【机械类毕业论文中英文对照文献翻译】化工工业离心泵
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机械类毕业论文中英文对照文献翻译
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【机械类毕业论文中英文对照文献翻译】化工工业离心泵,机械类毕业论文中英文对照文献翻译,机械类,毕业论文,中英文,对照,文献,翻译,化工,工业,离心泵
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CENTRIFUGAL PUMPS IN THE CHEMICAL INDUSTRYAbstract : A centrifugal pump converts the input power to kinetic energy in the liquid by accelerating the liquid by a revolving device - an impeller. The most common type is the volute pump. Fluid enters the pump through the eye of the impeller which rotates at high speed. The fluid is accelerated radially outward from the pump chasing. A vacuum is created at the impellers eye that continuously draws more fluid into the pump . This article stresses on a series of centrifugal pumps，From a brief introduction to the principles.Keywords : centrifugal pump ,Introduction ,Working principle , Cavitation ， Mechanism of Cavitation ，Solution and Remedies1. Introduction Pump ,device used to raise ,transfer ,or compress liquids and gases .Four general classes of pumps for liquids are described below .In all of them ,steps are taken to prevent cavitation (the formation of a vacuum) ,which would reduce the flow and damage the structure of the pump .Pumps used for gases and vapors are usually known as compressors .The study of fluids in motion is called fluid dynamics. Water pump ,device for moving water from one location to another ,using tubes or other machinery .Water pumps operate under pressures ranging from a fraction of a pound to more than 10,000 pounds per square inch .Everyday examples of water pumps range from small electric pumps that circulate and aerate water in aquariums and fountains to sump pumps that remove water from beneath the foundations of homes . One type of modern pumps used to move water is the centrifugal pump .Early version of the centrifugal pump ,the screw pump ,consists of a corkscrew-shaped mechanism in a pipe that ,when rotated ,pulls water upward .Screw pumps are often used in waste-water treatment plants because they can move large amounts of water without becoming clogged with debris .In the ancient Middle East the need for irrigation of farmland was a strong inducement to develop a water pump .Early pumps in this region were simple devices for lifting buckets of water from a source to a container or a trench .Greek mathematician and inventor Archimedes is thought to have devised the first screw pump in the third century BC .Later Greek inventor Ctesibius develop the first lift pump .During the late 17th and early 18th Centuries AD ,British engineer Thomas Savery ,French physicist Denis Papin ,And British blacksmith and inventor Thomas Newcomen contributed to the development of a water pump that used steam to power the pump piston .The steam-powered water pumps first wide use was in pumping water out of mines .Modern-day examples of centrifugal pumps are those used at the Grand Coulee Dam on the Columbia River .This pump system has the potential to irrigate over one million acres of land . Also known as rotary pumps ,centrifugal pumps have a rotating impeller ,also known as a blade ,that is immersed in the liquid .Liquid enters the pump near the axis of the impeller ,and the rotating impeller sweeps the liquid out toward the ends of the impeller blades at high pressure .The impeller also gives the liquid a relatively high velocity that can be converted into pressure in a stationary part of the pump ,known as the diffuser .In high-pressure pumps ,a number of impeller may be used in series ,and the diffusers following each impeller may contain guide vanes to gradually