CHAPTER-2 IMPACT OF JET

Transcription

1 CHAPTER-2 IMPACT OF JET FLUID POWER ENGINEERING ( ) 1. A jet of water of diameter 5cm moving with a velocity of 25 m/sec impinges on a fixed curved plate tangentially at one end at an angle of 30 with the horizontal. Determine force of the jet on the plate in the horizontal and the vertical direction if the jet is deflected through an angle of 130. Also find direction and resultant force. [Ans: N, N, N, 4.99 ] [14; V. L. Patel] 2. A jet of water impinges on a symmetrically curved vane at its center. The velocity of the jet is 60 m/s and the diameter 120 mm. The jet is deflected through an angle of 120. Calculate the force on the vane if the vane is fixed. Also determine the force if the vane moves with a velocity of 25 m/s in the direction of the jet. What will be the power and efficiency? [GTU; DEC 2010] 3. A jet of water having a velocity of 20 m/sec strikes a curved vane, which is moving with a velocity of 10 m/sec. The jet makes an angle of 20 with the direction of motion of vane at inlet and leaves at an angle of 130 to the direction of motion of vane at outlet. Calculate: (1) Vane angles, so that the water enters and leaves the vane without shock. (2) Work done per unit weight of water striking the vane per second. [Ans: , 6.565, N-m/N] [17.18; R. K. Bansal] 4. A jet of water having a velocity of 15 m/sec strikes a curved vane which is moving with a velocity of 5 m/sec. The vane is symmetrical and it so shaped that the jet is deflected through 120. Find the angle of the jet at inlet of the vane so that there is no shock. What is the absolute velocity of the jet at outlet in magnitude and direction and the work done per unit weight of water? Assume the vane to be smooth. [Ans: , 6.62m/s, , N-m/N] [17.21; R. K. Bansal] 5. A jet of water having a velocity of 15 m/sec, strikes a curved vane which is moving with a velocity of 5 m/sec in the same direction as that of the jet at inlet. The vane is so shaped that the jet is deflected through 135. The diameter of jet is 100mm. Assume the vane to be smooth, find: (1) Force exerted by the jet on the vane in the direction of motion. (2) Power exerted on the vane. (3) Efficiency of the vane [Ans: N, 6.703KW, 50.5%] [17.23; R. K. Bansal] 6. A jet of water of diameter 5 cm having a velocity of 30 m/sec strikes a curved vane horizontally at one of its tip which is moving with a velocity of 15 m/sec in the direction of jet. The jet leaves the vane at an angle of 60 to the direction of motion of the vane at outlet. Determine : (1) The force exerted by the jet on the vane in the direction of motion (2) The work done per second by jet. [Ans: N, 9.94KW] [21; V. L. Patel] 7. A jet of water having a velocity 25 m/s strikes on a series of vanes moving with a velocity 10 m/s. The jet makes an angle of 300 with the direction of motion of vanes when entering and leaves at an angle of 1500 with the direction of motion. Sketch the velocity triangles and calculate, Darshan Institute of Engineering and Technology, Rajkot 1

