AHMEDABAD INSTITUTE OF TECHNOLOGY

TOPIC: RECIPROCATING PUMPS NAME: (1)SAKARIYA BRIJESH ( ) (2)RAVAL JAINIL ( ) (3)RAVAL YASH ( ) (4)SHAH CHINTAN ( ) (5)SHAH DHARMIL ( S)

WHAT ARE RECIPROCATING PUMPS? PUMPS ARE THE HYDRAULIC MACHINES WHICH CONVERT THE MECHANICAL ENERGY INTO HYDRAULIC ENERGY WHICH IS MAINLY IN THE FORM OF PRESSURE ENERGY. PUMPS ARE THE HYDRAULIC MACHINES WHICH CONVERT THE MECHANICAL ENERGY INTO HYDRAULIC ENERGY WHICH IS MAINLY IN THE FORM OF PRESSURE ENERGY. IF THE MECHANICAL ENERGY IS CONVERTED INTO HYDRAULIC ENERGY, BY MEANS OF CENTRIFUGAL FORCE ACTING ON THE LIQUID, THE PUMP IS KNOWN AS CENTRIFUGAL PUMP. IF THE MECHANICAL ENERGY IS CONVERTED INTO HYDRAULIC ENERGY, BY MEANS OF CENTRIFUGAL FORCE ACTING ON THE LIQUID, THE PUMP IS KNOWN AS CENTRIFUGAL PUMP. BUT IF THE MECHANICAL ENERGY IS CONVERTED INTO HYDRAULIC ENERGY (OR PRESSURE ENERGY) BY SUCKING THE LIQUID INTO A CYLINDER IN WHICH A PISTON IS RECIPROCATING (MOVING BACKWARDS AND FORWARDS), WHICH EXERTS THE THRUST ON THE LIQUID AND INCREASES ITS HYDRAULIC ENERGY (PRESSURE ENERGY), THE PUMP IS KNOWN AS RECIPROCATING PUMP. BUT IF THE MECHANICAL ENERGY IS CONVERTED INTO HYDRAULIC ENERGY (OR PRESSURE ENERGY) BY SUCKING THE LIQUID INTO A CYLINDER IN WHICH A PISTON IS RECIPROCATING (MOVING BACKWARDS AND FORWARDS), WHICH EXERTS THE THRUST ON THE LIQUID AND INCREASES ITS HYDRAULIC ENERGY (PRESSURE ENERGY), THE PUMP IS KNOWN AS RECIPROCATING PUMP.

MAIN PARTS OF A RECIPROCATING PUMP

WORKING OF A RECIPROCATING PUMP FIGURE SHOWS A SINGLE ACTING RECIPROCATING PUMP, WHICH CONSISTS OF A PISTON WHICH MOVES FORWARDS AND BACKWARDS IN A CLOSE FITTING CYLINDER. FIGURE SHOWS A SINGLE ACTING RECIPROCATING PUMP, WHICH CONSISTS OF A PISTON WHICH MOVES FORWARDS AND BACKWARDS IN A CLOSE FITTING CYLINDER. THE MOVEMENT OF THE PISTON IS OBTAINED BY CONNECTING THE PISTON ROD TO CRANK BY MEANS OF A CONNECTING ROD. THE CRANK IS ROTATED BY MEANS OF AN ELECTRIC MOTOR. THE MOVEMENT OF THE PISTON IS OBTAINED BY CONNECTING THE PISTON ROD TO CRANK BY MEANS OF A CONNECTING ROD. THE CRANK IS ROTATED BY MEANS OF AN ELECTRIC MOTOR. SUCTION AND DELIVERY PIPES WITH SUCTION VALVE AND DELIVERY VALVE ARE CONNECTED TO THE CYLINDER. SUCTION AND DELIVERY PIPES WITH SUCTION VALVE AND DELIVERY VALVE ARE CONNECTED TO THE CYLINDER. THE SUCTION AND DELIVERY VALVES ARE ONE WAY VALVES OR NON RETURN VALVES, WHICH ALLOW THE WATER TO FLOW IN ONE DIRECTION ONLY. THE SUCTION AND DELIVERY VALVES ARE ONE WAY VALVES OR NON RETURN VALVES, WHICH ALLOW THE WATER TO FLOW IN ONE DIRECTION ONLY. SUCTION VALVE ALLOWS WATER FROM SUCTION PIPE TO THE CYLINDER WHILE DELIVERY VALVE ALLOWS WATER FROM CYLINDER TO DELIVERY PIPE ONLY. SUCTION VALVE ALLOWS WATER FROM SUCTION PIPE TO THE CYLINDER WHILE DELIVERY VALVE ALLOWS WATER FROM CYLINDER TO DELIVERY PIPE ONLY.