reduce the liquid velocity .For lower-pressure pumps ,the diffuser is generally a spiral passage ,known as a volute ,with its cross-sectional area increasing gradually to reduce the velocity efficiently .The impeller must be primed before it can begin operation ,that is ,the impeller must be surrounded by liquid when the pump is started .This can be done by placing a check valve in the suction line ,which holds the liquid in the pump when the impeller is not rotating .If this valve leaks ,the pump may need to be primed by the introduction of liquid from an outside source such as the discharge reservoir .A centrifugal pump generally has a valve in the discharge line to control the flow and pressure .For low flows and high pressures ,the action of the impeller is largely radial .For higher flows and lower discharge pressure ,the direction of the flow within the pump is more nearly parallel to the axis of the shaft ,and the pump is said to have an axial flow .The impeller in this case acts as a propeller .The transition from one set of floe conditions to the other is gradual ,and for intermediate condition , the device is called a mixed-flow pump . 2.The Centrifugal Pump The centrifugal pump is by far the most widely used type in the chemical and petroleum industries .It will pump liquids with very wide ranging properties and suspensions with a high solids content including ,for example ,cement slurries ,and may be constructed from a very wide rang of corrosion resistant materials .The whole pump casing may be constructed from plastic such as polypropylene or it may be fitted with a corrosion-resistant lining .Because it operates at high speed ,it may be directly coupled to an electric motor and it will give a high flow rate for its size . In this type of pump ,the fluid is fed to the centre of a rotating impeller and is thrown outward by centrifugal action .As a result of the high speed of rotation the liquid acquires a high kinetic energy and the pressure difference between the suction and delivery sides arises from the conversion of kinetic energy into pressure energy . The impeller consists of a series of curved vanes so shaped that the flow within the pump is as smooth as possible .The greater the number of vanes on the impeller ,the greater is the control over the direction of the liquid and hence the smaller are the losses due to turbulence and circulation between the vanes .In the open impeller ,the vanes are fixed to a central hub ,whereas in the closed type the vanes are held between two supporting plates and leakage across the impeller is reduced .As will be seen later ,the angle of the tips of the blades very largely determines the operating characteristics of the pump . The liquid enters the casing of the pump，normally in an axial direction，and is picked up by the vanes of the impellerIn the simple type of centrifugal pump，the liquid discharges into a volute，a chamber of gradually increasing crosssection with a tangential outletA volute type of pump is shown in Fig.(a)In the turbine pump-Fig(b)the liquid flows from the moving vanes of the impeller through a series of fixed vanes forming a diffusion ringThis gives a more gradual change in direction to the fluid and more efficient conversion of kinetic energy into pressure energy than is obtained with the volute typeThe angle of the leading edge of the fixed vanes should be such that the fluid is received without shockThe liquids flows along the surface of the impeller vane with a certain velocity whilst the tip of the vane is moving relative to the casing of the pumpThe direction of motion of the liquid relative to the pump casing-and