ASSIGNMENT-1 HYDROPOWER PLANT

Transcription

1 ASSIGNMENT-1 HYDROPOWER PLANT Theory 1. Give classification of hydro electric power plant. 2. Write advantages, disadvantages and application of hydro electric power plant. 3. Explain general layout and essential components of hydro electric power plant. 4. Discuss the factors for site selection for hydro electric power plant. Darshan Institute of Engineering and Technology, Rajkot 1

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3 ASSIGNMENT 2 IMPACT OF JET Theory 1. Derive an expression for force exerted by a jet of water on stationary plate for following cases: a) Stationary (fixed) vertical flat plate b) Stationary inclined flat plate c) Stationary curved plate 2. Derive an expression for force exerted by a jet of water on moving plate for following cases: a) Moving plate is vertical to the jet b) Moving plate is inclined to the jet c) Moving plate is curved 3. Derive an expression for the angle of swing of a vertical hinged plate. 4. Show that the efficiency of a free jet striking normally on a series of flat plates mounted on the periphery of a wheel can never exceed 50%. 5. Prove an expression for work done equation and efficiency when jet striking on series of radial curved vanes. 6. Explain jet propulsion. Also derive an expression for the work done and efficiency. Examples 1. Water is flowing through a pipe at the end of which a nozzle is fitted. The diameter of the nozzle is 100mm and the head of water at the centre of nozzle is 100m. Find the force exerted by the jet of water on a fixed vertical plate. The co-efficient of velocity is given as [Ans: KN] [17.2; R. K. Bansal] 2. A jet delivers water at the rate of 60 liters per second with velocity 30m/s. The jet strikes tangentially on the vane moving in the direction of the jet with the velocity of 15 m/s. The vane is so shaped that if stationary, it would deflect the jet through an angle 50. Calculate: (1) angle made by absolute velocity at outlet and (2) work done. [GTU; JUN-2012] 3. A jet of water from a nozzle is deflected through 60 from its original direction by a curved plate which it enters tangentially without shock with a velocity of 30 m/sec and leaves with a mean velocity of 25 m/sec. If the discharge from the nozzle is 0.8 kg/sec, calculate the magnitude and direction of the resultant force on the vane, if the vane is stationary. [Ans: 22.27N, ] [17.15; R. K. Bansal] 4. A jet of water of diameter 7.5 cm strikes a curved plate at its centre with a velocity of 20 m/sec. The curved plate is moving with a velocity of 8 m/sec in the direction of the jet. The jet is deflected through an angle of 165. Assuming the plate smooth. Find: Darshan Institute of Engineering and Technology, Rajkot 1

4 (1) Force exerted on the plate in the direction of jet, (2) Power of the jet, and (3) Efficiency of the jet. [Ans: 1.25KN, 10KW, 56.4%] [17.14; R. K. Bansal] 5. A jet of water having a velocity of 40 m/sec strikes a curved vane, which is moving with a velocity of 20 m/sec. The jet makes an angle of 30 with the direction of motion of vane at inlet and leaves at an angle of 90 to the direction of motion of vane at output. Draw the velocity triangles at inlet and outlet and determine the vane angles at inlet and outlet so that the water enters and leaves the vane without shock. [Ans: 53.79, 36.18,] [17.19; R. K. Bansal] 6. A jet of water moving at 12 m/sec impinges on a concave shaped vane and is deflected through an angle of 120. Assuming the vane to be symmetrical, find the angle of jet for shock-less entry at inlet when vane velocity is 6 m/sec. Calculate magnitude and direction of exit velocity and work done per unit mass per sec. Assume 10% loss in relative velocity due to friction on moving plate. [24; V. L. Patel] 7. A horizontal jet of water with a velocity of 25 m/sec impinges on a moving curved blade having velocity 10 m/sec. The blade is moving in the direction of a jet. The jet leaves the blade at an angle of 60 with the direction of the motion of the blade. Blade outlet angle is 40. Calculate : (1) Percentage by which relative velocity is reduced at outlet (2) Force per kg in the direction of motion if diameter of jet is 10 cm (3) Work done per kg. [Ans: 41.4%, 2.56KN, KW] [25; V. L. Patel] 8. A 5 cm diameter horizontal jet of water with a velocity of 20 m/sec strikes a curved vane tangentially at inlet tip. The vane is moving with 10 m/sec in the direction of jet. The force experienced by the vane in the direction of motion is 295 N. Calculate the angle made by absolute velocity of a jet at outlet with the direction of motion of vane. [Ans: ] [28; V. L. Patel] 9. A jet of water of diameter 25mm strikes a 20cm x 20cm square plate of uniform thickness with a velocity of 10 m/sec as the centre of the plate which is suspended vertically by a hinge on its top horizontal edge. The weight of the plate is 98.1 N. The jet strikes normal to the plate. What force must be applied at the lower edge of the plate so that plate is kept vertical? If the plate is allowed to deflect freely, what will be the inclination of the plate with vertical due to the force exerted by jet of water? [Ans: 24.5N, 30 ] [17.10; R. K. Bansal] 10. A metal plate of 6mm thickness and 150mm square swings about a horizontal edge. A horizontal jet of water 12mm in diameter impinges with its axis perpendicular to and 50mm below the edge of the hinge and keeps it steadily inclined at 30 to the vertical. Find the velocity of jet, if the metal plate weighs N/m 3. [Ans: 8.29m/s] [6; V. L. Patel] Darshan Institute of Engineering and Technology, Rajkot 2

5 11. A jet of water having a velocity 20 m/sec strikes on a series of vanes moving with a velocity 8 m/sec. The jet makes an angle of 30 with the direction of motion of vanes when entering and leaves at an angle of 150 with the direction of motion. Sketch the velocity triangles and calculate: (1) Vane angles at inlet and outlet (2) Work done when the vane discharging 300 lits/sec Take loss due to friction over the vane as 10% of relative velocity. [Ans: 47.01, 11.02, 51.33KW] [29; V. L. Patel] 12. A wheel having radial blades has 1 m diameter at inlet and 70 cm diameter at outlet. Water enters the wheel at a velocity of 40 m/sec at an angle of 30 with the tangent of vane tip velocity and leaves with a velocity of flow 5 m/sec. If the blade angles at inlet and outlet are 35 and 40 respectively find (1) The speed of wheel (2) The work done per kg of water and (3) Efficiency. [Ans: 116RPM, N-m/kg, 14.38%] [31; V. L. Patel] Darshan Institute of Engineering and Technology, Rajkot 3

