users, what is the minimum pipe diameter for the main distribution lines to still to be 'large'? We have to tenfold the flow rate, estimate a new resistance coefficient (which will be checked later) for a smooth pipe equal to 0.02 and keep the pipe frictional losses at the same 2% (0.0132 m). Recalculating the equations above: d' = 0.0899 m -- 8.99 cm (about 3.5 inches) v' -- 0.79 m/s, Reynolds number = 7
x 10 4
Check Fig. 6.3 for resistance coefficient, 0.02 was a good estimate Main seawater distribution pipes of about this size should assure the independence of each system user's flow rate from the actions of the other users.
u s u a l l y i n v o l v e s m u c h s m a l l e r flow rates than t h o s e at h e a d tanks. T h i s can be d o n e w i t h flexible t u b i n g on the d i s c h a r g e spigot and a vertical s u p p o r t stand. T h e a m o u n t o f c o n t r o l this will p r o v i d e o v e r the flow rate is p r o p o r t i o n a l to the m a g n i t u d e o f the p o s s i b l e e l e v a t i o n v a r i a t i o n at the p o i n t o f a p p l i c a t i o n relative to the total driving h e a d at that point. I f h is a substantial f r a c t i o n o f H (see Fig. 9.1), t h e r e will be a c o n s i d e r a b l e r a n g e for flow rate control.
9.2 Water level control T h e r e are a n u m b e r o f w a y s to c o n t r o l w a t e r levels in h e a d tanks, or any o t h e r t y p e o f tank. T h e s e are s h o w n in Fig. 9.2. T h e y w i l l all e f f e c t i v e l y c o n t r o l the w a t e r elevation, p r o v i d i n g that the flow into the tank is g r e a t e r than any flow d e m a n d s on the t a n k (not s h o w n ) . T h e first is the s i m p l e overflow. S i n c e this is built into the tank, it has the least c a p a b i l i t y to alter the w a t e r elevation. T h e o n l y p o s s i b i l i t y is to c h a n g e the e l e v a t i o n o f the entire tank, w h i c h for s m a l l h e a d tanks m a y not be too difficult. T h e r e m o v a b l e s t a n d p i p e can be s w i t c h e d for
132
Overflow
Removable Stand Pipe with "0" Ring Socketor Threaded Joints ~
I
"11
Removable Stand Pipe
Stand Pipe
Special Drain
(;
Internal , Stand Pipe V~
"0" Ring Socket or Threaded Joint
~ ormal Drain Drain
Auxiliary M~ Box I
l Syphon
Fig. 9.2. Water level control approaches. Least flexible to most flexible.
a longer or shorter one (within limits) to change water elevations. A related alternative is an external standpipe. This allows unrestricted access to the tank and easier drainage. As with the internal standpipe, water elevation in the tank can be controlled by selecting the length of the standpipe and both provide easier tank cleaning than the other options due to the inherent bottom drain capability. The siphon is the most flexible as the small auxiliary box can be readily moved up or down. It does not require any modifications to the main tank. The only constraints are that the siphon must be sufficiently large so as to have negligible frictional losses and must be secured at both ends. The small tank should contain at least 15 seconds of flow to keep the velocity effects negligible. It is helpful if the siphon is flexible and transparent. There are a number of other possible variations on the use of siphons in level and flow control and more detailed design information is presented by Garrett (1991). Under normal operating conditions all four approaches can accurately control the water level. During periods of water stoppage, critical flow needs supplied from the tank or even small leaks in the tank or standpipe may allow complete or partial tank drainage. This may be more important for siphon systems, as the siphon effect is broken when the water level drops below the siphon intake hose and it will not restart by itself when the water is restored. Also, all four approaches can fail by flooding, if overflow pipes or screens become clogged with debris.
133 If water levels become too high or to low, it is important to find out about it as soon as possible. Changes in water level are often the first noticeable sign of a failure. For these reasons, water levels are often instrumented to set off alarms or trigger other actions at predetermined high or low water elevations. As an example, if a pump is drawing from a tank that loses water and the pump is not automatically shut off, it will run dry and self destruct. There is a wide variety of programmable water level switches available, many made with synthetic materials. In addition, one can easily be made with a small float, a vertical rod, two brackets, two rod guides and two contact switches. The rod is connected to the float and is allowed, by the two guides, to go up and down with the water level. The brackets are fastened to the rod at the correct elevations and activate the contact switches as the rod moves up and down with the float.