2 a) Vane angles at inlet and outlet b) Work done when the vane discharging 325 litres/s Take loss due to friction over the vane as 10 % of relative velocity. [GTU; NOV-2011] 8. A jet of water of 40mm diameter strikes horizontally at the centre of a square plate of uniform thickness and having a mass of 16 kg and edge 25 cm with 10 m/sec. The square plate is suspended vertically by a hinge on its top horizontal edge. Find, (1) The force to be applied at the lower edge of the plate to keep it vertical. (2) The inclination of the plate with vertical under the action of the jet, if the plate is allowed to swing freely. [Ans: 62.83N, ] [3; V. L. Patel] 9. A rectangular plate, weighing 58.86N is suspended vertically by a hinge on the top horizontal edge. The centre of gravity of the plate is 10cm from the hinge. A horizontal jet of water 2cm diameter, whose axis is 15cm below the hinge impinges normally on the plate with a velocity of 5 m/sec. Find the horizontal force applied at the centre of the gravity to maintain the plate in its vertical position. Find the corresponding velocity of the jet, if the plate is deflected through 30 and the same force continues to act at the centre of gravity of the plate. [Ans: N, 9.175m/s] [17.9; R. K. Bansal] 10. A jet of water having a velocity of 35 m/sec impinges on a series of vanes moving with a velocity 20 m/sec. The jet makes an angle of 30 to the direction of motion of vanes when entering and leaves at an angle of 120. Draw the triangle of velocities at inlet and outlet and find: (1) The angle of vanes tips so that water enters and leaves without shock. (2) The work done per unit weight of water entering the vanes, and The efficiency. [Ans: 60, 1.25, 62.28N-m/N, 99.74%] [17.25; R. K. Bansal] 11. A jet of water having a velocity of 30 m/sec strikes a series of radial curved vanes mounted on a wheel which is rotating at 200 r.p.m. The jet makes an angle of 20 with the tangent to the wheel at inlet and leaves the wheel with a velocity of 5 m/sec at an angle of 130 to the tangent to the wheel at outlet. Water is flowing from outward in a radial direction. The outer and inner radii of the wheel are 0.5m and 0.25m respectively. Determine: (1) Vane angles at inlet and outlet (2) Work done per unit weight of water (3) Efficiency of wheel [Ans: 30.07, 24.39, 31.8N-m/N, 69.32%] [17.26; R.K. Bansal] Darshan Institute of Engineering and Technology, Rajkot 2

3 CHAPTER-3 HYDRAULIC TURBINE FLUID POWER ENGINEERING ( ) Impulse Turbine / Pelton Wheel 1. A Pelton wheel is to be designed for the following specifications: Shaft power = 11,772 KW; Head = 380 meters; Speed = 750 rpm; Overall efficiency = 86%; Jet diameter is not to exceed one-sixth of the wheel diameter. Determine: a) The wheel diameter, b) The number of jets required, and c) Diameter of the jet. Take Kv1 = and Ku1 = [18.2; R. K. Bansal][Answer: 0.989m, 2 jets, 0.165m] 2. A Pelton wheel is to be designed for a head of 60m when running at 200 rpm. The Pelton wheel develops kw shaft power. The velocity of the buckets = 0.45 times the velocity of the jet, overall efficiency = 85% and co-efficient of velocity = [18.11; R. K. Bansal][Answer: D=1.44m, d=85mm, w=425mm, h=102mm, Z=24] 3. A Pelton wheel is working under a gross head of 400m. The water is supplied through penstock of diameter 1m and length 4km from reservoir to the Pelton wheel. The co-efficient of friction for the penstock is given as The jet of water of diameter 150mm strikes the buckets of the wheel and gets deflected through an angle of 165. The relative velocity of water at outlet is reduced by 15% due to friction between inside surface of the bucket and water. If the velocity of the buckets is 0.45 times the jet velocity at inlet and mechanical efficiency as 85%, determine: a) Power given to the runner, b) Shaft power, c) Hydraulic efficiency, and d) Overall efficiency. [18.5; R. K. Bansal][Answer: kw, kw, 90.14%, 76.62%] 4. The following data is related to Pelton wheel turbine: a) Head at the base of the nozzle = 80 m b) Diameter of the jet = 100 mm c) Discharge of the nozzle = 0.30m 3 /s d) Power at the shaft = 206 kw and e) Power absorbed in mechanical resistance = 4.5 kw Determine: (1) Power lost in nozzle and (2) Power lost due to hydraulic resistance in the runner. [Dec-2010, Jun-2012][Answer: kW, 8.352kW] Reaction Turbine 5. An inward flow reaction turbine has external and internal diameters as 0.9m and 0.45m respectively. The turbine is running at 200 rpm and width of the turbine at inlet is 200mm. The velocity of flow through the runner is constant and is equals to 1.8 m/sec. The guide blades make an angle of 10 to the tangent of the wheel and the Darshan Institute of Engineering and Technology, Rajkot 1