WHEN CRANK STARTS ROTATING, THE PISTON MOVES TO AND FRO IN THE CYLINDER. WHEN CRANK STARTS ROTATING, THE PISTON MOVES TO AND FRO IN THE CYLINDER. WHEN CRANK IS AT A, THE PISTON IS AT THE EXTREME LEFT POSITION IN THE CYLINDER. WHEN CRANK IS AT A, THE PISTON IS AT THE EXTREME LEFT POSITION IN THE CYLINDER. AS THE CRANK IS ROTATING FROM A TO C (I.E. FROM =0 O TO =180 O ), THE PISTON IS MOVING TOWARDS RIGHT IN THE CYLINDER. THE MOVEMENT OF THE PISTON TOWARDS RIGHT CREATES A PARTIAL VACUUM IN THE CYLINDER. AS THE CRANK IS ROTATING FROM A TO C (I.E. FROM =0 O TO =180 O ), THE PISTON IS MOVING TOWARDS RIGHT IN THE CYLINDER. THE MOVEMENT OF THE PISTON TOWARDS RIGHT CREATES A PARTIAL VACUUM IN THE CYLINDER. BUT ON THE SURFACE OF THE LIQUID IN THE SUMP ATMOSPHERIC PRESSURE IS ACTING, WHICH IS MORE THAN THE PRESSURE INSIDE THE CYLINDER. BUT ON THE SURFACE OF THE LIQUID IN THE SUMP ATMOSPHERIC PRESSURE IS ACTING, WHICH IS MORE THAN THE PRESSURE INSIDE THE CYLINDER. THUS, THE LIQUID IS FORCED IN THE SUCTION PIPE FROM THE SUMP. THIS LIQUID OPENS THE SUCTION VALVE AND ENTERS THE CYLINDER. THUS, THE LIQUID IS FORCED IN THE SUCTION PIPE FROM THE SUMP. THIS LIQUID OPENS THE SUCTION VALVE AND ENTERS THE CYLINDER.

WHEN CRANK IS ROTATING FROM C TO A (I.E. FROM =180 O TO =360 O ), THE PISTON FROM ITS EXTREME RIGHT POSITION STARTS MOVING TOWARDS LEFT IN THE CYLINDER. WHEN CRANK IS ROTATING FROM C TO A (I.E. FROM =180 O TO =360 O ), THE PISTON FROM ITS EXTREME RIGHT POSITION STARTS MOVING TOWARDS LEFT IN THE CYLINDER. THE MOVEMENT OF THE PISTON TOWARDS LEFT INCREASES THE PRESSURE OF THE LIQUID INSIDE THE CYLINDER MORE THAN ATMOSPHERIC PRESSURE. THE MOVEMENT OF THE PISTON TOWARDS LEFT INCREASES THE PRESSURE OF THE LIQUID INSIDE THE CYLINDER MORE THAN ATMOSPHERIC PRESSURE. HENCE SUCTION VALVE CLOSES AND DELIVERY VALVE OPENS. HENCE SUCTION VALVE CLOSES AND DELIVERY VALVE OPENS. THE LIQUID IS FORCED INTO THE DELIVERY PIPE AND IS RAISED TO A REQUIRED HEIGHT. THE LIQUID IS FORCED INTO THE DELIVERY PIPE AND IS RAISED TO A REQUIRED HEIGHT.

