【正文】 aveling with a velocity u and at an angle θ to the tangential direction．The angular momentum of this mass of fluid = dM (urcosθ) The torque acting on the fluid dτ is equal to the rate of change of angular momentum with time，as it goes through the pump Dτ = dM α/αt(urcosθ)=2πrbρdrα/αt(urcosθ) The volumetric rate of flow of liquid through the pump： Q=2πrbα/αt Dr =Q ρ d(urcosθ)The total torque acting on the liquid in the pump is therefore obtained integrating dτ 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，τ=Q ρ(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 plete 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 bees blocked，provided it is not run in this condition for a prolonged period． (7)It is much smaller than other pumps of equal capacity．It 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 single—stage pump will not develop a high pressure．Multistage pumps will develop greater heads bat they are very much more expensive and cannot readily be made in corrosion—resistant material because of their greater plexity．It 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。 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. . 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 ponents 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。 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, mon 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.Phenomenon of 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 . 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 bees 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 bees equal to or greater than the operating pressure at the liquid surface. For example, if water at room temperature (about 77 176。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