4 discharge at the outlet of the turbine is radial. Draw the inlet and outlet velocity triangles and determine: i. The absolute velocity of water at inlet of runner (V1 = m/s) ii. The velocity of whirl at inlet (Vw1 = m/s) iii. The relative velocity at inlet (Vr1 = m/s) iv. The runner blade angles (θ = and Φ = 20.9) v. Width of the runner at outlet (B2 = 0.4m) vi. Mass of water flowing through the runner per second (m = kg/s) vii. Head at the inlet of the turbine (H = 9.97m) viii. Power developed & hydraulic efficiency of the turbine. (97.9KW, 98.34%) [18.15; R. K. Bansal] 6. The runner of the Francis turbine has an outer diameter 500mm and the inner diameter 350mm. It works under a head of 60m. The width at the inlet is 75mm. The angle of the blades at the inlet and outlet are 93 and 30 respectively. The flow enters the vanes at an angle of 23. Mechanical losses are 6% and the area taken by the vanes is 7% of the total area, hydraulic efficiency is 90% and the flow velocity is constant. Find the speed of the runner so that entry of water into runner is shock less. Find power produced by the turbine. [19; R. N. Patel][Answer: P = KW, N = 888 rpm] 7. A Kaplan turbine develops kW power at an average head of 39m. Assuming a speed ratio of 2, flow ratio of 0.6, diameter of the boss equals to 0.35 times the diameter of the runner and an overall efficiency of 90%. Calculate the diameter, speed and specific speed of the turbine. [18.28; R. K. Bansal][Answer: 2.5m, rpm, rpm] 8. A conical draft turbine tube having inlet and outlet diameter 1.2m and 1.8m discharges water at outlet with a velocity of 3m/s. The total length of draft tube is 7.2 m and 1.44 m of the length of draft tube immersed in water. If the atmospheric pressure head is 10.3 m of water and loss of head due to friction in draft tube is equal to 0.2 x velocity head at outlet of tube determine: a. Pressure head at inlet and b. Efficiency of draft tube. [May-2013] [Reference: 18.35; R. K. Bansal] Darshan Institute of Engineering and Technology, Rajkot 2

5 CHAPTER-4 CENTRIFUGAL PUMPS FLUID POWER ENGINEERING ( ) 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. Minimum starting speed b. Manometric efficiency of the pump c. Vane angle at inlet (Ө), absolute angle at the outlet (β) d. Absolute velocity (V2) & relative velocity (Vr2 ) at the outlet e. Width of the impeller at inlet and outlet f. Work done by impeller on water per second g. 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 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 Darshan Institute of Engineering and Technology, Rajkot 1

6 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 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 2

7 CHAPTER-5 RECIPROCATING PUMPS 1. A double acting reciprocating pump is fitted with an air vessel on suction side close to pump. The suction lift of pump is 4.5m. The length and diameter of suction pipe are 7.5m and 80mm resp. The stroke of piston and its diameter both are 200 mm each. Coefficient of friction is The atmospheric pressure head is 10.3m and separation pressure head 2.5m of water absolute. Determine: i. The speed at which separation commences ii. Maximum permissible speed without air vessel. 2. A double acting reciprocating pump running at 50rpm, delivers 40 litres per seconds has following specifications: Piston diameter=300mm, Poston rod diameter = 50mm, Storke= 400mm, Suction head= 4m, Delivery head= 8m. Calculate (i) Slip (ii) Force required to operate the pump during forward and reverse stroke of piston.(iii) Power required to drive the pump. 3. A triple cylinder pump raises the water level by 100m and the discharge is 100 lts/ sec. The diameter of the piston is 250 mm and stroke is 600mm. The velocity of water in the delivery pipe is 1.4m/s. The friction losses amount to 2m in the suction pipe and 18 m in the delivery pipe. Taking efficiency of the pump as 90 % and slip 2%. Find the speed and power input of the pump. B.E Semester V Darshan Institute of Engineering and Technology, Rajkot 1