DISCHARGE THROUGH RECIPROCATING PUMPS LET, LET, D = DIAMETER OF CYLINDER D = DIAMETER OF CYLINDER d = DIAMETER OF PISTON ROD d = DIAMETER OF PISTON ROD A = CROSS SECTION AREA OF CYLINDER A = CROSS SECTION AREA OF CYLINDER N = RPM OF CRANK N = RPM OF CRANK r = RADIUS OF CRANK r = RADIUS OF CRANK L = LENGTH OF STROKE = 2r L = LENGTH OF STROKE = 2r h s = SUCTION HEAD h s = SUCTION HEAD h d = DELIVERY HEAD h d = DELIVERY HEAD

Q = DISCHARGE OF * NO. OF REVOLUTION PER SECOND WATER IN ONE REVOLUTION WATER IN ONE REVOLUTION = A * L = A * L = ΠD 2 /4 * L m 3 / cycle = ΠD 2 /4 * L m 3 /cycle = ΠD 2 L/4 * N/60 m 3 / second = ΠD 2 L/4 * N/60 m 3 /second = ALN/60 = ALN/60

WORK DONE BY RECIPROCATING PUMPS WORK DONE/SECOND = WEIGHT OF WATER DELIVERED PER SECOND * HEAD LIFTED = W * ( h s + h d ) = W * (h s + h d ) = m * g * ( h s + h d ) = m * g * (h s + h d ) = ρ * Q * g * ( h s + h d ) = ρ * Q * g * (h s + h d ) = ρgQ * ( h s + h d ) = ρgQ * (h s + h d ) = ρgALN * ( h s + h d ) / 60 = ρgALN * (h s + h d ) / 60

POWER REQUIRED TO DRIVE THE PUMP P = W.D. / SECOND = ρgALN * ( h s + h d ) / 60 P = W.D. / SECOND = ρgALN * (h s + h d ) / 60 P = ρgALN * ( h s + h d ) / kW P = ρgALN * (h s + h d ) / kW

DOUBLE ACTING RECIPROCATING PUMP IN CASE OF DOUBLE-ACTING PUMP, THE WATER IS ACTING ON BOTH SIDES OF THE PISTON AS SHOWN IN FIGURE. IN CASE OF DOUBLE-ACTING PUMP, THE WATER IS ACTING ON BOTH SIDES OF THE PISTON AS SHOWN IN FIGURE. THUS, WE REQUIRE TWO SUCTION PIPES AND TWO DELIVERY PIPES FOR DOUBLE-ACTING PUMP. THUS, WE REQUIRE TWO SUCTION PIPES AND TWO DELIVERY PIPES FOR DOUBLE-ACTING PUMP. WHEN THERE IS A SUCTION STROKE ON ONE SIDE OF THE PISTON, THERE IS AT THE SAME TIME A DELIVERY STROKE ON THE OTHER SIDE OF THE PISTON. WHEN THERE IS A SUCTION STROKE ON ONE SIDE OF THE PISTON, THERE IS AT THE SAME TIME A DELIVERY STROKE ON THE OTHER SIDE OF THE PISTON. THUS FOR ONE COMPLETE REVOLUTION OF THE CRANK THERE ARE TWO DELIVERY STROKES AND WATER IS DELIVERED TO THE PIPES BY THE PUMP DURING THESE TWO DELIVERY STROKES. THUS FOR ONE COMPLETE REVOLUTION OF THE CRANK THERE ARE TWO DELIVERY STROKES AND WATER IS DELIVERED TO THE PIPES BY THE PUMP DURING THESE TWO DELIVERY STROKES.

