流体力学与传热 ：1-6 Metering of Fluids

1、1.6 Metering of Fluids,It is important to be able to measure and control the amount of material entering and leaving a chemical or other processing plant. Many different types of devices are used to measure the flow of fluids.,Very widely used for fluid metering are the pitot tube, venturi meter, or

2、ifice meter, and open-channel weirs,Most meters operate on all the fluid in the pipe or channel and are known as full-bore meter.,Others, called insertion meters, measure the flow rate, or more commonly the fluid velocity, at one point only,1.6.1 Insertion Meters,In this type of meter the sensing el

3、ement, which is small compared to the size of the flow channel, is inserted into the flow stream.,A few insertion meters measure the average velocity, but the majority measure the local velocity at one point only.,Pitot Tube,The pitot tube is used to measure the local velocity at a given point in th

4、e flow stream and not the average velocity in the pipe.,The impact tube has its opening normal to the direction of flow,the static tube has its opening parallel to the direction of flow,The opening of the impact tube is perpendicular to the flow direction. The pressure ps, measured by the impact tub

5、e, is,The opening of the static tube is parallel to the direction of flow, where po is the static pressure measured.,and solving for uo from two equations above,It should be noted that the pitot tube measures the velocity at one point only.,(1.6-1),The coefficient Cp is used to take into account dev

6、iations, which generally varies between about 0.98 and 1.0.,(1.6-2),For accurate use, the coefficient should be determined by calibration of the pitot tube.,This equation applies to incompressible fluids but can be used to approximate the flow of gases at moderate velocities and pressure changes of

7、about 10% or less of the total pressure.,The value of the pressure drop p is related to R, the reading on the manometer:,(1.6-3),where A is the density of the fluid in the manometer,Since the pitot tube measures velocity at only one point, several methods can be used to obtain the average velocity i

8、n the pipe.,For Pitot tube if the velocity is measured at the exact center of the tube to obtain umax, then by using Fig. 1.20, the V can be obtained.,Care should be taken to have the pitot tube at least 100 diameters downstream from any pipe obstruction.,1.6.2 Full-Bore Meters,The most common types

9、 of full-bore meters are venturi and orifice meters and variable- area meters such as Rotameters.,Other full-bore measuring devices include V-element, magnetic, vortex-shedding, turbine, and positive-displacement meters; ultrasonic meters.,1. Venturi Meter,Venturi meter is constructed from a short f

10、langed inlet section A , consisting of a short cylindrical portion and a truncated cone;,a flanged throat section B;,and a flanged outlet section C , consisting of a long truncated cone.,At the junction of the cylindrical and conical portion, an annular chamber is provided, and a number of small hol

11、es drilled from the inside of the tube to the annular chamber.,The annular chamber and the small holes has the function of averaging individual pressure, it is called piezometer ring.,A second piezometer ring is formed in the throat section.,A manometer or other means for measuring pressure differen

12、ce is connected between two piezometer ring.,The average pressure is transmitted through the upstream pressure connection.,In the venturi meter , the velocity is increased, and the pressure decreased in the upstream cone. The pressure drop in the upstream cone is used to measure the rate of flow thr

13、ough the instrument.,Since separation does not occur in the contracting cross section, the upstream cone can be made shorter than the downstream cone with but little friction.,To derive the equation for the venturi meter, friction is neglected and the pipe is assumed horizontal. Assuming turbulent f

14、low and writing the mechanical-energy-balance equation between points 1 and 2 for an incompressible fluid,The basic equation for venturi meter,The continuity equation for constant is,(1.6-6),Venturi coefficient,Eq(1.6-8) applies strictly to the frictionless flow of non-compressible fluids. To accoun

15、t for the small friction loss between locations 1 and 2, Eq(1.6-8) is corrected by introducing an empirical factor Cv and writing,(1.6-9),When d2 is less than d1/4, the approach velocity and the term can be neglected, since the error is less than 0.2 percent.,However, these coefficients can vary, an

16、d individual calibration is recommended if the manufacturers calibration is not available.,For many meters and a Re104 at point 1, Cv is about 0.98 for pipe diameters below 0.2 m and 0.99 for larger sizes.,Flow rate,The flow rate of practical interest is the mass and volumetric flow rates through th

17、e meter.,To calculate the volumetric flow rate, the velocity V2 is multiplied by the area A2,Pressure recovery,Friction cannot be completely eliminated, and a permanent loss in pressure and a corresponding loss in power do occur.,Because of the small angle of divergence in the recovery cone , the pe

18、rmanent pressure loss from venturi meter is relatively small.,2.12C. Orifice Meter,The venturi meter has certain practical disadvantages for ordinary plant practice.,It is expensive, it occupies considerable space, and its ratio of throat diameter and pipe diameter cannot be changed.,For a given met

19、er and definite manometer system, the maximum measurable flow rate is fixed, so if the flow range is changed, the throat diameter may be too large to give an accurate reading or too small to accommodate the next maximum flow rate.,The orifice meter meets these objections to the venturi but at the pr

20、ice of a larger power consumption.,The principle of the orifice meter is identical with that of the venturi.,The reduction of the cross section of the flowing stream in passing through the orifice increasing the velocity head at the expense of the pressure head, and reduction in pressure between the

21、 taps is measured by the manometer.,A typical sharp-edged orifice is shown in figure. A drilled plate having a hole of diameter D0 is mounted between two flanges in a pipe of diameter D1.,Pressure taps at points 1 upstream and 2 downstream measure p1 - p2. The exact positions of the two taps are som

22、ewhat arbitrary: in one type of meter the taps are installed about 1 pipe diameter upstream and 0.3 to 0.8 pipe diameter downstream.,The equation for the orifice is similar to equation for the venturi,where V2 is the velocity in the orifice, D0 is the orifice diameter, and C0 is the orifice coeffici

23、ent and always determined experimentally.,1.6-12,Co is almost constant and independent of D0/D1 provided Re is greater than about 20000 and D0/D1 is less than about 0.5.,It varies considerably with changes in D0/D1 and with Reynolds number at the orifice.,Under these conditions Co may be taken as 0.