9.3 Control of flow rate The desired flow can be controlled with a valve at the point of application. This is commonly done and in many cases is a satisfactory solution, if the rest of the distribution system has negligible frictional losses. More precise control of flow rate may be required under some conditions. Fig. 9.3 shows the discharge of an orifice to air. This can provide flow rates that are consistent for long periods of time to within a few percent, even for wide seasonal water-property variations and with raw seawater. However, the hole diameter (D) must be larger than the biggest particles to be encountered to avoid clogging. H can be the driving head directly from the head tank, if the distribution system to the point of use has negligible losses, or it can be the head of a small auxiliary head box at the point of application. For accuracy it is important that the flow velocity just upstream of the orifice be negligible. A large pipe is adequate if the flow velocity in the pipe is very low. It is also important that the edges of
n
Constant Water Elevation
Fig. 9.3. Discharge of circular orifice to air. O = C(rcD2/4)(2gn) ~
where Q = discharge flow (ft3/s or m3/s); C -- nondimensional coefficient -- 0.6-0.7; D = orifice diameter (ft or m); g --- gravitational constant (32.2 ft/s 2 or 9.81 m/s2).
134
Example 9.2. Submerged orifice flow control A submerged orifice discharging to air with a diameter of 1 cm is connected to an overflow head box in a manner similar to that shown in Fig. 9.3. This head box has an adjustable overflow pipe. At what elevation H above the center line of the orifice should the overflow pipe be set to get a desired flow rate of 0.1 l/s?
Q : C(:rDZ/4)(2gH) ~ Q -- 0.1 1/s : 0.0001 m3/s C = 0.65 D=
lcm--0.01m
g -- 9.81 m / s 2 Jr = 3.14 0.0001 = 0.65(3.14 x 0.012/4)(2 x 9.81 • H ) ~ H--0.196m
=20cm
This H value should get you close to the required flow rate. Fine adjustments should be made by checking the flow with a graduate tube and stopwatch.
the orifice be sharp, to prevent variations in flow separation and resulting changes in flow rate. This approach has been used successfully with orifices cut into threaded PVC caps on 4 and 6 in. lines with flows over 50 gpm (3.1 l/s) and down to flows as low as 0.25 gpm (0.0016 l/s) with raw seawater and auxiliary head boxes (see Example 9.2). A similar water flow control device for use inside tanks, but with its discharge underwater, has been demonstrated to be precise, inexpensive and reliable (Kinghorn, 1982a). Discharging to air above the water surface has the distinct advantage that the proper operation of the device can be easily checked visually and by sound. With a little experience, even small changes in flow due to partial clogging or loss of head are readily observed. The amount of servicing required depends on prior processing of the water (filtering, sterilization, sedimentation, etc.). With a little care, even under the worst conditions, such devices can often be left unattended for long periods. Another variation for very low flow rates in the order of 0.08 gpm (0.005 l/s) involves the use of nonwetting micropipette tips. These can be cut with a razor blade and fine flow adjustments accomplished by varying the discharge elevation above the water surface (see Fig. 16.1). With filtered water the tips will not clog, but with water containing high concentrations of phytoplankton daily attention is required. This approach provides very precise flow control and is an alternative to very expensive metering pumps. 9.4 Flow measurement
It is sometimes necessary to monitor flow rates in pipes and there are several approaches to this requirement. There are a number of industrially available induction or ultrasonic flow meters that can precisely monitor most flows from outside the pipe. Other types of flow meters have rotors or other appendages exposed to the flow but are generally undesirable for extended marine uses due to biofouling and seawater corrosion problems. However, remote reading propeller flow meters have been successfully used in freshwater hatcheries. Orifices or venturi
135
Example 9.3. A venturi flow measurement A 1-cm-diameter venturi is in a 2-cm-diameter pipe with an air-seawater manometer attached as shown in Fig. 9.4. The manometer deflection is 50 cm, what is the flow rate and average velocity of seawater in the pipe?
