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 Darshan Institute of Engineering and Technology, Rajkot 1

4 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: (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] Darshan Institute of Engineering and Technology, Rajkot 2

5 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] 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. [Nov-2011] Darshan Institute of Engineering and Technology, Rajkot 1

8 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. Give classification of the pumps. With neat sketch explain components & working of centrifugal pump. Enlist and explain the various types of impeller used in centrifugal pump. 2. Explain inlet & outlet velocity triangle for centrifugal pump & derive the work done equation. 3. Describe various heads & efficiencies of centrifugal pump. 4. Derive an expression for pressure rise in the impeller of the centrifugal pump by neglecting the frictional and other losses in the impeller. 5. How will you obtain an expression for minimum starting speed for a centrifugal pump? 6. Explain following terms in detail for centrifugal pump: 1. Specific speed (Ns) 2. Net positive suction head (NPSH) 3. Maximum suction lift (hs) 4. Priming 7. Write notes on Multi-stage Centrifugal pump with neat sketch. 8. Discuss the various characteristic curves of a centrifugal pump. 9. Explain the Cavitation in pumps. 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 0f 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 961/19.9 Darshan Institute of Engineering and Technology, Rajkot 1

10 3. 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/s, 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 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 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 Darshan Institute of Engineering and Technology, Rajkot 2

11 ASSIGNMENT 5 RECIPROCATING PUMPS Theory 1. Give classification of the Reciprocating pumps. With neat sketch explain construction & working of single acting reciprocating pump. 2. What is an air vessel? Explain with a neat sketch the working of air vessel in reciprocating pump. 3. Give expression for discharge, work done power and slip of reciprocating pump. 4. Compare the reciprocating pump with centrifugal pump. Draw theoretical indicator diagram of reciprocating pump. 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 % slip and acceleration head at the beginning and middle of the delivery stroke. 2. 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 a5 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 1

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13 ASSIGNMENT 6 RECIPROCATING COMPRESSOR Theory 1. Discuss the application of compressed air and give detail classification of air compressors. 2. Define below terms: a. Brake power b. Indicated power c. Frictional power d. Mechanical efficiency e. Compression ratio (Pressure ratio) f. Free air delivered g. Single-double acting h. Isothermal efficiency i. Overall Isothermal efficiency j. Adiabatic efficiency 3. Explain principle of working of single stage single acting reciprocating air compressor with schematic diagram. 4. Prove the work done equation for compression of single stage single acting reciprocating compressor neglecting (without) clearance volume for following three mode of compression: I. Polytropic compression (PV n = C) II. Adiabatic compression (PV γ = C) III. Isothermal compression (PV = C) OR Prove that the work done/kg of air in single stage single acting reciprocating air compressor without clearance is given by, [( ) ] 5. What are the methods used to approach approximate isothermal compression? 6. Why clearance volume is provided in reciprocating air compressor? Prove the work done equation for compression of single stage single acting reciprocating air compressor with clearance volume for polytropic compression (PV n = C). OR Derive an expression for indicated work of reciprocating air compressor considering its clearance. 7. Define volumetric efficiency. Derive the expression for volumetric efficiency referred to suction and ambient conditions. Discuss the factors affecting on it. 8. Justify the need for multi-staging in reciprocating air compressor. Discussed advantages and disadvantages of multi-stage compression. 9. Explain the working of two stage reciprocating air compressor and give the expression of work done of two stage single acting reciprocating air compressor Darshan Institute of Engineering and Technology, Rajkot 1

14 neglecting (without) clearance volume for perfect (complete) and imperfect (incomplete) intercooling with P-V and T-S diagram. OR Why intercooling is employed in multistage compression? Give explanation. 10. Derive an expression of work done for two stage single acting reciprocating air compressor with clearance volume for perfect and imperfect intercooling with P-V and T-S diagram. 11. 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 Show that for multi stage compression, the intermediate pressure for optimum condition is to be geometric mean of its two neighboring pressures OR 12. Derive an expression for optimum intermediate pressure and work done in two stage reciprocating air compressor with imperfect intercooling with ideal intercooler pressure. OR Show that optimum intermediate pressure for two stage air reciprocating compressor neglecting clearance with incomplete intercooling is given by, ( ) 13. Describe the methods of controlling output of reciprocating air compressor. Darshan Institute of Engineering and Technology, Rajkot 2