the required angle of the fixed vanesis found by compounding these two velocitiesIn Figc，c. is the velocity of the liquid relative to the vane and is the tangential velocity of the tip of the vane；compounding these two velocities gives the resultant velocity of the liquidIt is apparent，therefore，that the required vane angle in the diffuser is dependent on the throughput，the speed of rotation，and the angle of the impeller bladesThe pump will therefore operate at maximum efficiency only over a narrow range of conditions Virtual head of a centrifugal pumpThe maximum pressure is developed when the whole of the excess kinetic energy of the fluid is converted into pressure energy. As indicated belowthe head is proportional to the square of the radius and to the speed，and is of the order of 60m for a singlestage centrifugal pump；for higher pressures，multistage pumps must be usedConsider the liquid which is rotating at a distance of between r and r+dr from the centre of the pump(Figd)dThe mass of this element of fluid dm is given by 2rdrd，where is the density of the fluid and 6 is the width of the element of fluid。If the fluid is traveling with a velocity u and at an angle to the tangential directionThe angular momentum of this mass of fluid = dM (urcos) The torque acting on the fluid d is equal to the rate of change of angular momentum with time，as it goes through the pumpD = dM /t(urcos)=2rbdr/t(urcos) (2.1) The volumetric rate of flow of liquid through the pump：Q=2rb/t (2.2)Dr =Q d(urcos) (2.3)The total torque acting on the liquid in the pump is therefore obtained integrating d between the limits denoted by suffix 1 and suffix 2，where suffix 1 refers to the conditions at the inlet to the pump and suffix 2 refers to the condition at the discharge Thus，=Q (cos- cos) The advantages and disadvantages of the centrifugal pump The main advantages are： (1) It is simple in construction and can，therefore， be made in a wide range of materials (2)There is a complete absence of valves (3)It operates at high speed(up to 100 Hz)and，therefore，can be coupled directly to an electric motor. In general，the higher the speed the smaller the pump and motor for a give n duty (4)It gives a steady delivery (5)Maintenance costs are lower than for any other type of pump (6)No damage is done to the pump if the delivery line becomes blocked，provided it is not run in this condition for a prolonged period (7)It is much smaller than other pumps of equal capacityIt can，therefore，be made into a sealed unit with the driving motor and immersed in the suction tank (8)Liquids containing high proportions of suspended solids are readily handled The main disadvantages are： (1)The singlestage pump will not develop a high pressureMultistage pumps will develop greater heads bat they are very much more expensive and cannot readily be made in corrosionresistant material because of their greater complexityIt is generally better to use very high speeds in order to reduce the number of stages required (2)It operates at a high efficiency over only a limited range of conditions; this applies especially to turbine pumps (3)It is not usually self-priming. (4)If a non-return valve is not incorporated in the delivery or suction line, the liquid will run back into the suction tank as soon as the pump stops (5)Very viscous liquids cannot he handled efficiently 3. Cavitation in centrifugal pump （1）The term cavitation comes from the Latin word cavus, which means a hollow space or a cavity. Websters Dictionary defines the word cavitation as the rapid formation and collapse of cavities in a flowing liquid in regions of very low pressure. In any discussion on centrifugal pumps various terms like vapor pockets, gas pockets, holes, bubbles, etc. are used in place of the term cavities. These are one and the same thing and need not be confused. The term bubble shall be used hereafter in the discussion. In the context of centrifugal pumps, the term cavitation implies a dynamic process of formation of bubbles inside the liquid, their growth and subsequent collapse as the liquid flows through the pump. Generally, the bubbles that form inside the liquid are of two types: Vapor bubbles or Gas bubbles. 