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7 ASSIGNMENT 3 HYDRAULIC TURBINES Theory 1. Give the classification of hydraulic turbines. 2. Define below terms: a) Gross head b) Net head c) Hydraulic efficiency d) Volumetric efficiency e) Mechanical efficiency f) Overall efficiency g) Speed ratio h) Jet ratio 3. Differentiate between: a) The impulse and reaction turbine b) Radial and axial flow turbine c) Inward and outward radial flow turbine d) Kaplan and propeller turbine. 4. Explain the components and working of a Pelton wheel. Give an expression for the work done equation & expression for maximum efficiency of the Pelton wheel. 5. Explain the components & working of the Francis turbine with the help of a neat sketch. 6. What is the function of draft tube? Explain various types of draft tube. 7. Explain various components & working of Kaplan turbine with the help of a neat sketch. 8. Derive an expression for specific speed of a hydraulic turbine. 9. Explain the Governing of Pelton turbine & Francis turbine. 10. What is Cavitation? What are the effects & precaution of cavitation in hydraulic turbine? Examples Impulse Turbine / Pelton Wheel 1. A Pelton wheel is required to develop 8000 kw while working under head of 380m at a speed of 500 rpm. If overall efficiency is 88%, find: a. Flow rate through the turbine, b. Runner diameter, c. No. of nozzles and d. No. of buckets in runner. Assume jet ratio of 10, co-efficient of velocity as 0.97 and speed ratio of [Jan 2013] 2. The following data relate to a Pelton wheel: Tangential velocity of bucket = 25 m/s Head of water = 65 m Deflection of jet on bucket = 165 Discharge through the nozzle=110 litres/sec Co-efficient of nozzle=0.95 Determine the power developed by the runner and the efficiency. Darshan Institute of Engineering and Technology, Rajkot 1

8 [Nov-2011] 3. The gross available head for a Pelton wheel is 600m, out of which one third is lost due to friction in the penstock which takes water to the nozzle of the Pelton wheel. The rate of flow of water through the nozzles fitted at the end of the penstock is 2 m³/s. The angle of deflection of jet is 165. The reduction in relative velocity while passing through buckets as 15%. Take speed ratio, Ku = 0.45 and co-efficient of velocity Cv = 0.978, D/d = 1/10, mechanical efficiency = 95%, Determine, a) Power developed by the turbine, b) Hydraulic efficiency, c) The unit power, and d) The dimensionless specific speed. [Dec-2013] Reaction Turbine 4. The internal and external diameters of an outward flow reaction turbine are 2m and 2.75m respectively. The turbine is running at 250 rpm and rate of flow of water through the turbine is 5 m 3 /s. The width of the runner is constant at inlet and outlet and is equal to 250mm. The head on the turbine is 150m. Neglecting thickness of the vanes and taking discharge radial at outlet determine: a. Vane angles at inlet and outlet b. Velocity of flow at inlet and outlet. [18.22; R. K. Bansal][Answer: 6.072, 3.68, 3.183m/s, 2.315m/s] 5. A Francis turbine develops 160 kw at 150 rpm under head of 10 m. The peripheral velocity at inlet and flow velocity at inlet of runner are 0.3(2gH) 0.5 and 0.9(2gH) 0.5 respectively. The overall efficiency of turbine is 78% and hydraulic efficiency is 82%. Assuming radial discharge at outlet, find (i) Guide blade angle and runner vane angle at inlet and (ii) Diameter and width of runner at inlet. [Jan-2013] OR 5. Francis turbine designed to develop 160 kw working under a head 10 m and running at 200 rpm. The hydraulic losses in turbine are 15% of available energy. The overall efficiency of turbine is 80%. Assume flow ratio=0.94 and speed ratio=0.25. Calculate: (1) Guide blade angle and runner vane angle at inlet and (2) Diameter and width at inlet. [Jun-2012] 6. A Kaplan Turbine produces 25MW operating under a head of 40 m. The blade tip diameter is 2.5 times the hub diameter and the overall efficiency is 0.9. If the speed and flow ratio are 2.0 and 0.6 respectively, calculate the diameter and speed of the turbine. [May-2013] 7. A turbine is to operate under a head of 25 m at 200rpm. The discharge is 9 m 3 /sec. If the efficiency is 90% determine, specific speed of machine, power generated, type of turbine and performance under head of 20 m. [Dec-2010] [Reference: 18.37; R. K. Bansal] Darshan Institute of Engineering and Technology, Rajkot 2

9 ASSIGNMENT 4 CENTRIFUGAL PUMPS Theory 1. What is pump? Give classification of the pumps. Write down difference between Positive displacement pumps and Rotodynamic pumps. 2. Explain how centrifugal pumps are classified? With neat sketch explain components & working of centrifugal pump. Enlist and explain the various types of impeller used in centrifugal pump. 3. Explain inlet & outlet velocity triangle for centrifugal pump & derive the work done equation. 4. Describe various heads & efficiencies of centrifugal pump. 5. Derive an expression for pressure rise in the impeller of the centrifugal pump by neglecting the frictional and other losses in the impeller. 6. Define the slip in Centrifugal pump. Explain briefly with sketch, the slip in centrifugal pump. How it can be eliminated? 7. How will you obtain an expression for minimum starting speed for a centrifugal pump? 8. Define and derive following terms for centrifugal pump: 1. Specific speed (Ns) 2. Maximum suction lift (hs) 3. Priming 9. Define and derive equation of NPSH in centrifugal pump? How its value significantly affects efficiency of centrifugal pump. 10. Write brief notes on Multi-stage Centrifugal pump with neat sketch. 11. Discuss the various characteristic curves of a centrifugal pump. 12. What is cavitation? What are its causes? How it can be prevented in centrifugal pump? 13. With neat sketch explain construction and working of submersible pump. 14. With neat sketch explain construction and working of Mud pump and Deep well pump. Darshan Institute of Engineering and Technology, Rajkot 1