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9 CHAPTER 6 RECIPROCATING COMPRESSOR CASE (A) : Single -Multi Stage, Single-Double acting Compression without Clearance Volume 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 and ambient condition per minute, kg of air dealt with per kwh (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) Volumetric efficiency measured at suction and ambient condition, isothermal efficiency, adiabatic efficiency, overall isothermal efficiency (7) Size of the cylinder and swept volume per stroke or cycle, if compressor runs at 240 rpm and piston speed is 150 m/min (8) Mean effective pressure Answers: (a) Polytropic compression: (1) m(suction) = kg/min, ma (ambient) = kg/min, m/kwh = kg/kwh, (2) T2 = 470 K, V2 = m 3 /min, (3) Ws = kw, Wc = kw, Wd = kw, Wnet = I.P = kw, (4) Q = kw, ΔU = kw, (5) B.P = kw, (6) ηv(suction) = 100%, ηv(ambient) = 94.73%, ηiso = 79.22%, ηad = 94.36%, ηiso(o) = 79.22%, (7) d = m, l = m, Vs = m 3 /cycle, (8) Pm = kpa (b) Adiabatic compression: (1) m/kwh = kg/kwh (2) T2 = K, V2 = m 3 /min (3) Ws = kw, Wc = kw, Wd = kw, Wnet = kw, (4) Q = 0 kw, ΔU = kw (5) B.P = kw, (8) Pm = kpa (c) Isothermal compression: (1) m/kwh = kg/kwh (2) T2 = T1 = 300 K, V2 = m 3 /min (3) Ws = kw, Wc = kw, Wd = Ws = kw, Wnet = kw (4) Q = Wnet = kw, ΔU = 0 kw (5) B.P = kw, (8) Pm = kpa V.L Patel- Page 6.51/02 [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 Darshan Institute of Engineering and Technology, Rajkot 1

10 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 (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? Answers: For imperfect intercooling: (1) P2 = bar, (2) I.P (two stage) = kw, I.P (single stage) = kw, % saving in power = 12.10% For perfect intercooling: (1) P2 = bar, (2) I.P (two stage) = kw, I.P (single stage) = kw, % saving in power = 12.83%, for minimum work d1/d2 = [Attention Note: clearly mention from above solution, why and which intercooling is preferable?] V.L Patel- Page 6.89/29 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. Answers: (1) P2 = 3 bar, (2) VLP = 0.01 m 3 /cycle, VHP = m 3 /cycle, (3) B.P = kw, (4) Q = kw, (5) (ΔT)w = 17.95:C, (6) % saving in power using three stage compression = 4.248%, % excess power required using single stage = 16.34% V.L Patel- Page 6.91/30 [Attention Note: is it economical to achieve 9 bar delivery pressure in single stage?] Darshan Institute of Engineering and Technology, Rajkot 2

11 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. Answers: (1) I.P = kw, (2) Va = m 3 /min, (3) Q = kw, (4) VSLP = m 3, VCLP = m 3, VSHP = m 3, VCHP = m 3, (5) ηiso = 86.78% 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. Answers: (1) X = 3 stages, (2) Exact stage pressure ratio = 3.115, (3) P2 = bar, P3 = bar (4) V1: V2: V3 is 15.33:3.915:1, (5) I.P (three stage) = kw, % excess power using single stage compression = 21.70% V.L Patel- Page 6.111/43 [Attention Note: why subcooling of air does not introduce in intercooler?? Justify.] 6. In a three stage compressor, air is compressed from 20 kpa to 98 kpa.calculate for 1 m 3 of air per second, (1) Work under ideal condition for n = 1.3 (2) Isothermal work (3) Saving in work due to multi-staging (4) Isothermal efficiency GTU Jun-2011 Answers: (1) W = kw, (2) Wiso = kw, (3) Wsave = kw, (4) ηiso = 93.99% Darshan Institute of Engineering and Technology, Rajkot 3