1.Vapor bubbles are formed due to the vaporisation of a process liquid that is being pumped. The cavitation condition induced by formation and collapse of vapor bubbles is commonly referred to as Vaporous Cavitation. 2.Gas bubbles are formed due to the presence of dissolved gases in the liquid that is being pumped (generally air but may be any gas in the system). The cavitation condition induced by the formation and collapse of gas bubbles is commonly referred to as Gaseous Cavitation. （2）Important Definitions: To enable a clear understanding of mechanism of cavitation, definitions of following important terms are explored. Static pressure, Dynamic pressure, Total pressure, Static pressure head, Velocity head, Vapour pressure. Static pressure ：The static pressure in a fluid stream is the normal force per unit area on a solid boundary moving with the fluid. It describes the difference between the pressure inside and outside a system, disregarding any motion in the system. For instance, when referring to an air duct, static pressure is the difference between the pressure inside the duct and outside the duct, disregarding any airflow inside the duct. In energy terms, the static pressure is a measure of the potential energy of the fluid. Dynamic pressure：A moving fluid stream exerts a pressure higher than the static pressure due to the kinetic energy ( mv2) of the fluid. This additional pressure is defined as the dynamic pressure. The dynamic pressure can be measured by converting the kinetic energy of the fluid stream into the potential energy. In other words, it is pressure that would exist in a fluid stream that has been decelerated from its velocity v to zero velocity. Total pressure：The sum of static pressure and dynamic pressure is defined as the total pressure. It is a measure of total energy of the moving fluid stream. i.e. both potential and kinetic energy. Velocity head：Vapor pressure is the pressure required to keep a liquid in a liquid state. If the pressure applied to the surface of the liquid is not enough to keep the molecules pretty close together, the molecules will be free to separate and roam around as a gas or vapor. The vapor pressure is dependent upon the temperature of the liquid. Higher the temperature, higher will be the vapor pressure. （3） Cavitation Damage：Cavitation can destroy pumps and valves, and cavitation causes a loss of efficiency in pumps immediately, and also a continuously increasing loss of efficiency as the equipment degrades due to erosion of the pump components by cavitation. Therefore It is important to understand the phenomena sufficiently to predict and therefore reduce cavitation and damage from cavitation, and also to diagnose and find practical solutions to cavitation problems。 1）Cavitation Enhanced Chemical ErosionPhenomenon of Cavitation Pumps operating under cavitation conditions become more vulnerable to corrosion and chemical attack. Metals commonly develop an oxide layer or passivated layer which protects the metal from further corrosion. Cavitation can remove this oxide or passive layer on a continuous basis and expose unprotected metal to further oxidation. The two processes (cavitation & oxidation) then work together to rapidly remove metal from the pump casing and impeller. Stainless steels are not invulnerable to this process. 