DISCHARGE THROUGH DOUBLE ACTING RECIPROCATING PUMP DISCHARGE = WATER DISCHARGE + WATER DISCHARGE IN FORWARD STROKE IN REVERSE STROKE IN FORWARD STROKE IN REVERSE STROKE = ΠD 2 L/4 + Π(D 2 – d 2 ) L/4 = ΠD 2 L/4 + Π(D 2 – d 2 ) L/4 = ΠD 2 L/4 + ΠD 2 L/4 - Π d 2 L/4 = ΠD 2 L/4 + ΠD 2 L/4 - Πd 2 L/4 = Π (2D 2 - d 2 ) L/4 m 3 / cycle = Π (2D 2 - d 2 ) L/4 m 3 /cycle = Π (2D 2 - d 2 ) L/4 * N/60 m 3 / second = Π (2D 2 - d 2 ) L/4 * N/60 m 3 /second Q = 2ALN/60 ( NEGLECTING d 2 ) Q = 2ALN/60 ( NEGLECTING d 2 )

WORK DONE BY DOUBLE ACTING RECIPROCATING PUMP WORK DONE/SECOND = WEIGHT OF WATER DELIVERED PER SECOND * HEAD LIFTED WORK DONE/SECOND = WEIGHT OF WATER DELIVERED PER SECOND * HEAD LIFTED = ρgQ * ( h s + h d ) = ρgQ * (h s + h d ) W.D./SECOND = 2ρgALN * ( h s + h d ) / 60 W.D./SECOND = 2ρgALN * (h s + h d ) / 60

POWER REQUIRED TO DRIVE THE DOUBLE ACTING RECIPROCATING PUMP P = W.D./SECOND P = W.D./SECOND = 2ρgALN * ( h s + h d ) / 60 = 2ρgALN * (h s + h d ) / 60 = 2ρgALN * ( h s + h d ) / kW = 2ρgALN * (h s + h d ) / kW

SLIP OF RECIPROCATING PUMP SLIP OF A PUMP IS DEFINED AS THE DIFFERENCE BETWEEN THE THEORETICAL DISCHARGE AND THE ACTUAL DISCHARGE OF THE PUMP. SLIP OF A PUMP IS DEFINED AS THE DIFFERENCE BETWEEN THE THEORETICAL DISCHARGE AND THE ACTUAL DISCHARGE OF THE PUMP. THE ACTUAL DISCHARGE OF A PUMP IS LESS THAN THE THEORETICAL DISCHARGE DUE TO LEAKAGE. THE ACTUAL DISCHARGE OF A PUMP IS LESS THAN THE THEORETICAL DISCHARGE DUE TO LEAKAGE. THE DIFFERENCE OF THE THEORETICAL DISCHARGE AND THE ACTUAL DISCHARGE IS KNOWN AS SLIP OF THE PUMP. THE DIFFERENCE OF THE THEORETICAL DISCHARGE AND THE ACTUAL DISCHARGE IS KNOWN AS SLIP OF THE PUMP.

SLIP = DISCHARGE BETWEEN THEORETICAL AND ACTUAL DISCHARGE = Q th - Q act = Q th - Q act = ΠD 2 L/4 - Q act = ΠD 2 L/4 - Q act PERCENTAGE OF SLIP = ( Q th - Q act / Q th ) * 100% PERCENTAGE OF SLIP = (Q th - Q act / Q th ) * 100% = ( 1 - Q act / Q th ) * 100% = ( 1 - Q act / Q th ) * 100% = ( 1 – C d ) * 100% = ( 1 – C d ) * 100% Where C d = Co – efficient of Discharge

NEGATIVE SLIP OF RECIPROCATING PUMP? SLIP IS USUALLY POSITIVE BUT IN RECIPROCATING PUMPS IT IS POSSIBLE TO HAVE NEGATIVE SLIP, THIS IS POSSIBLE WHEN THE SUCTION PIPE IS LONG, DELIVERY HEAD IS LOW AND PUMP IS RUNNING AT HIGH SPEEDS. SLIP IS USUALLY POSITIVE BUT IN RECIPROCATING PUMPS IT IS POSSIBLE TO HAVE NEGATIVE SLIP, THIS IS POSSIBLE WHEN THE SUCTION PIPE IS LONG, DELIVERY HEAD IS LOW AND PUMP IS RUNNING AT HIGH SPEEDS. WHEN SUCTION VALVE REMAIN OPEN DURING DELIVERY STROKE OF PISTON SOME QUANTITY OF WATER DIRECTLY GOES FROM SUCTION SIDE TO DELIVERY SIDE. WHEN SUCTION VALVE REMAIN OPEN DURING DELIVERY STROKE OF PISTON SOME QUANTITY OF WATER DIRECTLY GOES FROM SUCTION SIDE TO DELIVERY SIDE.

