BASIC EQUATION. Rotational speed. u = linear velocity in m/s r = radius in m ω = angular velocity in rad/s D = diameter in m N = rotation per minute

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1 CENTRIFUGAL PUMP

2 BASIC EQUATION Rotational speed u = rω = πdn 60 u = linear velocity in m/s r = radius in m ω = angular velocity in rad/s D = diameter in m N = rotation per minute Power Power = F V = P A V = ρgh AV = ρgh Q Work Power = ρgq h Work = Torque Angular velocity Work = Force Distance

3 TURBOMACHINES Turbomachines are the commonly employed devices that either supply or extract energy from a flowing fluid by means of rotating propellers or vanes. PUMP: Pump adds energy to a system, with the result that the pressure is increased. It also causes flow to occur or it increases the rate of flow. TURBINE: A turbine extracts energy from a system and converts it to some other useful form, typically, to electric power. Hydroturbine: is a machine that generates power from high-pressure water; relatively large conduits or tunnels deliver fluid to closed turbines in order to generate power. Another example: steam turbine and air turbine.

4 PUMP CLASSIFICATION

5 CENTRIFUGAL PUMP A centrifugal pump consists of two principal parts: (1) Impeller: which imparts a rotary motion to the liquid. (2) Housing or casing: which directs the liquid into the impeller region and transports it away under a high pressure. The impeller is mounted on a shaft and is often driven by an electric motor. The casing includes the suction and discharge nozzles and houses the impeller assembly. The portion of the casing surrounding the impeller is termed the volute. Liquid enters through the suction nozzle to the impeller eye and travels along the shroud, developing a rotary motion due to the impeller vanes.

6 It leaves the volute casing peripherally at a higher pressure through the discharging nozzle. Some single-suction impellers are open, with the front shroud removed. Double-suction impellers have liquid entering from both sides.

8 HEAD OF PUMP (Manometric head) This is defined by British Standards as the sum of the actual lift (H) + the friction losses in the pipes (hf)+ the discharge velocity head. H s = H + h t + V u v 2g = P v P x ρg + V v v v V x 2g However, for special pumps allowance must also be made for the velocity of flow towards the suction intake and any pressure differences at the water surfaces in the supply and receiving tanks. Commonly the suction and delivery pipes are of equal diameter. In which case: H s = P v P x ρg

11 VELOCITY TRIANGLE

12 Legend: At inlet (1) u x = r x ω = Tangetial velocity of impeller v x = Absolute velocity at α x to tangent v }x = v x u x = Relataive velocity to impeller blade Component velocity for v x : v ~x = Whirl velocity v tx = Radial flow velocity β x = Inlet blade angle At outlet (2) u v = r v ω = Tangetial velocity of impeller v v = Absolute velocity at α v to tangent v }v = v v u v = Relataive velocity to impeller blade Component velocity for v v : v ~v = Whirl velocity v tv = Radial flow velocity β v = Inlet blade angle

14 BLADE TYPE 1. Forward blade 2. Radial blade 3. Backward blade FORWARD BLADE

15 RADIAL BLADE

16 BACKWARD BLADE

17 THE EFFECT OF BLADE TYPE Centrifugal pumps do not always have backward curved vanes. But when they do, it is mostly for fluids in the incompressible regime of operation such as water. For compressible operation of fluids such as air, forward curve-vaned centrifugal pumps are used. The net ideal head developed by a centrifugal pump is given by: H uƒ = A BQ Q = volume flow rate at the impeller outlet A, B = constant for a given impeller running at a given speed Additionally, B cot β v.

18 Do note that the value of the actual head developed by the pump will be lower than this ideal value owing to shocks Hˆ Š Œ = K x Q u Q v Q u = design volume flow rate Q = actual volume flow rate Friction can be calculated by: h t = K v Q v which together constitute hydraulic losses.

19 The power required to drive the pump to provide a given flow-rate is given as: P = ρgq H uƒ The representative curves are given below.

20 As is evident from the power-discharge characteristics of the radial and forward vaned centrifugal pump, the power requirement increases monotonically with an increase in discharge. Hence, if the pump motor is rated for maximum power, then it will remain under-utilized for most of the operating time, and result in an increased cost due to its higher rating. On the other hand, if a motor is rated at the design point, and due to some reason the flow-rate exceeds the design flow rate, then the power requirement will shoot up (in case of forward and radial vanes only), causing overloading and motor failure. However, for backward curve-vaned centrifugal pumps, if the flow-rate exceeds the design flow rate (occurs quite close to the maxima of the power-discharge curve), then contrary to the earlier case, the power requirement drops down as evident from the curves. This enables the motor which is rated at the design power to handle the entire range of flow-rates without any problems. The actual design point is located corresponding to the flowrate at which maximum efficiency occurs.

21 EULER HEAD Torque = kadar perubahan momentum sudut Momentum sudut = (jisim) (halaju tangen) (jejari) Momentum sudut masuk = mv ~x r x Momentum sudut keluar = mv ~v r v m = kadar jisim mengalir sesaat Kadar perubahan momentum sudut: T = mv ~v r v mv ~x r x m = ρav = ρq T = ρq v ~v r v v ~x r x Diketahui power ialah: P = Tω P = ρq v ~v r v v ~x r x ω Diketahui: u = rω u x = r x ω u v = r v ω r x = and r v =

22 Diketahui power ialah: P = ρq v ~v r v v ~x r x ω u v = ρq v ~v ω v u v ~x ω ω = ρq v ~v u v v ~x u x Power juga boleh ditulis sebagai: P = ρgq h Jika power adalah maksimum, nilai h ialah nilai maksimum, iaitu niai power dalam keadaan tiada kehilangan tenaga (losses, friction, etc). Nilai h boleh ditulis sebagai H (Euler head) P = ρgq H = ρq v ~v u v v ~x u x H = 1 g v ~vu v v ~x u x Ia kenali sebagai Euler head (turus Euler). Unitnya dalam meter (m). Ia adalah turus ideal yang dihasilkan oleh impeller (pendesak) dalam system pam.

23 PUMP EFFICIENCY (kecekapan pam) Manometric efficiency η s Š = Kuasa air yang dihasilkan Kuasa impeller = ρgq H s ρgq H = ρgq ρgq H s 1 g v ~vu v v ~x u x η s Š = gh s v ~v u v v ~x u x Mechanical efficiency η sƒ = Kuasa impeller Kuasa yang diberikan kepada syaf η sƒ = 1 g v ~vu v v ~x u x P š

24 Overall efficiency η Š = Kuasa air yang dihasilkan Kuasa yang diberikan kepada syaf η Š = ρgq H s P š

BASIC EQUATION. Rotational speed = = ABC 60

BASIC EQUATION. Rotational speed = = ABC 60 CENTRIFUGAL PUMP BASIC EQUATION Rotational speed = =?@ = ABC 60 = = linear velocity in m/s? = radius in m @ = angular velocity in rad/s B = diameter in m C = rotation per minute Power OPQR? = S U = O V