10 Examples 1. A centrifugal pump has the following dimensions: inlet radius = 80 mm, outer radius = 160 mm, width of impeller at the outlet = 50 mm, β1 = 0.45 radians, β2 = 0.25 radians, width of the impeller at the outlet = 50 mm. Assuming shockless entry. Determine (i) the discharge, (ii) pressure rise through the impeller, (iii) % of total work converted into kinetic energy and (iv) the head developed by the pump when the impeller rotates at 90 radians/second. R.K Bansal 957/ Find the power required to drive the centrifugal pump which delivers 0.04 m 3 /s of water to a height of 20 m through a 15 cm diameter pipe and 100 m long. The overall efficiency of the pump is 70% and coefficient of friction is R.K Bansal 961/ The axis of centrifugal pump is 2.5 m above the water level in the sump and the static lift from the pump centre is 32.5 m. The friction losses in the suction and delivery pipes are 1 m and 8 m respectively; suction and delivery pipes are each 12 cm diameter at outlet, the diameter and width of the impeller are 30 cm and 1.8 cm respectively and the vanes are set back at an angle of 30ᵒ with tangent to the wheel. For a speed of 1800 rpm, mechanical efficiency 0.75 and manometric efficiency 80%. Make calculation for the discharge and the power required to drive the pump. Assume radial entry. D.S Kumar 1070/ A centrifugal pump impeller has diameter of 60 cm and width of 6 cm at the outlet. The pumps runs at 1450 rpm and delivers 0.8 m 3 /s against head of 80 m.the leakage loss after the impeller is 4% of discharge, the external mechanical loss is 10 kw and the hydraulic efficiency is 80%. Determine the blade angle at outlet, the power required and the overall efficiency of the pump. D.S Kumar 1072/ A centrifugal pump with 1.2 m outlet diameter and 0.6 m inner diameter runs at 200 rpm and pumps 1880 Liters/sec, the average lift being 6 m. The angle which the vanes make at exit with the tangent to the impeller is 26ᵒ and the radial velocity of flow is 2.5 m/s. determine the (i) manometric efficiency and (ii) the least speed to start pumping against head of 6 m. R.K Bansal 967/ The impeller of the centrifugal pump is 30 cm diameter and 5 cm width at the periphery, and has blades whose tip angles backwards 60 from the radius. The pump delivers 17 m 3 /min and the impeller rotates at 1000 rpm. Assuming that the pump is designed to admit radially, calculate (i) speed and direction of water as it Darshan Institute of Engineering and Technology, Rajkot 2

11 leaves the impeller (ii) torque exerted by the impeller on water (iii) shaft power required (iv) lift of the pump. D.S Kumar 1075/ The following requirements are to be satisfied by a centrifugal pump whose impeller has internal and external diameters are 20 cm and 40 cm respectively. Suction and delivery heads = 5 m and 20 m, diameter of suction and delivery pipes = 12 cm and 8 cm, discharge = m 3 /s while running at 950 rpm. If the vane outlet angle is 45ᵒ, the flow velocity is constant and equal to 1.8 m/s and power required to drive the pump is 15 kw, make calculations for (i) the vane angle of impeller at inlet, (ii) the overall and manometric efficiency of the pump. D.S Kumar 1078/17.16 Practice Examples 1. A centrifugal pump discharges 0.15 m 3 /sec of water against a head of 12.5 m, the speed of the impeller being 600 rpm. The outer and inner diameters of impeller are 500mm and 250mm respectively and the vanes are bent back at 35 to the tangent at exit. If the area of flow remains 0.07 m 2 from inlet to outlet, calculate: a. Manometric efficiency of the pump b. Vane angle at inlet (Ө), absolute angle at the outlet (β) c. Absolute velocity (V2) & relative velocity (Vr2 ) at the outlet d. Width of the impeller at inlet and outlet e. Work done by impeller on water per second f. Loss of head at inlet to impeller when the discharge is reduced by 40% without changing the speed. R.K Bansal 954/ The external and internal diameter of an impeller of a centrifugal pump which is running at 1000 rpm, are 200mm and 400mm respectively. The discharge through pump is 0.04 m 3 /sec and velocity of flow is constant and equal to 2.0 m/sec. The diameters of the suction and delivery pipes are 150mm and 100mm respectively and suction and delivery heads are 6m (abs.) and 30 m (abs.) of water respectively. If the outlet vane angle is 45 and power required to drive the pump is KW, determine: R.K Bansal 959/19.8 a. Flow velocities in suction and delivery pipe Darshan Institute of Engineering and Technology, Rajkot 3