24、61 for both flange taps and vena-contracta taps.,Furthermore, if D0/D1 is less than 0.25, the term differs negligibly from unity, and Eq.(1.6-12 ) becomes,The mass flow rate is given by,Unless considerable precision is desired, equation is adequate for orifice design .,A check on the value of the Re

25、 should be made, however, since the coefficient 0.61 is not accurate when Re is less than about 20000.,It is especially important that enough straight pipe both above and below the orifice to ensure a flow pattern that is normal and undisturbed by fittings, valves, or other equipment.,Pressure recov

26、ery,The pressure recovery in an orifice is poor, which is one disadvantage of the orifice meter.,The fraction of orifice differential that is permanently lost depends on the value of the .,2.12D. Flow-Nozzle Meter,A typical flow nozzle is shown in figure. It is essentially a short cylinder with the

27、approach being elliptical in shape. This meter has characteristics similar to those of the venturi meter but is shorter and much less expensive.,The length of the straight portion of the throat is about one-half the diameter of the throat, D2. The upstream pressure tap p1 is 1 pipe diameter from the

28、 inlet-nozzle face, and the downstream tap p2 is 1/2 pipe diameter from the inlet-nozzle face.,The equation for the nozzle meter is the same as venturi meter, with the coefficient Cn for the nozzle replacing Cv for the venturi.,For the flow nozzle the coefficient Cn ranges from 0.95 at a pipe Re of

29、104, 0.98 at 105, and 0.99 at 106 or above. The permanent pressure loss is calculated by equation,2.12E. Variable-Area Flow Meters Rotmeters,In the orifice, nozzle, or venturi, the variation of velocity through a constant area generates a variable pressure drop, which is related to the flow rate.,An

30、other class of meters, called area meters, consists of device in which the pressure drop is constant, or nearly so, and the area through which the fluid flow varies with flow rate.,The area is related, through proper calibration, to the flow rate.,Rotameter consists essentially of a gradually tapere

31、d glass tube mounted vertically in a frame with large end up.,The fluid flow upward through the tapered tube and suspends freely a float.,The entire fluid stream must flow through the annular space between the float and the tube wall.,The tube is marked in divisions, and the reading of the meter is

32、obtained from the scale reading at the reading edge of the float, which is taken at the largest cross section of the float.,Theory and calibration of rotameters,For a given flow rate, the equilibrium position of the float in a rotameter is established by a balance of three forces:,(1) The gravity of

33、 the float: vffg,(2) the buoyant force of the fluid on the float: vfg,(3) the the drag force on the float:,For equilibrium,For a given meter operating on a certain fluid, the right-hand side of equation above is constant and independent of the flow rate. Therefore ,when the flow rate increases, the

34、position of the float must change to keep the drag force constant.,If the change in drag coefficient is small, the total flow rate is proportional to the annular area between the float and the wall,For a linearly tapered tube with a diameter at the bottom about equal to the float diameter, the area

35、for flow is a quadratic function of the height of the float.,When the clearance between float and tube wall is small, the term a2h2 is relatively unimportant and the flow almost a linear function of the height h.,Therefore rotameters tend to have a linear relationship between flow rate and position

36、of the float.,For a given float of density f and a fluid density , the volumetric flow rate q is given by,1.6-17,volumetric flow rate q is the reading on the rotameter, and K is a constant which is determined experimentally.,If a fluid B is used instead of , at the same height or reading of q on the

37、 rotameter and assuming K does not vary appreciably, the following approximation can be used:,For gases where f and B,1.6-18,Note that the reading on the rotameter is taken at the highest and widest point of the float.,problem,orifice and venturi meters measure the velocity of the entire stream of f

38、luid The pitot tube measures the velocity of fluid. Rotameter must be installed in the pipe line, and the fluid must flow through the tapered tube and suspends freely a float.,Disadvantages for Venturi meter are: The disadvantage for orifice meter is:,In the orifice and venturi meter, the variation

39、of velocity through ( ) area generates a ( ) pressure drop. In the rotameter, the variation of flowrate through ( ) area generates a ( ) pressure drop.,For a orifice , nozzle and venturi meter, when the Reynolds number is greater than critical Re, then orifice coefficient Co is ( ) of the Reynolds n

40、umber for a given Metering devices for a velocity must take ( ) from any pipe obstruction.,Both the holes and annular space provided for a piezometer ring has a function of ( ) Rotameter tends to have a linearity between flowrate and position of float due to having ( ) conical degree,Fundament of local velocity measured by pitot tube is based on the ( ) tested by both the impact tube and static tube, respectively,Example 1,Sulphuric acid of specific gravity 1.3 is flowing through a pipe of 50 mm internal diameter.