Q - - K(rrdZ/4)(2gh) o.5 d D
=lcm =2cm
-0.01m =0.02m
d/D = 0.5 h
--50cm
g
-- 9.81 m / s 2
=0.5m
K
= 1.0 (to be confirmed)
Q --- (3.14)(1.0)(0.01)2/4[(2)(9.81)(0.5)] 0.5 -- 0.000246 m3/s = 0.25 1/s V = Q / p i p e area = 0.78 m / s At this point, it is not known if the assumed K value is reasonable and within the specified conditions.
Re = V d / v v
= 1.0459 x 10 -6 mZ/s, from Table A-3 for 20~
and 35 g / k g salinity
Re = (0.78)(0.01)/1.0459 x 10 -6 = 7.5 x 103 which is greater than minimum of 5 x 103 Reynolds number is within the specified range and flow rate estimate should be close. Actual calibration of flow rates versus manometer deflections would be more accurate than such calculations.
combined with a simple manometer or differential pressure gauge provide a cheap and reliable alternative to expensive industrial equipment (see Fig. 9.4). The manometer is an air-seawater type and may require a vertical height of around 6 ft (2 m). It has a captive air bubble and the measurement is the difference in the elevation of the two sides (see Example 9.3). It is helpful if the tubing from the devices to the manometer's glass or clear plastic tubing is flexible and transparent. If any bubbles are in the lines, other than the big one at the top of the manometer, the accuracy of the measurement can be greatly degraded. The venturi has much lower frictional losses than the orifice and this may be an important consideration for some applications. The manometer deflection, h, happens to be the actual frictional head loss for the orifice, but this is not true for the venturi. The orifice ports should be a few pipe diameters on either side of the orifice. The orifice edge should be sharp to get consistent flow separation. The loss coefficient K is dependent on the diameter ratio d/D (higher ratios higher values) and somewhat on the Reynolds number (Re), especially with Re below 5 x 103. More precise values for K can be found in fluid mechanics texts (Roberson and Crowe, 1990). More recent fluid mechanics texts tend to eliminate coverage of manometers. If a differential pressure gauge is to be used in place of a manometer in Fig. 9.4 or Example 9.3, the manometer deflection (head of manometer fluid) can be converted to a pressure reading. The maximum and minimum manometer deflections can likewise be converted to maximum and minimum pressure readings needed to specify the pressure gauge.
136
Closed ,~ve
s
~6~__~d ~; I
/ ~
Clear'"'"-~Flexible
Water
Tubn ig
IIhManometer Deflection I
Venturi
|
To ...... Manometer
Orifice \
J
Air-Water Manometer Fig. 9.4. Flow rate measurement in pipes using venturi and orifices. Re = Reynolds number = Vd/v
Q = K(rcd2/4)(2gh) ~
where V -- average pipe velocity (ft/s or m/s); d = throat diameter of venturi or orifice (ft or m); v -- kinematic viscosity of fluid, see Table A-3 (ft2/s or mZ/s); D = pipe inside diameter (ft or m)" Q -- flow rate (ft3/s or m3); h - manometer deflection (ft or m); g -- gravitational constant (32.2 ft/s 2 or 9.81 m/s2); K = nondimensional flow coefficient; K = for venturi -- 0.95-1.05 for Re greater than 5 x 103 and d/D of 0.4-0.6 - - the higher the d/D the higher the K" K = for orifice --- 0.60-0.75 for Re greater than 5 x 103 and d/D of 0 . 1 - 0 . 6 - - the higher the d/D the higher the K, much higher values are possible at lower Re and higher d/D.
Occasionally, flow might have to be measured in open channels. Some of the available open channel flow measurement devices can be used down to relatively low flow rates of about 0.5 gpm (0.028 l/s), even though such equipment is usually associated with very high rates. Open-channel flow measurement devices include V-notch, rectangular, and trapezoidal weirs and Parshall flumes. They all involve the prediction of flow rate based on the backing up of water upstream of the device. For more information see Davis and Sorensen (1969) and Leupold and Stevens (1975). All the flow measurement and control devices mentioned have to be checked and calibrated with various versions of 'graduate tube (bucket) and stopwatch'. Calibrating with actual measurements can result in excellent subsequent flow measurement and control.