12 b. Manometric head and Manometric efficiency c. The Mechanical efficiency and Overall efficiency of the pump 3. A three stage centrifugal pump has impellers 30 cm in diameter and 1.5 m wide at outlet. The vanes are curved back at the outlet at 30ᵒ to the tangent at outlet and occupy 8% of the outlet area. While running at 1000 rpm delivering 40 litres per sec with manometric efficiency is 85% and the overall efficiency is 75%. Determine the (i) head generated by the pump, (ii) Torque exerted by the impeller and shaft power. D.S Kumar 1069/ A centrifugal pump of 1.25 m diameter is designed to pump 1.5 m 3 /s through 75 m height whilst running at 600 rpm. At outlet the vanes are set back at angle of 25 with tangent to the wheel. If the measured power is 1325 kw and the pump has an effective circumferential area of 0.4 m 2 at outlet, workout: (i) theoretical head with the assumption of infinite number of vanes, (ii) theoretical head with the assumption that the net power imparted to the water flowing through the impeller gets transformed into head without any hydraulic loss, and (iii) hydraulic & overall efficiencies if external mechanical loss is equivalent to 45 kw and the leakage loss amounts to 4%. D.S Kumar 1071/ A centrifugal pump having impeller diameter of 1 m has backward curved vanes which make angle of 25ᵒ with the wheel tangent at the blade tip is 10 m/s and the slip coefficient is Determine: (i) actual work input/kg of water flow (ii) absolute velocity of fluid at the impeller tip and (iii) hydraulic efficiency, considering that kinetic energy at the outlet is wasted. How the hydraulic efficiency would change if the pump is fitted with a diffusion chamber of 75% efficiency so that exit velocity is reduced to 12m/s. D.S Kumar 1073/ The Impeller of the centrifugal pump has a diameter of 10cm and breadth 3.5 cm at the inner periphery; the corresponding dimensions at the outer periphery are 20 cm and 1.7 cm respectively. The pump runs at 1500 rpm, has 7 vanes at entry and exit angles equal to 16 and 30 respectively. Calculate (i) theoretical discharge for shockless entry, (ii) the theoretical head developed, (iii) the actual head produced, the losses and power required to drive the pump. D.S Kumar 1074/ Water enters radially through a centrifugal pump whose impeller has a diameter of 30 cm and breadth 15 cm; the corresponding dimensions at the outer periphery are Darshan Institute of Engineering and Technology, Rajkot 4

13 60 cm and 7.5 cm. the blades are curved backward at 30 to the tangent at exit and the discharge is 225 lit/sec. if the rotational speed of the impeller is 1200 rpm and the pump delivers water to a height of 115 m, calculate: (i) the theoretical head develop (ii) the pressure rise across the impeller assuming losses are equal to 10% of velocity head at the exit, (iii) the pressure rise and the loss of head in the volute casing, (iii) power required to drive the pump assuming 65% overall efficiency, (iv) mechanical efficiency. D.S Kumar 1079/17.17 Darshan Institute of Engineering and Technology, Rajkot 5

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15 ASSIGNMENT 5 RECIPROCATING PUMPS Theory 1. Give classification of the Reciprocating pumps. With neat sketch explain construction & working of single acting single stage reciprocating pump. 2. Explain function of an air vessel? Explain with neat sketch the working of reciprocating pump with an air vessel. 3. Give expression for discharge, work done and power of reciprocating pump. 4. Define (i) slip (ii) % slip (iii) negative slip in relation with reciprocating pump. 5. Prove from the first principles that the work saved in a single acting reciprocating pump by fitting an air vessel is 84.8%. 6. Draw theoretical indicator diagram of reciprocating pump. 7. Draw an indicator diagram for single acting reciprocating pump by considering effect of acceleration and friction in suction and delivery pipes. Find an expression for the work done per second for it. 8. Compare the Reciprocating pump with Centrifugal pump. Darshan Institute of Engineering and Technology, Rajkot 1

16 Examples 1. The cylinder bore diameter of a single acting reciprocating pump is 150 mm and its stroke is 300 mm. The pump runs at 50 rpm and lifts water through a height of 25 m. The delivery pipe is 22 m long and 100 mm in diameter. Find the theoretical discharge and theoretical power required to run the pump. If the actual discharge is 4.2 litres/sec. Find the (i) % slip and (ii) acceleration head at the beginning and middle of the delivery stroke. GTU May The length and diameter of a suction pipe of a single acting reciprocating pump are 5 m and 10 cm respectively. The pump has a plunger of diameter 5 cm and a stroke length of 35 cm. the Centre of the pump is 3 m above the water surface in the pump. The atmospheric pressure head is running at 35 rpm. Determine: (1) Pressure head due to acceleration at the beginning of the suction stroke, (2) Maximum pressure head due to acceleration and (3) Pressure head in the cylinder at the beginning and at the end of the stroke. Darshan Institute of Engineering and Technology, Rajkot 2

17 ASSIGNMENT 6 RECIPROCATING COMPRESSOR Theory 1. Classify air compressors and state applications of compressed air. 2. Explain principle of working of single stage single acting reciprocating air compressor with schematic diagram. 3. Prove that the work done/kg of air in single stage single acting reciprocating air compressor without clearance is given by, [( ) ] 4. Why clearance volume is provided in reciprocating air compressor? Derive an expression for indicated work of reciprocating air compressor considering its clearance. OR 5. Define volumetric efficiency. Derive the expression for volumetric efficiency referred to suction and ambient conditions. Discuss the factors affecting on it. 6. Justify the need for multi-staging in a reciprocating air compressor. What are its merits and demerits over single stage compression? Show this process on P V diagram. 7. Explain the working of two stage reciprocating air compressor and give the expression of work done without clearance volume for perfect (complete) and imperfect (incomplete) intercooling with P-V and T-S diagram. 8. Show that for a two stage reciprocating air compressor with complete intercooling the total work of compression becomes minimum (maximum efficiency) when the pressure ratio in each stage is equal. OR Derive an expression for the optimum value of the intercooler pressure (condition of minimum work) in a two stage reciprocating air compressor for perfect intercooling condition. OR Darshan Institute of Engineering and Technology, Rajkot 1

18 In a two stage air compressor in which intercooling is perfect prove that the work done in compression is minimum when pressure in the intercooler is geometric mean between initial and final pressure. Darshan Institute of Engineering and Technology, Rajkot 2 OR Draw P-V diagram for two stage reciprocating air compressor. Write equation for indicated work per cycle and find out optimum intermediate pressure for minimum work supply. Examples 1. A single stage, single acting reciprocating air compressor takes in air 5 m 3 /min at 1 bar and 27 C and compresses to a delivery pressure of 7 bar. Determine each of the below neglecting clearance with the help of P-V and T-S diagram, when compression takes place (a) polytropically (PV 1.3 = constant), (b) adiabatically (PV 1.4 = constant), and (c) isothermally (PV = constant). Take ambient conditions bar and 15 C. (1) Mass of the air measured at suction condition per minute (2) Temperature and volume of air at the end of compression (3) Work done by air during suction, work done on air during compression, work done on air during delivery and net work done on air (I.P) (4) Heat transfer and change in internal energy during compression (5) Brake power of compressor if the mechanical efficiency is 80% (6) Isothermal efficiency and adiabatic efficiency [Attention Note: State the remarkable conclusions and implications from above results] 2. In a two stage single acting reciprocating air compressor, the pressure and temperature in the cylinder at the start of compression are 1 bar and 35 C respectively. The diameter of L.P cylinder is twice that of H.P cylinder. The air enters the H.P cylinder at 40 C and is then compressed to 17.5 bar. The law of compression is PV 1.22 = C for both the cylinders. The free air conditions are bar and 15 C and compressor delivers 2.4 m 3 of free air per minute. Neglecting the effect of clearance. Determine, each of the below considering perfect and imperfect intercooling, 1) Intercooler pressure