VARIATION OF VELOCITY AND ACCELERATION IN THE SUCTION AND DELIVERY PIPES DUE TO ACCELERATION OF THE PISTON WHEN CRANK STARTS ROTATING, THE PISTON MOVES FORWARDS AND BACKWARDS IN THE CYLINDER.AT THE EXTREME LEFT POSITION AND RIGHT POSITION OF THE PISTON IN THE CYLINDER, THE VELOCITY OF THE PISTON IS ZERO. WHEN CRANK STARTS ROTATING, THE PISTON MOVES FORWARDS AND BACKWARDS IN THE CYLINDER.AT THE EXTREME LEFT POSITION AND RIGHT POSITION OF THE PISTON IN THE CYLINDER, THE VELOCITY OF THE PISTON IS ZERO. THE VELOCITY OF THE PISTON IS MAXIMUM AT THE CENTRE OF THE CYLINDER, THIS MEANS THAT AT THE START OF A STROKE (MAY BE SUCTION OR DELIVERY STROKE), THE VELOCITY OF THE PISTON IS ZERO AND THIS VELOCITY BECOMES MAXIMUM AT THE CENTRE OF EACH STROKE AND AGAIN BECOMES ZERO AT THE END OF EACH STROKE. THE VELOCITY OF THE PISTON IS MAXIMUM AT THE CENTRE OF THE CYLINDER, THIS MEANS THAT AT THE START OF A STROKE (MAY BE SUCTION OR DELIVERY STROKE), THE VELOCITY OF THE PISTON IS ZERO AND THIS VELOCITY BECOMES MAXIMUM AT THE CENTRE OF EACH STROKE AND AGAIN BECOMES ZERO AT THE END OF EACH STROKE. THUS AT THE BEGINNING OF EACH STROKE, THE PISTON WILL BE HAVING AN ACCELERATION AND AT THE END OF EACH STROKE, THE PISTON WILL BE HAVING A RETARDATION. THUS AT THE BEGINNING OF EACH STROKE, THE PISTON WILL BE HAVING AN ACCELERATION AND AT THE END OF EACH STROKE, THE PISTON WILL BE HAVING A RETARDATION. THE WATER IN THE CYLINDER IS IN CONTACT WITH THE PISTON AND HENCE THE WATER, FLOWING FROM THE SUCTION PIPE OR TO THE DELIVERY PIPE WILL HAVE AN ACCELERATION AT THE BEGINNING OF EACH STROKE AND A RETARDATION AT THE END OF EACH STROKE. THE WATER IN THE CYLINDER IS IN CONTACT WITH THE PISTON AND HENCE THE WATER, FLOWING FROM THE SUCTION PIPE OR TO THE DELIVERY PIPE WILL HAVE AN ACCELERATION AT THE BEGINNING OF EACH STROKE AND A RETARDATION AT THE END OF EACH STROKE. THIS MEANS THE VELOCITY OF FLOW OF WATER IN THE SUCTION AND DELIVERY PIPE WILL NOT BE UNIFORM. HENCE, AN ACCELERATIVE OR RETARDING HEAD WILL BE ACTING ON THE WATER FLOWING THROUGH THE SUCTION OR DELIVERY PIPE. THIS MEANS THE VELOCITY OF FLOW OF WATER IN THE SUCTION AND DELIVERY PIPE WILL NOT BE UNIFORM. HENCE, AN ACCELERATIVE OR RETARDING HEAD WILL BE ACTING ON THE WATER FLOWING THROUGH THE SUCTION OR DELIVERY PIPE. THIS ACCELERATIVE OR RETARDING HEAD WILL CHANGE THE PRESSURE INSIDE THE CYLINDER. THIS ACCELERATIVE OR RETARDING HEAD WILL CHANGE THE PRESSURE INSIDE THE CYLINDER.