15 Examples CASE (A) : Single-Multi Stage, Single-Double acting Compression without Clearance Volume 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. Answers: (a) Polytropic compression: (1) m = kg/min (2) T2 = K, V2 = 0.36 m 3 /min (3) I.P = kw (4) Q = kw (5) B.P = kw, (6) ηiso = 77.92%, ηad = 93.96%, (7) D = m, L = m (b) Adiabatic compression: (1) m = kg/min (2) T2 = K, V2 = 0.40 m 3 /min (3) I.P = kw (4) Q = 0 kw (5) B.P = kw (c) Isothermal compression: (1) m = kg/min (2) T2= T1= 293 K, V2 = m 3 /min (3) I.P = kw (4) Q = I.P = kw (5) B.P = kw [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?] V.L Patel- Page 6.62/10 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 Answers: (1) I.P (for two stage) = kw, (2) I.P (for single stage) = kw, (3) Saving in power = 9.86% V.L Patel- Page 6.59/7 3. A two stage single acting RAC takes in air at a pressure 1 bar, 20 C and compresses to pressure of 55 bar. The air is cooled in intercooler at constant pressure of 10 bar to a temperature of 40 C. The diameter of L.P cylinder is 175 mm and both the Darshan Institute of Engineering and Technology, Rajkot 3

16 cylinder have 225 mm stroke. If the compression follow the law of PV 1.25 = C. Find indicated power if the compressor runs at 150 rpm. Answers: I.P = 6.89 kw 4. 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. Answers: dlp = 0.41 m, dhp = 0.24 m 5. 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. Answers: (1) dlp = m, dip = m, dhp = m, (2) I.P = kw CASE (B) : Single-Multi Stage, Single-Double Acting Compression with Clearance Volume 6. A 23 kw electric motor drives a single cylinder, single acting reciprocating air compressor running at 300 rpm. Mechanical efficiency = 87%. The air inlet conditions are bar and 15 C respectively, delivery pressure = 8 bar, index of compression and re-expansion = 1.3. Clearance volume is 7% of the stroke volume. Diameter of cylinder is same as its stroke length. Calculate, 1) FAD in m 3 of air per minute 2) Volumetric efficiency 3) Cylinder dimensions V.L Patel- Page 6.74/18 Answers: (1) V1-V4 = m 3 /min, (2) ηv = 72.70%, (3) d = l = m 7. 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. Answers: (1) I.P = kw, (2) B.P = kw, (3) Pm = bar, (4) ηv = %, (5) d = m, l = m V.L Patel- Page 6.84/25 Darshan Institute of Engineering and Technology, Rajkot 4

17 8. A single stage, single acting reciprocating air compressor has bore of mm, stroke of 115 mm, clearance volume is 70 cm 3, suction pressure and temperature are bar, 20 C respectively, delivery pressure is 5.2 bar, speed of compressor is 105 rpm, polytropic index is 1.32 for compression and expansion. Determine, 1) Delivery of air in kg/min 2) Indicated power if the delivery pressure increased to 25 bar by the addition of a H.P cylinder of same stroke together with an intercooler which reduces temperature to 38 C. 3) Bore of the H.P cylinder allowing clearance volume to 6 % of the swept volume and same index V.L Patel- Page 6.99/35 Answers: (1) mad = kg/min, (2) I.P = kw, (3) dhp = m 9. A single acting two stage compressor with complete intercooling delivers 6 kg/min of air at 16 bar. Assuming intake at 1 bar and 15 C and compression and expansion with the law PV 1.3 = C. Calculate, 1) Power required to run the compressor 2) Isothermal efficiency 3) Free air delivery in m 3 /min 4) Volumetric efficiency and swept volumes of each cylinder, if the clearance volume ratios for L.P and H.P cylinders are 0.04 and 0.06 and speed of compressor is 420 rpm. Answers: (1) I.P = 27 kw, (2) ηiso = %, (3) Va (FAD) = m 3 /min, (4) ηvlp = %, ηvhp = %, VSLP = m 3, VSHP = m A single acting, two stage reciprocating air compressor running at 5 rps delivers air at a pressure of 18 bar while suction pressure is 98 kpa and 300 K. intermediate pressure is 4 bar, while the temperature of air after the intercooler is 305 K. Clearance volume of L.P cylinder is 5% of swept volume. Capacity of compressor under free air delivery at 1 bar, 15:C is 2.25 m 3 /min. Find: 1) Volumetric efficiency 2) Work supplied 3) Dimension of L.P cylinder if bore = stroke length 4) Isothermal efficiency Answers: (1) ηv = %, (2) W = kw, (3) dlp = m, (4) ηiso = % [Note: how volumetric efficiency is affected at higher altitude?] 11. A two stage reciprocating air compressor takes air at 1 bar, 20 C and delivers it at 15 bar runs at 300 rpm. There is 10% pressure drop in the intercooler. If the compression and expansion follow the law PV 1.4 = constant in the both the cylinder. If the L.P cylinder has a bore of 22 cm and stroke of 33 cm and there is perfect intercooling. Clearance volume is 6 % of stroke volume in L.P cylinder. If Clearance volume in H.P cylinder is 3% of stroke volume and the bore to stroke in H.P cylinder is 1:1.5. Determine, 1) Minimum power required Darshan Institute of Engineering and Technology, Rajkot 5