12 CASE (B) : Single-Multi Stage, Single-Double acting Compression with Clearance Volume 7. 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) For what length of stroke air is delivered (2) The volume of air delivered per stroke in liters at suction conditions and FAD (free air delivered) refers to ambient conditions (3) The temperature of the compressed air (4) The heat rejected during the compression (5) B.P of the compressor if compression occurs polytropically (PV 1.3 = constant), adiabatically (PV 1.4 = constant), and isothermally (PV = constant) taking mechanical efficiency 80% (6) Volumetric efficiency referred to suction and ambient conditions (7) Isothermal efficiency, adiabatic efficiency, overall isothermal efficiency (8) % of air delivered with reference to air compressed, mass of air compressed, mass of air delivered (9) Mean effective pressure Answers: (1) l = m, (2) V1- V4 = liters/stroke, Va = m 3 /min, (3) T2 = K, (4) Q = kw, (5) B.P for polytropic compression = kw, B.P for adiabatic compression = 1.385, B.P for isothermal compression = kw, (6) ηv (refers to suction conditions) = 94.51%, ηv (refers to ambient conditions) = 94.51%, (7) ηiso = 84.50%, ηad = 96.1%, ηiso(ov) = 67.64%, (8) mad/mac = 91.95%, mac = X 10-3 kg, mad = 3.093X 10-3 kg, (9) Pm = kpa V.L Patel- Page 6.66/12 [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?] 8. 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 (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 Answers: (1) Vs = m 3 (2) ηv(ambient) = 75.89%, (3) d = m, l = 0.40 m, (4) I.P = kw V.L Patel- Page 6.68/13 Darshan Institute of Engineering and Technology, Rajkot 4

13 [Attention Note: up to which extent clearance can be minimized? What are the constrains for optimum clearance?] 9. 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. Answers: (1) B.P = kw, (2) dlp = 0.24 m, dhp = 0.08 m, (3) % power saving = 8.638% V.L Patel- Page 6.97/ 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. Answers: (1) I.P = kw, (2) Saving in power = kw, (3) VSLP = m 3, VSHP = m 3, (4) B.P = kw V.L Patel- Page 6.113/44 [Attention Note: how to get better mechanical efficiency? Discussed the factors involved.] 11. 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 Answers: (1) P2 = 3 bar, P3 = 9 bar, (2) Vas (LP) = m 3, (3) T10 = K, V10-V11 = 6.23 X 10-4 m 3, (4) W = kj/kg of air V.L Patel- Page 6.101/36 Darshan Institute of Engineering and Technology, Rajkot 5

14 [Attention Note: which one is true? Clearance volume will be decrease, remains constant or increase stage by stage in RAC] 12. A two stage double acting air compressor operating at 200 rpm takes air at 1 bar, 27 C. The diameter and stroke length of L.P cylinder are 35 cm, 40 cm respectively. The stroke of H.P cylinder is same as L.P cylinder. Clearance volume is 4% of swept volume in both cylinders. The L.P cylinder discharges air at a pressure of 4 bar. The air passes through the intercooler so that it enters the H.P cylinders at 27 C, 3.9 bar. Finally air is discharges at 15.6 bar. The compression and expansion in the both the cylinder follow the same PV1.3 = constant. Determine, (1) B.P required to run compressor if mechanical efficiency is 80% (2) Diameter of H.P cylinder (3) Heat rejected in intercooler Answers: (1) B.P = kw, (2) dhp = m, (3) Q = kw V.L Patel- Page 6.120/47 Darshan Institute of Engineering and Technology, Rajkot 6