IF THE RATIO OF LENGTH OF CONNECTING ROD TO THE RADIUS OF CRANK (I.E., L/R) IS VERY LARGE, THEN THE MOTION OF THE PISTON CAN BE ASSUMED AS SIMPLE HARMONIC IN NATURE. FIGURE SHOWS THE CYLINDER OF A RECIPROCATING SINGLE-ACTING PUMP, FITTED WITH A PISTON WHICH IS CONNECTED TO THE CRANK. LET THE CRANK IS ROTATING AT A CONSTANT ANGULAR SPEED. IF THE RATIO OF LENGTH OF CONNECTING ROD TO THE RADIUS OF CRANK (I.E., L/R) IS VERY LARGE, THEN THE MOTION OF THE PISTON CAN BE ASSUMED AS SIMPLE HARMONIC IN NATURE. FIGURE SHOWS THE CYLINDER OF A RECIPROCATING SINGLE-ACTING PUMP, FITTED WITH A PISTON WHICH IS CONNECTED TO THE CRANK. LET THE CRANK IS ROTATING AT A CONSTANT ANGULAR SPEED. LET, LET, ω = Angular speed of the crank in rad/sec ω = Angular speed of the crank in rad/sec A= Area of the cylinder A= Area of the cylinder a = Area of the pipe a = Area of the pipe l = Length of the pipe l = Length of the pipe r = radius of the crank r = radius of the crank

IN THE BEGINNING, THE CRANK IS AT A AND THE PISTON IN THE CYLINDER IS AT A POSITION SHOWN BY DOTTED LINES. IN THE BEGINNING, THE CRANK IS AT A AND THE PISTON IN THE CYLINDER IS AT A POSITION SHOWN BY DOTTED LINES. THE CRANK IS ROTATING WITH AN ANGULAR VELOCITY ‘ ω’ AND LET IN TIME ‘t’ SECONDS, THE CRANK TURNS THROUGH AN ANGLE ‘θ’ FROM A. THE CRANK IS ROTATING WITH AN ANGULAR VELOCITY ‘ω’ AND LET IN TIME ‘t’ SECONDS, THE CRANK TURNS THROUGH AN ANGLE ‘θ’ FROM A. THE DISPLACEMENT OF PISTON IN TIME ‘t’ IS ‘x’ AS SHOWN IN FIGURE. THE DISPLACEMENT OF PISTON IN TIME ‘t’ IS ‘x’ AS SHOWN IN FIGURE.

NOW, θ = ANGLE TURNED BY CRANK IN RADIANS IN TIME ‘t’ = ωt = ωt THE DISTANCE x TRAVELLED BY THE PISTON IS GIVEN AS, x = DISTANCE AF = AO – FO x = DISTANCE AF = AO – FO = r – r cosθ = r – r cosθ = r – r cos(ωt) = r – r cos(ωt) THE VELOCITY OF THE PISTON IS OBTAINED BY DIFFERENTIATING THE ABOVE EQUATION W.R.T. ‘t’ VELOCITY OF PISTON V = dx/dt = d[r – r cos(ωt)]/dt VELOCITY OF PISTON V = dx/dt = d[r – r cos(ωt)]/dt = 0 – r[-sin(ωt)] * ω = 0 – r[-sin(ωt)] * ω = ωr sin ωt = ωr sin ωt

NOW FROM CONTINUITY EQUATION, THE VOLUME OF WATER FLOWING INTO CYLINDER PER SECOND IS EQUAL TO THE VOLUME OF WATER FLOWING FROM THE PIPE PER SECOND. NOW FROM CONTINUITY EQUATION, THE VOLUME OF WATER FLOWING INTO CYLINDER PER SECOND IS EQUAL TO THE VOLUME OF WATER FLOWING FROM THE PIPE PER SECOND. VELOCITY OF * AREA OF = VELOCITY OF * AREA OF VELOCITY OF * AREA OF = VELOCITY OF * AREA OF WATER IN CYLINDER CYLINDER WATER IN PIPE PIPE WATER IN CYLINDER CYLINDER WATER IN PIPE PIPE V * A= v * a V * A= v * a WHERE v = VELOCITY OF WATER IN PIPE v = V * A / a = (A/a) * V = (A/a) * ωr sin ωt v = V * A / a = (A/a) * V = (A/a) * ωr sin ωt