2）Materials Selection There is no metal, plastic, or any other material known to man, that can withstand the high levels of energy released by cavitation in the forms of heat and pressure. In practice however, materials can be selected that result in longer life and customer value in their ability to withstand cavitation energies, so that attention to pump construction materials is valuable and productive. Where cavitation is not a problem or not predicted to be a problem, common materials such as cast iron and bronze are suitable for pump construction. There are millions of cast iron and bronze pumps that work fine for 20 years or more without any problem even though many of those pumps experience some cavitation. （4）Mechanism of Cavitation：The phenomenon of cavitation is a stepwise process as shown in Figure (below).Step One, Formation of bubbles inside the liquid being pumped.The bubbles form inside the liquid when it vaporises i.e. phase change from liquid to vapor. But how does vaporization of the liquid occur during a pumping operation?Vaporization of any liquid inside a closed container can occur if either pressure on the liquid surface decreases such that it becomes equal to or less than the liquid vapor pressure at the operating temperature, or the temperature of the liquid rises,Collapse of a Vapor Bubble raising the vapor pressure such that it becomes equal to or greater than the operating pressure at the liquid surface. For example, if water at room temperature (about 77 F) is kept in a closed container and the system pressure is reduced to its vapor pressure (about 0.52 psia), the water quickly changes to a vapor. Also, if the operating pressure is to remain constant at about 0.52 psia and the temperature is allowed to rise above 77 F, then the water quickly changes to a vapor.Just like in a closed container, vaporization of the liquid can occur in centrifugal pumps when the local static pressure reduces below that of the vapor pressure of the liquid at the pumping temperature. Step Two, Growth of bubbles Unless there is no change in the operating conditions, new bubbles continue to form and old bubbles grow in size. The bubbles then get carried in the liquid as it flows from the impeller eye to the impeller exit tip along the vane trailing edge. Due to impeller rotating action, the bubbles attain very high velocity and eventually reach the regions of high pressure within the impeller where they start collapsing. The life cycle of a bubble has been estimated to be in the order of 0.003 seconds。 Step Three, Collapse of bubbles，As the vapor bubbles move along the impeller vanes, the pressure around the bubbles begins to increase until a point is reached where the pressure on the outside of the bubble is greater than the pressure inside the bubble. The bubble collapses. The process is not an explosion but rather an implosion (inward bursting). Hundreds of bubbles collapse at approximately the same point on each impeller vane. Bubbles collapse non-symmetrically such that the surrounding liquid rushes to fill the void forming a liquid microjet. The micro jet subsequently ruptures the bubble with such force that a hammering action occurs. Bubble collapse pressures greater than 1 GPa (145x106 psi) have been reported. The highly localized hammering effect can pit the pump impeller. The pitting effect is illustrated schematically in this the figure. After the bubble collapses, a shock