15 CHAPTER-8 CENTRIFUGAL COMPRESSOR 1. Following data relates to the Centrifugal compressor. Total pressure ratio = 4 Isentropic efficiency = 0.78 Speed = RPM Stagnation temperature at inlet = K Absolute velocity at inlet = 150 m/s Assuming suitable value of slip factor and power input factor. Calculate impeller outlet diameter. Answers: D2 = m 2. A centrifugal compressor running at 1440 rpm handles air at 101 kpa and 20 C and compresses it to a pressure of 6 bar isentropically. The inner and outer diameters of the impeller are 14 cm and 25 cm respectively, the width of the blade at the inlet is 2.5 cm. The blade angles are 16 and 40 at entry and exit. Calculate mass flow rate of the air degree of reaction, power input and width of the blades at outlet. 3. A centrifugal air compressor has a pressure ratio of 4:1 with an isentropic efficiency 88% when running at rpm and including air at 25 C. Curved vanes at inlet give the air a pre-whirl of 18 to axial direction at all radii and the mean diameter of eye is 245 mm. The absolute air velocity at inlet is 120 m/s. Impeller tip diameter is 580 mm. Calculate slip factor. 4. A centrifugal compressor (ηc = 0.85) runs at rpm inducting air at 200 C, the work done by the impeller is 160 kj/kg K. Guide vanes at inlet gives the air a prewhirl at 25 Mean eye diameter is 225 mm, the absolute air velocity at inlet is 130 m/s. At the exit the blades are radial and the slip factor is Calculate (i) the pressure ratio and (ii) impeller tip diameter. 5. 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. Answer: (1) α = 27.90⁰, (2) P2 = 2.47 bar 6. Following operating conditions are relates to the centrifugal compressor. Mass flow rate = 15 kg/sec Speed = RPM Overall static pressure ratio = 4:1 Isentropic efficiency = 80% Slip factor = 0.9 Flow coefficient at impeller exit = 0.3 Darshan Institute of Engineering and Technology, Rajkot 1

16 Hub diameter of eye = 15 cm Velocity of air at inlet = 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. Answer: (1) D1 = m, D2 = m (2) b2 = m, (3) P = 2940 kw 7. 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 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%. Answer: (1) β1 = 35.4⁰, (2) To2= K, (3) Po2 = bar 8. 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. Answer: (1) Po4= 10.5 bar, To4 = K, (2) W (single stage) = kj/kg of air Darshan Institute of Engineering and Technology, Rajkot 2

17 CHAPTER 9 AXIAL AIR COMPRESSORS 1. The following data refers to a test on an axial flow compressor. Atmospheric temperature and pressure at inlet are 18 C and 1 bar. Total head temperature in delivery pipe is 165 C. Total head pressure in delivery pipe is 3.5 bar. Static pressure in delivery pipe is 3 bar. Calculate (a) total head isentropic efficiency, (b) polytropic efficiency, and (c) air Velocity in delivery pipe. Answer: 85.2 %. 87.5%, m/s 2. The first stage of an axial flow compressor is designed for free vortex condition, with no inlet guide vanes. The rotational speed is 9000 rpm, and stagnation temperature rise is 20 C. The hub-tip ratio is 0.6, the work done factor is 0.94 and isentropic efficiency of the stage is Assuming an inlet velocity of 150 m/s and ambient conditions of 1 bar and 300K, compute (a) the tip radius and corresponding rotor angles, if the Mach number relative to' the tip is limited to 0:92, (b) mass flow entering the stage (c) stage stagnation pressure ratio and power required and (d) the rotor air angle at the root section. Answer: 0.292m, kg/s, 1.226, β1= 47.71, KW, β2 = Air at bar and 288 K enters an axial flow compressor stage with an axial velocity 150 m/s. There are no inlet guide vanes. The rotor stage has a tip diameter of 60 cm and a hub diameter of 50 cm and rotates at 100 rps. The air enters the rotor and leaves the stator in the axial direction with no change in velocity or radius. The air is turned through 30 as it passes through rotor. Assuming the constant specific heats and that the air enters and leaves the blades at the blades angles, (i) construct the velocity diagram at mean dia. for the stage, (ii) mass flow rate, (ill) power required, and (iv) degree of reaction Answer: kg/s, KW, An axial flow compressor stage has the following data, Temperature and pressure at inlet Degree of reaction = 0.5 Mean blade ring diameter = 27 C and 1.0 bar = 36 cm Darshan Institute of Engineering and Technology, Rajkot 1