18 2) Bore and stroke of the H.P cylinder V.L Patel- Page 6.131/AE-4 Answers: (1) Pmin = kw, (2) dhp = m, l = 0.21 m [Note: If there is an ideal intercooler pressure then what will be influence on power required to run the compressor?] Darshan Institute of Engineering and Technology, Rajkot 6

19 ASSIGNMENT 7 ROTARY COMPRESSORS Theory 1. Discuss the basic principle and classification of rotary air compressor. 2. Describe the working of root blower with neat sketch and P-V diagram. 3. Explain vane type compressor with neat sketch and P-V diagram. 4. Describe the working of a screw compressor and list its applications. 5. Describe the working of scroll compressor with neat sketch. State its advantages. 6. Give compare reciprocating compressor with rotary compressor. 7. Give compare scroll compressor with rotary compressor. Examples 1. A two lobe root blower compresses 0.05 m 3 of air from 1 bar to 1.5 bar per revolution if the speed is 220 rpm. Calculate the root efficiency, volume of air handled per cycle and power required to drive the blower. Answer: 86%, m 3 /cycle, 5 kw V.L Patel- Page 9.4/1 2. A vane type rotary compressor has a free air delivery of 0.05 m 3 per revolution when it compressed air from 1 bar to 1.5 bar. Determine the work expended/rev in driving the compressor and the efficiency of compressor when the ports are so placed that (i) there is no internal compression (ii) there is 35 % pressure rise due to internal compression before back flow occurs. Also determine power required to drive the compressor. If the speed is 120 rpm in each case. Answer: (i) 86%, 5 kw (ii) 94.6%, kw V.L Patel Page 9.15/2 3. Compare the work inputs required for roots blower and a vane type compressor having same induced volume of 0.03 m 3 per revolution. The inlet pressure being bar and the pressure ratio is 1.5. For the vane type assume that the internal compression takes place through half of the pressure range. V.L Patel- Page 9.17/4 Answer: Root blower W = kj, vane type W = kj/rev 4. A vane type rotary compressor has an air delivery of 0.01 m 3 per revolution when it compressed air from 1 bar to 2 bar. Determine the efficiency of compressor when the ports are so placed that (i) there is no internal compression (ii) there is 45 % pressure rise due to internal compression before back flow occurs. Darshan Institute of Engineering and Technology, Rajkot 1

20 Answer: (i) 76.65% (ii) 94.19% R.N Patel- Page 9.19/8 5. A vane type rotary compressor work between pressure limits of 1 bar and 1.5 bar and gives 4 m 3 /min free air delivered when running at 200 rpm. Determine the power required to drive the compressor when the ports are so placed that (i) there is no internal compression (ii) there is 50 % pressure rise due to internal adiabatic compression before back flow occurs. Answer: (i) kw (ii) kw R.N Patel-Page 9.19/9 6. Determine the compression efficiency of roots blower if it compressors 0.06 m 3 of air per revolution of the rotor to raise the pressure of air from bar to bar. Answer: 68.74% R.N Patel Page 9.20/10 Darshan Institute of Engineering and Technology, Rajkot 2

21 ASSIGNMENT 8 CENTRIFUGAL COMPRESSORS Theory 1. Describe with neat sketch the principle of operation and essential parts of centrifugal compressors and state its advantages with applications. OR Describe principle construction and working of centrifugal compressor. 2. Explain static and stagnation (total head) properties with T-S diagram. 3. Explain inlet and outlet velocity triangles for the centrifugal compressor. 4. Define below terms. a. Isentropic efficiency b. Slip factor c. Power input factor d. Pressure (loading) coefficient e. Static and stagnation property 5. Define degree of reaction for centrifugal compressor stage and prove its expression. 6. Explain the phenomenon of surging, choking and stalling in centrifugal compressor. 7. What are the various losses occurring in centrifugal compressor? Examples 1. Following data relates to the Centrifugal compressor. Speed = 7000 RPM Impeller tip diameter = 50 cm Static temperature of air at inlet= 282 K Axial velocity of air at inlet = 120 m/s Slip factor = 0.9 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. Answers: Case-a: (1) P02/P01 = 1.346, P = J/kg, Case-b: (1) P02/P01 = 1.09, P = J/kg 2. Following data relates to the Centrifugal compressor. Free air delivered = 1200 m 3 /min Pressure ratio = 1.5 Index of compression = 1.5 Speed = 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. Darshan Institute of Engineering and Technology, Rajkot 1