wave emanates outward from the point of collapse. This shock wave is what we actually hear and what we call cavitation. The implosion of bubbles and emanation of shock waves (red color) . In nutshell, the mechanism of cavitation is all about formation, growth and collapse of bubbles inside the liquid being pumped. But how can the knowledge of mechanism of cavitation can really help in troubleshooting a cavitation problem. The concept of mechanism can help in identifying the type of bubbles and the cause of their formation and collapse. (5)Solution and Remedies：For vaporization problems (cavitation) (1.To cure vaporization problems you must either increase the suction head, lower the fluid temperature, or decrease the N.P.S.H. Required. We shall look at each possibility: 1).Increase the suction head: Raise the liquid level in the tank Raise the tank Put the pump in a pit Reduce the piping losses. These losses occur for a variety of reasons that include : 1.The system was designed incorrectly. There are too many fittings and/or the piping is too small in diameter. 2.A pipe liner has collapsed. 3.Solids have built up on the inside of the pipe. 4.The suction pipe collapsed when it was run over by a heavy vehicle. 5.A suction strainer is clogged.6.Be sure the tank vent is open and not obstructed. Vents can freeze in cold weather 7.Something is stuck in the pipe, It either grew there or was left during the last time the system was opened . Maybe a check valve is broken and the seat is stuck in the pipe. 8.The inside of the pipe, or a fitting has corroded. 9.A bigger pump has been installed and the existing system has too much loss for the increased capacity. 10.A globe valve was used to replace a gate valve. 11.A heating jacket has frozen and collapsed the pipe. 12.A gasket is protruding into the piping. 13.The pump speed has increased. Install a booster pump Pressurize the tank 2) lower the fluid temperatureInjecting a small amount of cooler fluid at the suction is often practical. Insulate the piping from the suns rays. Be careful of discharge recirculation lines, they can heat up the suction fluid. 3) reduce the N.P.S.H. RequiredUse a double suction pump. This can reduce the N.P.S.H.R. by as much as 27% or in some cases it will allow you to raise the pump speed by 41% Use a lower speed pump Use a pump with a larger impeller eye opening. If possible install an Inducer. These inducers can cut N.P.S.H.R. by almost 50%. Use several smaller pumps. Three half capacity pumps can be cheaper than one large pump plus a spare. This will also conserve energy at lighter loads. (2. For suction cavitation: 1. Remove debris from suction line. 2. Move pump closer to source tank/sump 3. Increase suction line diameter. 4. Decrease suction lift requirement 5. Install larger pump running slower which will decrease the Net Positive Suction Head Required by the pump(NPSHR). 6. Increase discharge pressure. 7. Fully open Suction line valve. (3. For discharge cavitation: 1. Remove debris from discharge line. 2. Decrease discharge line length 3. Increase discharge line diameter. 4. Decrease discharge static head requirement. 5. Install larger pump, which will maintain the required flow without discharge cavitating. 6. Fully open discharge line valve. (4. For Recirculation cavitation:1.Designing the pump for lower suction-specific speeds and limiting the range of operation to flow capacities above the point of recirculation. 