 THE ACCELERATION OF WATER IN PIPE IS OBTAINED BY DIFFERENTIATING ABOVE EQUATION WITH RESPECT TO ‘ t ’.  THE ACCELERATION OF WATER IN PIPE IS OBTAINED BY DIFFERENTIATING ABOVE EQUATION WITH RESPECT TO ‘t’.  ACCELERATION OF WATER IN PIPE = dv/dt = d[ (A/a) * ωr sin ωt ] = (A/a) * ω 2 r cos ωt  MASS OF WATER IN PIPE = ρ * [AREA OF PIPE * LENGTH OF PIPE] = ρ * [a * l] = ρal  FORCE REQUIRED TO = MASS OF * ACCELERATION OF  ACCELERATE THE WATER IN PIPE WATER IN PIPE WATER IN PIPE = ρal * (A/a) * ω 2 r cos ωt = ρal * (A/a) * ω 2 r cos ωt  PRESSURE = FORCE REQUIRED TO ACCELERATE THE WATER / AREA OF PIPE = [ρal * (A/a) * ω 2 r cos ωt] / ρg = (l/g) * (A/a) * ω 2 r cos ωt = [ρal * (A/a) * ω 2 r cos ωt] / ρg = (l/g) * (A/a) * ω 2 r cos ωt  THE PRESSURE HEAD DUE TO ACCELERATION IN THE SUCTION AND DELIVERY PIPE IS OBTAINED FROM ABOVE EQUATION BY USING SUBSCRIPTS ‘s’ AND ‘d’, h as = (l s /g) * (A/a s ) * ω 2 r cos ωt h as = (l s /g) * (A/a s ) * ω 2 r cos ωt h ad = (l d /g) * (A/a d ) * ω 2 r cos ωt h ad = (l d /g) * (A/a d ) * ω 2 r cos ωt

INDICATOR DIAGRAM THE INDICATOR DIAGRAM FOR A RECIPROCATING PUMP IS DEFINED AS THE GRAPH BETWEEN THE PRESSURE HEAD IN THE CYLINDER AND THE DISTANCE TRAVELLED BY PISTON FROM INNER DEAD CENTRE FOR ONE COMPLETE REVOLUTION OF THE CRANK. THE INDICATOR DIAGRAM FOR A RECIPROCATING PUMP IS DEFINED AS THE GRAPH BETWEEN THE PRESSURE HEAD IN THE CYLINDER AND THE DISTANCE TRAVELLED BY PISTON FROM INNER DEAD CENTRE FOR ONE COMPLETE REVOLUTION OF THE CRANK. AS THE MAXIMUM DISTANCE TRAVELLED BY THE PISTON IS EQUAL TO THE STROKE LENGTH AND HENCE THE INDICATOR DIAGRAM IS A GRAPH BETWEEN PRESSURE HEAD AND STROKE LENGTH OF THE PISTON FOR ONE COMPLETE REVOLUTION. AS THE MAXIMUM DISTANCE TRAVELLED BY THE PISTON IS EQUAL TO THE STROKE LENGTH AND HENCE THE INDICATOR DIAGRAM IS A GRAPH BETWEEN PRESSURE HEAD AND STROKE LENGTH OF THE PISTON FOR ONE COMPLETE REVOLUTION. THE PRESSURE HEAD IS TAKEN AS ORDINATE AND STROKE LENGTH AS ABSCISSA. THE PRESSURE HEAD IS TAKEN AS ORDINATE AND STROKE LENGTH AS ABSCISSA.