22 Answers: (1) α2 = 10.81:, (2) β1 = 20.9: 3. Following data refers to the Centrifugal compressor. Speed = RPM Isentropic efficiency = 0.82 Inducing temperature of air = 17:C Impeller mean eye diameter = 200 mm Work done by impeller = 175 kj/kg Absolute velocity at inlet = 120 m/s 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. Answers: (1) P02/P01 = 3.95, (2) D2 = m, (3) α1 = 70:, α2 = 16.66:, (4) β1 = 41.71:, β2 = 46.70:, (5) Cr1 = m/s, Cr2 = m/s 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, 30:C Isentropic efficiency = 0.8 Slip factor = 0.94 Absolute velocity at inlet = 150 m/s Specific heat of air = 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. Answer: (1) T02-T01= K, (2) D2 = 0.55 m, (3) Ae = m2, (4) u2 = m/s, (5) P = kw 5. Following data relates to the Centrifugal compressor. Total pressure ratio = 4 Isentropic efficiency = 0.9 Speed = RPM Inducing air temperature = 288 K Mean eye diameter = 400 mm Absolute velocity at inlet = 90 m/s Impeller tip diameter = 750 mm Angle of prewhirl = 20: Calculate the number of impeller radial vanes by using Stanitz formula. Answer: Z 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 Darshan Institute of Engineering and Technology, Rajkot 2

23 radial direction is 26: 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. Answer: (1) P = kw, (2) Det = m, (3) P02/P01 = The following data refers to a single sided centrifugal compressor. Overall diameter of the impeller= 50 cm Eye tip diameter = 30 cm Eye root diameter = 15 cm 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. Answer: (1) P02/P01 = 3.11, (2) P = kw, (3) β1t = 32.48:, βr1 = 51.85: 8. 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. Answer: (1) P = kw (2) D1 = m, D2 = 1.41 m (3) b1 = m (4) β1 = 15.15: (5) α2 = 7.7: 9. 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 Darshan Institute of Engineering and Technology, Rajkot 3

24 Static pressure at impeller exit = 2.2 bar Stagnation pressure and temp. at inlet = bar, 288 K If the air leaving the guide vanes has a velocity of 90 m/s at 75: 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. Answer: (1) M1r = 0.679, (2) ηc = , (3) P = kw 10. In a radial blade Centrifugal compressor has following data: Speed = RPM Total head pressure ratio = 4 Atmospheric pressure and temperature are= 1 bar, 27:C Diameter of hub at impeller eye = 15 cm Axial velocity at inlet = 120 m/s Absolute velocity at the diffuser exit = 120 m/s Mass flow rate = 8 kg/s Total to total adiabatic efficiency = 80% Pressure coefficient = 0.72 Find: (1) eye tip diameter, (2) impeller tip diameter, (3) power required to drive the compressor and (4) static conditions at exit. Answer: (1) Det = m, (2) D2 = m, (3) P = kw, (4) T3 = 475 K, P3 = bar. 11. 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. Answer: (1) m = m/s, (2) Dt = m, Dh = m, (3) ηo = 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 15:C 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. Answer: (1) T02 T01 = K, (2) uet = m/s, u2 = m/s, (3) m, (4) kw, (5) Det = m Darshan Institute of Engineering and Technology, Rajkot 4

25 13. 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 22:C 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. Answer: (1) P02 = bar, To2 = 233.8:C, (2) u2 = m/s Darshan Institute of Engineering and Technology, Rajkot 5