2. Raising the suction head. Selected from :1.J.M.Coucson ,J.F.Richardson ,Chemical Engineering ,Butterworth-Heinemann Ltd.,19952. Delgosha, O. C., Patella, R. F., Reboud, J. L.: Experimental and Numerical Studies in a Centrifugal Pump with Two-Dimensional Curved Blades in Cavitating Condition. Journal of Fluids Engineering, vol.125, pp.970978, (2003).3.Zhang, J. F., Yuan, S. Q., Fu, Y. D.: Numerical Forecast of the Influence of Splitter Blades on the Flow Field and Characteristics of a Centrifugal pump, Chinese Journal of Chemical Engineering, vol.45, pp.131-137, (2009).4. P.D. Lyapkov, Trudy VNII, No.5, Gostoptekhizdat, Moscow (1959).5. Zhang, J. F., Yuan, S. Q., Fu, Y. D.: Numerical Forecast of the Influence of Splitter Blades on the Flow Field and Characteristics of a Centrifugal pump, Chinese Journal of Chemical Engineering, vol.45, pp.131-137, (2009).化工工业离心泵摘要 ：离心泵是通过叶轮的旋转把液体的内能转换成动能的一种旋转装置。液体由吸入口进入蜗壳，通过高速旋转的叶轮，液体呈放射状加速从泵中向外输出，这时叶轮附近留出一个真空，不断吸引更多的流体进入泵的叶轮附近，这样由叶轮的旋转来完成液体的进出。这篇文章主要讲述了关于离心泵的发展史，离心泵工作原理的分析，汽蚀的基本原理和预防汽蚀的措施等的一系列问题。从而帮助我们加深对离心泵的理解。关键词：离心泵 介绍 工作原理 汽蚀 汽蚀原理 预防措施1.介绍 泵的提出，最先是用于转移或压缩液体和气体的设备。在所有泵中，我们一步步采取措施来防止气蚀，气蚀将减少流量并且破坏泵的结构。用来处理气体和蒸汽的泵称为气体压缩机，研究流体的运动的科学称为流体力学。水泵是用管子连接的机械把水从一个地方传到另一个地方。水泵的操作压力从一磅到一万磅每平方英尺。日常生活中，泵是很多见的，有用于在鱼池和喷泉使水循环和向水中充气的电泵，还有用于从住宅处把水引走的污水泵。离心泵的早期形式-螺杆泵，是通过一个管子连接一根螺杆组成的，它是利用螺杆的旋转把水提升上去。螺旋泵经常用在污水处理厂中，因为它们可以运输大量的水，而不会因为碎片而堵塞。在远古的中东，因为对农场进行灌溉的需求，所以有一种强大的动力去推进水泵的进程。在这些区域里，早期的泵是为了将水一桶一桶的从水源或河渠中提升到容器中。古希腊的发明家和数学家阿基米德被认为是公元前3世纪首先提出螺旋泵的发明家。之后，古希腊发明家发明了第一个提水泵。在十七世纪末和十八世纪初，英国的工程师Thomas Savory，法国的物理学家Denis Papin，和英国的铁匠和发明家Tomas Newcomen,它们发明了用蒸汽驱动活塞的水泵。蒸汽驱动的水泵首先广泛的被应用是在从煤矿往外输水过程中。现在离心泵使用的例子，是来自于哥伦比亚河上使用的大古利水坝。这个泵有超过灌溉一百万英亩的土地能力。离心泵被认为是旋转泵，它有一个旋转地叶轮，叶轮上有叶片，叶片是侵入液体中的。液体也是由叶轮轴向进入泵，并且旋转的叶轮将液体甩向叶片根部。同时叶轮也给液体一个较高的速度，这个速度通过泵的一个固定部件转化成压力。我们一般称为扩压 器。在高压泵里，很多叶轮可以被系列选用，并且在一个叶轮后有一个扩压器，也可能含有导轮，可以逐渐的降低液体的速度。对于低压泵来说，扩压泵一般就是一个螺旋形的通道，成为蜗壳，作用原理是拦截面逐渐增加可以有效降低流体的速度。在泵工作前，叶轮必须被灌注，也就是在泵启动时，叶轮必须被液体包围。也可以通过在吸入线上放另一个截止阀来实现，截止阀在泵停止工作时是液体保留在泵内。如果截止阀泄露了，泵可以通过阀的入口，从外面的水源比如说蓄水池来取水灌注。一般离心泵在排水线的地方也有一个阀控制流体和压力。对于小流量和高压力来说，叶轮作用很大部分是放射状的。对于高速流体和低压排水压力，泵中流体的方向可以近似于与轴的轴向平行，这时泵有一个轴流。这时叶轮就近似于螺旋推进器。从一种流动的状态转换到另一种流动的状态是渐进的，对于中间状态，设备可称为混流泵。2.离心泵 离心泵是化工和石油工业中应用最广泛的一种泵。它能输送性能非常广泛的液体和固体含量高的悬浮液，像泥泥浆，可以用多种抗腐蚀材料建造。泵的整个外壳可用像聚丙烯这样的塑料来建造，或者用腐蚀衬里加工。由于它的高速运转，可将其直接耦合到电动机上，由电动机的规格大小决定流量高低。 在这样的泵中，液体被吸入到旋转叶轮的中心，通过离心作用向外流动。由于高速旋转，液体在吸入口和因动能转化为压能的出口侧获得较高的动能和压力差。叶轮由一系列弧形叶片组成，因此能使液体的流动尽可能平稳。叶轮中叶片越多，则液体的流动方向越好控制，那么液体循环流动时因波动引起的损失就越少。在开式叶轮中，叶片被固定在中心轮毂上，而在闭式中叶片则是用两块钢板支撑以减少漏液。由此可以看出，在很大程度上，叶片末端的角度决定了泵的工作特性。流体通常在轴向上通过叶片的上升进入泵壳。在这种简单类型的离心泵中，液体由切向方向随着横截面逐步流到蜗壳中。图（a）所示为旋涡型泵。图（b）中，在涡轮泵中的液体随移动的叶轮在一系列固定叶片中形成扩散环。这种旋涡能逐渐改变流体的流动方向，并有效地将动能转化成压能。固定叶片前缘处的流体应该没有受到冲击。沿着叶轮叶片，液体的流动具有一定速度，同时，叶片末端相对于泵体有移动。液体的运动方向相对于泵壳和固定叶片所需的角度一样是两个速度的合成方向。在图c中，c.是液体相对于叶片的速度，是叶片上某点的切向速度；将这两个速度合成即可得到液体的速度。因此，很明显，在扩散环中所需要的叶轮角由叶轮的产量、旋转速度和叶片的角度决定。所以，泵在很严格的条件下才能有最大的运行效能。2.1离心泵的有效压头当流体所剩余的动能全部转化为压能时，压力最大。如下文所述，有效压头和半径的平方以及速度成正比，压力更高时，必须使用多级泵。考虑到液体在离泵中心r到r+dr 的距离内旋转，如图dd.所示。这一部分流体的质量为dM =2rdrd，其中是流体的密度，b是这部分流体的宽度。如果流体在与切向方向成角上以速度u流动，则这部分质量流体的角动量为=dM(urcos)流体通过泵所产生的扭转力等于角动量对时间的改变量d=dM(u r cos)=2r bdr( u r cos) (2.1)液体的体积流速为： Q=2 r b (2.2)Dr=Qd(u r cos) (2.3) 因此，液体在泵中受到总的扭转力由d在小标1和2之间积分而得，下标1引用的是泵入口处的条件，小标2是出口时的条件。于是有：=Q（u2r2cos2 u1r1cos1）2.2离心泵的优缺点主要优点有：（1）制造简单，可用多种材料加工。（2）无阀门。（3）高速运转（高达100赫兹），因此可直接耦合到电动机上。一般地，速度越大，泵和电动机的效率越小。（4）能平稳传送。（5）维修费用比其他类型的泵少。（6）输送堵塞时，只要不是长时间运作，泵就不会被损坏。（7）与其它泵相比，体积较小。因此，它可以利用电动机做成密封装置沉浸在吸收罐中。（8）能容易输送含有高比例悬浮固体的液体。主要缺点有：（1）单级泵不能提高压力。而多级泵能提高压头，但价格昂贵而且由于它们的复杂性不能用抗腐蚀的材料加工建造。通常用较高的速度来减少所需要的级数。（2）只有在有限条件下才能以最高效能运作：尤其是涡轮泵。（3）它不能自动注水。（4）在输送和吸收管道中，如果没有止回阀，液体就会在泵停止瞬间倒流到吸入槽内。（5）不能有效处理粘性液体。3. 离心泵中的汽蚀（1）“汽蚀”一词来源于拉丁语高弓足，这意味着一个中空的空间或空腔。韦氏词典定义的字是在一个非常低的压力区域流动的液体腔内迅速形成和崩溃的“腔”。在离心泵中的任何地方像蒸气泡沫，气体泡沫，气体破洞，气泡等各种条件长期作用都会造成汽蚀。这是一个各种结果同时作用的事情，不能简单地看待。汽蚀的形成讨论如下。在离心泵的蜗壳中，汽蚀意味着一个气泡内的液体，他们的形成，成长和随后通过泵的液体流动崩溃所经历的动态过程。一般来说，液体内气泡的形成有两种类型：蒸汽气
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