19 2) Indicated power required for two stage and single stage compression to achieve same delivery pressure, % saving in power with two stage compression and what should be the ratio of diameter of cylinder for minimum work? [Attention Note: clearly mention from above solution, why and which intercooling is preferable?] 3. In a two stage single acting reciprocating compressor, intake pressure and temperature are 1 bar and 20 C respectively. Air is taken into the compressor at the rate of 6 m 3 /min and compressed to a final pressure of 9 bar. The law of compression in both the cylinders is PV 1.3 = C. If the intermediate pressure is ideal and intercooling is perfect and the compressor runs at 600 rpm. Neglecting the clearance and determine, 1) Intermediate pressure 2) Volume of L.P. and H.P cylinder 3) Power required to drive the compressor if mechanical efficiency is 80%. 4) The rate of heat rejected in the intercooler 5) Rise in temperature of cooling water if the mass flow rate of water through the intercooler is 8 kg/min. Take Cpa = 1 kj/kg k for air and Cpw = 4.2 kj/kg k for water. 6) % saving of power by using three stage compressor and % excess power required if compressor runs at single stage to achieve same delivery pressure. [Attention Note: is it economical to achieve 9 bar delivery pressure in single stage?] 4. A single acting two stage RAC with complete intercooling delivers 10 kg/min of air at 16 bar at 400 rpm. The suction occurs at 1 bar and 15 C. The polytropic index is Calculate, 1) indicated power 2) FAD per minute 3) Heat rejected in intercooler 4) Swept volume and clearance volume of L.P cylinder if the clearance ratios for L.P and H.P cylinders are 0.04 and 0.06 respectively. Darshan Institute of Engineering and Technology, Rajkot 3

20 5. A multistage single acting reciprocating air compressor has perfect intercooling. The pressure and temperature at the end of suction stroke in L.P cylinder is 1 bar, 15 C respectively. If 8.4 m 3 /min of FAD at 60 bar when the work done is minimum. Calculate, 1) Number of stages if pressure ratio per stage is not to exceed 4 2) Exact stage pressure ratio 3) Intermediate pressures 4) Ratio of cylinder volume 5) Total indicated power and % excess power required by using single stage compression to achieve same delivery pressure. Take n = 1.3. Neglecting clearance. 6. The diameter of reciprocating air compressor cylinder is 140 mm and stroke length of the piston is 180 mm and the clearance volume is 77 cm 3. The pressure and temperature at the end of suction and at beginning of compression is 0.97 bar and 13 C. The delivery pressure is constant at 4 bar. Taking the law of compression and expansion as PV 1.3 = constant. Calculate, (1) The heat rejected during the compression (2) B.P of the compressor if mechanical efficiency 80% (3) Volumetric efficiency referred to suction and ambient conditions (4) Isothermal efficiency, adiabatic efficiency, overall isothermal efficiency (5) % of air delivered with reference to air compressed, mass of air compressed, mass of air delivered [Attention Notes: 1. Illustrate that clearance volume play a vital role in reciprocating air compressor. 2. How volumetric efficiency referred to suction and ambient conditions distinguished from each other?] 7. A single stage double acting reciprocating air compressor is required to deal with 17 m 3 of air per minute measured at bar and 15 C. The pressure and temperature at the end of suction is bar and 32 C, the delivery pressure being 6.3 bar, the speed is 550 rpm. Assuming a clearance volume is 5% of the stroke volume, law of compression and expansion is PV 1.32 = constant. Calculate, (1) The necessary swept volume Darshan Institute of Engineering and Technology, Rajkot 4

21 (2) Volumetric efficiency referred to suction and ambient condition (3) Cylinder dimension if stroke to bore ratio 1.5 (4) I.P of the compressor [Attention Note: up to which extent clearance can be minimized? What are the constrains for optimum clearance?] 8. A single acting, two stage reciprocating air compressor has to deals with 3 m 3 /min of air under atmospheric conditions 1 bar, 25 C at 220 rpm and delivers it at 80 bar, assuming perfect intercooling between stages. Find out, (1) Minimum power to drive the compressor (2) Diameter of L.P and H.P cylinder and common stroke length (3) % saving in minimum power if compression is assumed as three stage Take piston speed is 154 m/min, mechanical efficiency of compressor is 80%, volumetric efficiency is 85% same for each stage, law of compression in both the cylinders is PV 1.3 = C. Practice Examples 1. A single stage, single acting reciprocating compressor compresses 1.8 m 3 of air per min from 1 bar and 20 C to 8 bar delivery pressure. Determine each of the below neglecting clearance, when compression takes place polytropically (PV 1.3 = constant), adiabatically (PV 1.4 = constant), and isothermally (PV = constant). 1) Mass of the air inducted in kg/min 2) Temperature and volume of air at the end of compression 3) Indicated power 4) Heat transfer during compression 5) Brake power of compressor if the mechanical efficiency is 85% 6) Isothermal efficiency, adiabatic efficiency 7) Size of the cylinders if compressor runs at 220 rpm and piston speed 130 m/min. Provide your explanation on the answers with P-V and T-S diagram. [Attention Note: If above compressor is employed with two stage compression with perfect intercooling to achieve same delivery pressure then what will be consequence on brake power consumption in case?] Darshan Institute of Engineering and Technology, Rajkot 5

