【正文】 nt of a water pump that used steam to power the pump’ piston .The steampowered water pump’s first wide use was in pumping water out of mines .Modernday 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 highpressure 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 lowerpressure pumps ,the diffuser is generally a spiral passage ,known as a volute ,with its crosssectional 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 mixedflow pump . 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 corrosionresistant 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 impeller．In the simple type of centrifugal pump，the liquid discharges into a volute，a chamber of gradually increasing cross—section with a tangential outlet．A 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 ring．This 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 type．The angle of the leading edge of the fixed vanes should be such that the fluid is received without shock．The 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 pump．The direction of motion of the liquid relative to the pump casingand the required angle of the fixed vanes—is found by pounding these two velocities．In Fig．c， c. is the velocity of the liquid relative to the vane and is the tangential velocity of the tip of the vane；pounding these two velocities gives the resultant velocity of the liquid．It 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 blades．The 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 below．the head is proportional to the square of the radius and to the speed，and is of the order of 60m for a single—stage centrifugal pump；for higher pressures，multistage pumps must be used．Consider the liquid which is rotating at a distance of between r and r+dr from the centre of the pump(Fig．d)． d The mass of this element of fluid dm is given by 2πrdrdρ，where ρ is the density of the fluid and 6 is the width of the element of fluid。If the fluid is tr