18 Rotational speed Blade height at entry = rpm = 6 cm Air angles at rotor at stator exit = 25 Axial velocity of flow = 180m/s Work done factor = 0.88 Stage efficiency = 85 % Mechanical efficiency = 96.7 % Determine: FLUID POWER ENGINEERING ( ) (a) Air angles at the rotor and stator entry, (b) Mass flow rate of air, (c) Power required to drive the compressor, (d) The loading coefficient, (e) Pressure ratio developed by the stage and (f) Mach number at the rotor entry. Answer: 54.82, kg/s, KW, 0.444, 1.6, The following data refers to an axial flow air compressor having number of similar stages with equal work done per stage and uniform velocity of flow throughout. Overall stagnation pressure ratio = 3.5 Stagnation inlet temperature = 600 C Relative air angle at rotor inlet = 130 Relative air angle at rotor outlet = 100 Blade velocity Degree of reaction = 0.5 = 185 m/s Overall stagnation isentropic efficiency = 87% The data refer to mean blade height and the measurement of angles is done in the same sense from the blade velocity direction. Calculate (a) Stagnation (Total head) outlet temperature and (b) Number of stages. Answer: (a) = K, (b) =8 6. The first stage of an axial flow compressor develops a pressure ratio of 2. The inlet pressure and temperature are 1.01 bar and 30 C respectively. The overall efficiency of compressor is 83 %. The flow coefficient is The velocity diagram is symmetrical and at the mean radius the ratio of change of whirl velocity to axial velocity is 0.5. Determine the compressor speed if the mean diameter is 50 cm. Also find the absolute velocity of the air leaving the stationary inlet guide vanes. Answer: rpm, m/s 7. An axial compressor has a mean diameter of 60 cm and runs at 15,000 rpm. If the actual temperature rise and pressure ratio developed are 30 C and 1.3 respectively, Darshan Institute of Engineering and Technology, Rajkot 2

19 determine (a) power required to drive the compressor while delivering 57 kg/s of air, assuming mechanical efficiency 86 % and initial temperature of 35 C (b) the stage efficiency and (c) the degree of reaction if the temperature at the rotor exit is 55 C. Answer: KW, An axial flow air compressor of 50 % reaction design has blades with inlet ant outlet angles of 45 and 10 respectively. The compressor is to produce a pressure ratio of 6:1 with an overall isentropic efficiency of 0.85 when inlet static temperature is37 C. The blade speed and axial velocity are constant through out compressor. Assuming a value of 200 m/s for blade speed. Find the number of stages required if the work done factor is (i) unity and (ii) 0.87 for all stages. Answer: 9, Find the polytropic efficiency of an axial flow compressor from the following data: The total head pressure ratio = 4 Overall total head isentropic efficiency = 85% Total head inlet temperature = 290K The inlet and outlet air angles from the rotor blades of the above compressor are 45 and 10 respectively. The rotor and stator blades are symmetrical. The mean blade speed and axial velocity remain constant throughout the compressor. Assuming a value of 220m/s for blade speed and the work done factor as 0.86, find the number of stages required. Also find the inlet Mach number relative to rotor at the mean blade height of the first stage. Assume, R = KJ/kg K. Answer: 6, 0.8, % Darshan Institute of Engineering and Technology, Rajkot 3