22 2. In a two stage single acting air compressor the L.P cylinder draws in 0.15 m 3 of air at a temperature of 15 C and a pressure of 1 bar. It is compressed adiabatically to 2 bar and then delivered to a intercooler where the air is cooled at constant pressure to 15 C. This air is then drawn in to the H.P cylinder and compressed adiabatically to 4 bar and delivered to the receiver. Calculate, 1) Indicated power required when compressor running at 100 rpm 2) Indicated power during single stage compression 3) Saving in power if compressor runs at two stage considering complete intercooling 3. Determine the size of L.P and H.P cylinders of a compound double acting RAC which runs at 100 rpm and requires 75 kw indicated power. The suction and delivery pressures are bar and 8.45 bar respectively and the intercooler pressure is 2.8 bar. The piston speed is m/min and polytropic index is Assume perfect intercooling between two stages. 4. A three stage single acting RAC is required to compress 8 m 3 /min of air from 1 bar, 300 K to a final pressure of 81 bar, assuming intercooling is perfect in between stages and the compressor is design for minimum work. Determine, (1) Dimensions of each cylinder for the speed of 900 rpm. Take polytropic index = 1.25 throughout. Given that the stroke of the compressor is equal to the diameter of L.P cylinder, (2) Theoretical power required to drive compressor. 5. A single stage, single acting reciprocating air compressor delivers air at 7 bar. The pressure and temperature at the end of suction are 1 bar and 27 C. It delivers 2.3 m 3 of free air per minute when speed is 150 rpm. If clearance volume of 5 % of the stroke volume, ambient pressure and temperature are bar and 15 C. Take n = Determine, 1) Indicated power 2) Power required to run the compressor if mechanical efficiency is 80% 3) Mean effective pressure in bar 4) Volumetric efficiency 5) Cylinder size if stroke to bore ratio 1.3. Darshan Institute of Engineering and Technology, Rajkot 6

23 7. A two stage single acting reciprocating air compressor is required to delivers air at 70 bar from a induction pressure of 1 bar at a rate of 2.4 m 3 /min measured at bar and 15 C. The compression is carried out in two stages with an ideal intermediate pressure and complete intercooling. The clearance volume is 3% of swept volume in each cylinder. The index of compression and expansion is 1.25 for both the cylinder. The temperature at the end of induction stroke in each cylinder is 32 C. The mechanical efficiency is 85%. Take speed of compressor 750 rpm. Determine, (1) Indicated power (2) Saving in power over single stage compression between the same pressures (3) Swept volume of each cylinder (4) The required power output of the drive motor. [Attention Note: how to get better mechanical efficiency? Discussed the factors involved.] 8. A three stage, reciprocating compressor has L.P cylinder of 300 mm bore and 200 mm stroke, clearance volume of L.P cylinder is 5% of swept volume, intake pressure and temperature are 1 bar, 17 C respectively, the final delivery pressure is 27 bar, intermediate pressures are ideal and intercooling is perfect, the compression and expansion index can be taken as 1.3 throughout. Determine, (1) Intermediate pressures (2) Effective swept volume of L.P cylinder (3) The temperature and volume of air delivered per stroke at 27 bar (4) Work done per kg of air [Attention Note: which one is true? Clearance volume will be decrease, remains constant or increase stage by stage in RAC] Darshan Institute of Engineering and Technology, Rajkot 7

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25 ASSIGNMENT 7 ROTARY COMPRESSORS Theory 1. Explain Root blower with the neat sketch and derive expression for the Roots efficiency. 2. Explain vane type compressor with neat sketch and P-V diagram. 3. Describe the working of a screw compressor and list its applications. 4. With neat sketch explain construction and working of Scroll compressor. State the advantages of scroll compressor. 5. Compare Screw compressor and Scroll compressor. Darshan Institute of Engineering and Technology, Rajkot 1

26 ASSIGNMENT 8 CENTRIFUGAL COMPRESSORS Theory 1. Describe principle construction and working of centrifugal compressor with pressure and velocity diagram. 2. Explain inlet and outlet velocity triangles and work done equation for the centrifugal compressor. 3. With the help of velocity triangles and head-capacity curves, discuss salient features of radial, backward and forward curved vanes in a centrifugal compressor and state function of volute casing. OR Explain the effect of blade shape of impellers on performance of Centrifugal compressor. Also classify the blades based on curvature. 4. Define following terms. a) Isentropic efficiency d) Pressure (loading) coefficient b) Slip factor e) Pre-whirl c) Power input factor 5. What is pre-whirl? Sketch the velocity diagrams with and without pre whirl for a centrifugal compressor. 6. Define degree of reaction (R) for a centrifugal compressor stage and prove that; cos ec 2 R 2 1 cot 2 where ϕ is flow coefficient 7. Explain the phenomenon of surging, choking and stalling in centrifugal compressor. 8. Give comparison between Centrifugal compressor and Reciprocating compressor. Darshan Institute of Engineering and Technology, Rajkot 1

27 Examples 1. Following data relates to the Centrifugal compressor. Speed Impeller tip diameter = 7000 RPM = 50 cm Static temperature of air at inlet= 282 K Axial velocity of air at inlet Slip factor = 0.9 = 120 m/s Power input factor = 1.04 Isentropic efficiency = 82% Specific heat of air = 1005 J/kg K Assume no whirl at inlet. Determine the pressure ratio developed and power required per kg of air to drive the compressor. Repeat the example if there is no slip and power input factor is unity. 2. Following data relates to the Centrifugal compressor. Free air delivered Pressure ratio = 1.5 Index of compression = 1.5 Speed = 1200 m 3 /min = 5000 RPM Velocity of flow at inlet and outlet= 3600 m/min Width of impeller at inlet and outlet= 177 mm and 67.5 mm Assuming all pressure rise to take place in impeller. Find, (1) the angle at which air from impeller enters the casing, (2) impeller blade angle at inlet. 3. Following data refers to the Centrifugal compressor. Speed Isentropic efficiency = 0.82 Inducing temperature of air Impeller mean eye diameter Work done by impeller Absolute velocity at inlet = RPM = 17⁰C = 200 mm = 175 kj/kg = 120 m/s Darshan Institute of Engineering and Technology, Rajkot 2