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27 ASSIGNMENT 9 AXIAL COMPRESSORS Theory 1. What is an axial flow compressor? With suitable sketch explain working and construction of axial compressor. 2. Explain inlet and exit velocity triangles for axial flow compressor stage. 3. Explain aerofoil blading & Lift and Drag coefficient for blade. 4. State advantages of an axial flow compressor. Give comparison between centrifugal and an axial flow compressor. 5. Discuss performance characteristic of an axial flow compressor. Examples 1. An axial flow compressor of 50% reaction design has blades inlet and outlet angles of 45: and 10: respectively. The compressor is to be produced a stagnation pressure ratio of 7.5 with an overall total head efficiency of 0.85 when inlet stagnation is 37:C. The blade speed and axial velocity of flow are constant throughout the compressor. The work done factor is Taking the value of 200 m/s for blade speed. Find the number of stages required. Answer: Number of stages = 12 R.L Patel 11.47/1 2. An axial flow compressor has 8 stages and the following data apply to each stage at the mean diameter. Blade speed = 210 m/s Degree of reaction = 0.5 Stage efficiency = 0.85 Polytropic efficiency = 0.88 Angle of absolute air velocity at rotor inlet = 15: Angle of absolute air velocity at rotor inlet = 45: Work done factor = 0.86 Inlet stagnation pressure = 1 bar Inlet stagnation temperature = 27: Determine the total pressure ratio of the first stage and overall static pressure ratio. Answer: (i) (ii) 3.98 R.L Patel 11.48/2 3. First stage of an axial flow compressor delivers 20 kg/s of air at 9000 rpm.stage temperature rise 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. Answer: (i) inlet blade angles α1= 12: β1 = 44.64:, outlet blade angles α2 = 44.64, β2 = 12: (ii) h = m R.L Patel 11.50/3 4. The following data refers to an axial flow compressor. Darshan Institute of Engineering and Technology, Rajkot 1

28 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 = 45: and 10: 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 (ii) Number of stages required (iii) Inlet Mach number relative to rotor at the mean blade height of the first stage. Answer: (i) 6 stages (ii) 0.8 R.L Patel 11.54/5 5. A multi stage axial flow compressor absorbs 2211 kw when delivering 10 kg/s of air from stagnation conditions 1bar and 15C:. 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. Answer: (i) 9 stages (ii) bar (iii) 87.2% R.L Patel 11.59/8 6. The following data refers toan axial flow compressor. Pressure of air at inlet ofan axial flow compressor = 768 mm of Hg Temperature of air at inlet ofan axial flow compressor = 41C: Diameter at mean blade section = 500 mm Peripheral velocity = 100 m/s Mass flow rate through the stage = 25 kg/s Work done factor = 0.95 Mechanical efficiency = 92% Stage efficiency = 88% If air angles are β1 = 51:, α1 = α3 =7:and the air is turned through 42: 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 R.L Patel 11.61/9 Answer: (i) α2 =50.18: (ii) h = 19 cm (iii) (iv) (v) kw (vi) 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 30:relativ 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 Darshan Institute of Engineering and Technology, Rajkot 2

29 required to drive the compressor when there are 8 stages and the mechanical efficiency is 99%. Answer: (i) m/s (ii) 56.1 kg/s (iii) kw Page 11.69/12 8. The following data refers toan axial flow compressor. Stage stagnation temperature rise = 22 K Mass flow of air = 25 kg/s Rotational speed = 150 rev/s Axial velocity through the stage = 157 m/s Mean blade speed = 200 m/s Work done factor = 0.95 Reaction at mean radius = 50% Rotor blade aspect ratio = 3 Inlet stagnation pressure and temperature = bar, 288 K Solidity = 0.8 Determine, (i) The blade and air angle at the mean radius (ii) The mean radius (iii) The blade height (iv) The pitch and chord (v) The number of blades Answers: (i) β1 = 45.2:, β2 = 14.93:(ii) m (iii) h = 0.11 m (iv) S = m, m (v) An axial flow air compressor stage has a mean diameter of 60 cm. and runs at rpm if the actual temperature rise and pressure ratio developed are 30 C and 1.35 respectively. Determine, (I) Power required to drive the compressor while delivering 57 kg/s of air, if the mechanical efficiency is 86 percent and inlet temperature rise is 35 C, (II) The stage loading coefficient and,(iii) The degree of reaction if the temperature at the rotor exit is 55 C. Darshan Institute of Engineering and Technology, Rajkot 3

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31 ASSIGNMENT 10 MISCELLANEOUS HYDRAULIC MACHINES Theory 1. Explain construction and working of below miscellaneous machines with diagram. a) Hydraulic press b) Hydraulic accumulator c) Hydraulic intensifier d) Hydraulic crane e) Hydraulic jack f) Hydraulic lift g) Hydraulic ram h) Fluid couplings i) Fluid torque converter j) Air lift pump Darshan Institute of Engineering and Technology, Rajkot 1