28 Slip factor = 0.78 If guide vanes at inlet give the air a prewhirl of 20⁰. Determine (1) the total pressure ratio, (2) impeller tip diameter, (3) absolute angle at inlet and angle at which air enters the casing, (4) blade angle at impeller inlet and outlet, (5) relative velocity at inlet and outlet. 4. A single sided Centrifugal compressor is required to deal with following data. Mass flow rate = 10 kg/s Total head pressure ratio = 4.5 Speed = 270 rps Ambient air conditions at entry = 1 bar, 30⁰C Isentropic efficiency = 0.8 Slip factor = 0.94 Absolute velocity at inlet Specific heat of air = 150 m/s = 1005 J/kg K If the air enters without prewhirl. Calculate, (1) rise in total temperature, (2) tip diameter of impeller, (3) inlet eye annulus area, (4) impeller tip speed, (5) power required to drive the compressor. 5. The air entering the impeller of a centrifugal compressor has an absolute axial velocity of 100 m/s. At the impeller exit the relative air angle measured from the radial direction is 26⁰ 36. The radial component of the velocity is 120 m/s, the tip speed of the radial vanes is 500 m/s, air flow rate is 2.5 kg/s, mechanical efficiency is 95%, the eye of the impeller has a hub to tip radius ratio of 0.3, the total to total efficiency is 80%, stagnation pressure and temperature at the compressor inlet are bar and 288 K.. Determine (1) the power required to drive the compressor, (2) the suitable inlet diameter assuming the inlet flow is incompressible and (3) overall total pressure ratio assuming velocity at exit from the diffuser is negligible. 6. The following data refers to a single sided centrifugal compressor. Overall diameter of the impeller= 50 cm Eye tip diameter Eye root diameter = 30 cm = 15 cm Darshan Institute of Engineering and Technology, Rajkot 3

29 Rotational speed = RPM Air mass flow rate = 10 kg/s Inlet total head temperature = 300 K Power input factor = 1.04 Slip factor = 0.9 Total head isentropic efficiency = 80% Find, (1) the total head pressure ratio (2) power required to drive the compressor (3) the inlet angle of the vanes at the root and tip of impeller eye. 7. Following data relates to the centrifugal compressor. Volume flow rate = 10 m 3 /s Speed = 6000 RPM Pressure ratio = 4 Isentropic efficiency = 0.83 Velocity of flow at inlet and outlet = 60 m/s Outer diameter to inner diameter = 2 Slip factor = 0.9 Blade area coefficient = 0.92 at inlet Determine: (1) theoretical power required, (2) impeller diameter at inlet and outlet, (3) width of impeller at inlet, (4) impeller blade angle at inlet, and (5) diffuser blade angle at inlet. 8. Following operating conditions are relates to the centrifugal compressor. Mass flow rate = 8 kg/s Diameter at inlet = 450 mm Diameter at outlet = 800 mm Radial component of velocity at impeller exit = 52 m/s Slip factor = 0.9 Impeller speed = RPM Static pressure at impeller exit = 2.2 bar Stagnation pressure and temperature at inlet = bar, 288 K Darshan Institute of Engineering and Technology, Rajkot 4

30 If the air leaving the guide vanes has a velocity of 90 m/s at 75⁰ to the tangential direction. Determine (1) the relative Mach number assuming frictionless flow through the guide vane, (2) impeller total head isentropic efficiency and (3) power required to drive the compressor. Practice Examples 1. A centrifugal compressor has inlet guide vanes fitted at the eye such that free vortex flow is achieved at entry to the blade. At the tip radius of the eye the inlet relative Mach number is not to exceed 0.75 and an impeller total to total efficiency is 0.9 is required. The air leaves the tip of the inlet guide vanes with a velocity of 90 m/s, the impeller tip diameter is 0.45 m, and the outlet diameter is 0.76 m. The radial component of velocity at exit from the impeller is 50 m/s and the impeller rotates at rpm. If a slip factor is 0.9 is assumed. Find: (1) the guide vane angle at the tip and, (2) the static pressure at impeller outlet. 2. Following operating conditions are relates to the centrifugal compressor. Mass flow rate Speed Overall static pressure ratio = 4:1 = 15 kg/sec Isentropic efficiency = 80% Slip factor = 0.9 Flow coefficient at impeller exit = 0.3 Hub diameter of eye Velocity of air at inlet = RPM = 15 cm = 140 m/s Velocity of air at exit from impeller= 140 m/s Stagnation temperature at inlet = 300 K Stagnation pressure at inlet = 1 bar Determine (1) impeller diameters, (2) width of impeller at exit, (3) power required to drive the compressor assume equal pressure ratio in the impeller and diffuser. 3. A centrifugal compressor has 17 radial vanes of tip diameter 165 mm and rotates at rpm and the air mass flow rate is 0.6 kg/s with no whirl at inlet. Calculate the. At the inlet to the impeller the mean diameter of the eye is 63.5 mm while the annulus Darshan Institute of Engineering and Technology, Rajkot 5

31 height at the eye is 25 mm. the static pressure and temperature at the impeller inlet are 0.93 bar and 293 K respectively. Determine: theoretical power required to run the compressor. (1) The blade angle at the mean diameter at impeller inlet, (2) the stagnation temperature at impeller exit and (3) the stagnation pressure impeller exit if the total to total efficiency of the impeller is 90%. 4. A two stage centrifugal compressor having intercooler has two impellers of same tip diameter and both of them are running at same speed. The first stage has a pressure ratio of 3.5:1 and the isentropic efficiency is 0.8 while the pressure coefficient is The intercooler removes 80% of the temperature rise occurring in the first stage. If the coefficient for the second stage are same as those for the first stage. Calculate: (1) the delivery conditions of air and (2) work done by each stage per kg of air. Assume that initial conditions are 0.95 bar and 17⁰C. 5. A 580 kw motor drives a centrifugal compressor of 480 mm outer diameter at a speed of 2000 rpm. At the impeller outlet the blade angle is 26.5 measured from the radial direction and the flow velocity at exit from the impeller is 122 m/s. If a mechanical efficiency is 95% is assumed. Assume there is no slip and the flow at inlet is incompressible and ambient air conditions are bar and 288 K. Determine: (1) the air flow is to be expected, (2) the eye tip and hub diameters if a radius ratio of 0.3 is chosen for the impeller eye and if the velocity at inlet is 95 m/s with zero whirl, (3) overall total to total isentropic efficiency If an overall total pressure ratio of 5.5 is required. 6. A single sided centrifugal compressor delivers 8.15 kg per second with a total pressure ratio 4.4. The compressor runs at RPM. The entry to the eye for which the internal diameter is 12.7 cm is axial and the mean velocity at the eye section is 148 m/s with no prewhirl. Static conditions at the eye section are 15⁰C and 1 bar. The slip factor is 0.94 and the isentropic efficiency is Neglecting losses calculate, (1) the rise in total temperature during compression, (2) the tip speed of the impeller eye and tip speed of the impeller outlet, (3) impeller tip diameter, (4) power required to drive the compressor, (5) eye external diameter. Darshan Institute of Engineering and Technology, Rajkot 6

32 7. A two stage centrifugal compressor delivers air with an overall pressure ratio of 12:1 without intercooling between stages. The pressure and temperature of the surrounding air are 1 bar and 22⁰C respectively. The overall isentropic efficiency is 72% while that of the first stage is 77%. If the actual works done in both the stages are equal. Determine: (1) the pressure and temperature at the exit from the first stage, (2) the approximate tip velocity of the first stage impeller assuming approximate value for the pressure coefficient. Darshan Institute of Engineering and Technology, Rajkot 7

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34 ASSIGNMENT 9 AXIAL FLOW COMPRESSORS Theory 1. With a suitable sketch explain the working principle of an axial flow compressor. Draw the stage velocity triangles and derive an equation for work input. 2. Derive an expression for pressure ratio per stage of an axial flow compressor in terms of isentropic efficiency, work done, blade velocity, blade angles and inlet temperature. 3. Sketch symmetrical, unsymmetrical aerofoil and compressor cascade. Define and show the important angles, chord, pitch. 4. For 50% degree reaction of axial flow compressor prove that α1 = β2 and α2 = β1, notations carry usual meaning. 5. State applications of an axial flow compressor. Give comparison between an axial flow compressor and centrifugal compressor. 6. Define following terms with reference to axial flow compressor: a) Flow coefficient b) Blade loading coefficient c) Work done factor d) Radial equilibrium 7. Explain the phenomenon of surging and stalling in an axial flow air compressor. 8. Explain various losses associated in a stage of axial flow compressor. Darshan Institute of Engineering and Technology, Rajkot 1

35 Examples 1. An axial flow compressor has 8 stages and the following data apply to each stage at the mean diameter. Blade speed Degree of reaction = 0.5 = 210 m/s Stage efficiency = 0.85 Polytropic efficiency = 0.88 Angle of absolute air velocity at rotor inlet = 15⁰ Angle of absolute air velocity at rotor inlet = 45⁰ Work done factor = 0.86 Inlet stagnation pressure Inlet stagnation temperature = 1 bar = 27⁰ Determine the total pressure ratio of the first stage and overall static pressure ratio. 2. First stage of an axial flow compressor delivers 20 kg/s of air at 9000 rpm. Stage temperature rise is 20 0 C. Men blade velocity is 180 m/s and axial velocity is 150 m/s. The work done factor is 0.96 and blade occupies 10% of the axial area of flow. Taking 50% reaction, calculate (i) Inlet and outlet blade angles of moving blades and fixed blades (ii) Blade height at entry Assume ambient condition as 288 K and 1 bar. 3. The following data refers to an axial flow compressor. The total pressure ratio = 4 Overall total head isentropic efficiency = 0.85 Inlet stagnation temperature = 290 K The inlet and outlet angles from the rotor blades = 45⁰ and 10⁰ Work done factor = 0.86 Assuming blade speed is 220 m/s. The rotor and stator blades are symmetrical. The mean blade speed and axial velocity remain constant through the compressor. Find, (i) Polytropic efficiency Darshan Institute of Engineering and Technology, Rajkot 2

36 (ii) Number of stages required (iii) Inlet Mach number relative to rotor at the mean blade height of the first stage. 4. A multi stage axial flow compressor absorbs 2211 kw when delivering 10 kg/s of air from stagnation conditions 1 bar and 15C⁰. If the polytropic efficiency of the compressor is 0.9 and the stage stagnation pressure ratio is constant. Calculate, (i) The number of stages (ii) Final delivery pressure (iii) Overall isentropic efficiency of the compressor. 5. The following data refers to an axial flow compressor. Pressure of air at inlet of an axial flow compressor Temperature of air at inlet of an axial flow compressor Diameter at mean blade section Peripheral velocity Mass flow rate through the stage = 768 mm of Hg = 41C⁰ = 500 mm = 100 m/s = 25 kg/s Work done factor = 0.95 Mechanical efficiency = 92% Stage efficiency = 88% If air angles are β1 = 51⁰, α1 = α3 =7⁰and the air is turned through 42⁰ through the rotor. Determine: (i) Air angle at the stator entry (ii) Blade height at entry (iii) Hub to tip ratio (iv) Stage loading coefficient (v) Power input (vi) Stage pressure ratio 6. Each stage of an axial flow compressor is of 0.5 reaction, has the same mean blade speed and the same flow outlet angle of 30⁰relativ to the blades. The mean flow coefficient is constant for all stages at 0.5. At inlet to the first stage the stagnation temperature and pressure is 278 K, stagnation pressure is bar, the static pressure is bar and the floe area is m 2. Determine the axial velocity, mass flow rate and power required to drive the compressor when there are 8 stages and the mechanical efficiency is 99%. 7. The following data refers to an axial flow compressor. Stage stagnation temperature rise = 22 K Mass flow of air = 25 kg/s Darshan Institute of Engineering and Technology, Rajkot 3