IDEAL INDICATOR DIAGRAM THE GRAPH BETWEEN PRESSURE HEAD IN THE CYLINDER AND STROKE LENGTH OF THE PISTON FOR ONE COMPLETE REVOLUTION OF THE CRANK UNDER IDEAL CONDITIONS IS KNOWN AS IDEAL INDICATOR DIAGRAM. THE GRAPH BETWEEN PRESSURE HEAD IN THE CYLINDER AND STROKE LENGTH OF THE PISTON FOR ONE COMPLETE REVOLUTION OF THE CRANK UNDER IDEAL CONDITIONS IS KNOWN AS IDEAL INDICATOR DIAGRAM. FIGURE SHOWS THE IDEAL INDICATOR DIAGRAM, IN WHICH LINE ‘EF’ REPRESENTS THE ATMOSPHERIC PRESSURE HEAD EQUAL TO 10.3 M OF WATER. FIGURE SHOWS THE IDEAL INDICATOR DIAGRAM, IN WHICH LINE ‘EF’ REPRESENTS THE ATMOSPHERIC PRESSURE HEAD EQUAL TO 10.3 M OF WATER.

LET, LET, H atm = ATMOSPHERIC PRESSURE HEAD = 10.3 m OF WATER H atm = ATMOSPHERIC PRESSURE HEAD = 10.3 m OF WATER L = LENGTH OF THE STROKE L = LENGTH OF THE STROKE h s = SUCTION HEAD h s = SUCTION HEAD h d = DELIVERY HEAD h d = DELIVERY HEAD

DURING SUCTION STROKE, THE PRESSURE HEAD IN THE CYLINDER IS CONSTANT AND EQUAL TO SUCTION HEAD( h s ), WHICH IS BELOW THE ATMOSPHERIC PRESSURE (H atm ) HEAD BY A HEIGHT OF H. DURING SUCTION STROKE, THE PRESSURE HEAD IN THE CYLINDER IS CONSTANT AND EQUAL TO SUCTION HEAD(h s ), WHICH IS BELOW THE ATMOSPHERIC PRESSURE (H atm ) HEAD BY A HEIGHT OF H. THE PRESSURE HEAD DURING SUCTION STROKE IS REPRESENTED BY A HORIZONTAL LINE AB WHICH IS BELOW THE LINE EF BY A HEIGHT OF ‘ h s ’. THE PRESSURE HEAD DURING SUCTION STROKE IS REPRESENTED BY A HORIZONTAL LINE AB WHICH IS BELOW THE LINE EF BY A HEIGHT OF ‘h s ’. DURING DELIVERY STROKE, THE PRESSURE HEAD IN THE CYLINDER IS CONSTANT AND EQUAL TO DELIVERY HEAD ( h d ) WHICH IS ABOVE THE ATMOSPHERIC HEAD BY A HEIGHT OF ( h d ). DURING DELIVERY STROKE, THE PRESSURE HEAD IN THE CYLINDER IS CONSTANT AND EQUAL TO DELIVERY HEAD (h d ) WHICH IS ABOVE THE ATMOSPHERIC HEAD BY A HEIGHT OF (h d ). THUS, THE PRESSURE HEAD DURING DELIVERY STROKE IS REPRESENTED BY A HORIZONTAL LINE CD WHICH IS ABOVE THE LINE EF BY A HEIGHT OF h d. THUS, THE PRESSURE HEAD DURING DELIVERY STROKE IS REPRESENTED BY A HORIZONTAL LINE CD WHICH IS ABOVE THE LINE EF BY A HEIGHT OF h d. THUS, FOR ONE COMPLETE REVOLUTION OF THE CRANK, THE PRESSURE HEAD IN THE CYLINDER IS REPRESENTED BY THE DIAGRAM A-B-C-D-A. THUS, FOR ONE COMPLETE REVOLUTION OF THE CRANK, THE PRESSURE HEAD IN THE CYLINDER IS REPRESENTED BY THE DIAGRAM A-B-C-D-A. THIS DIAGRAM IS KNOWN AS IDEAL INDICATOR DIAGRAM. THIS DIAGRAM IS KNOWN AS IDEAL INDICATOR DIAGRAM.

W.D. / SECOND = ρgALN * ( h s + h d ) / 60 W.D. / SECOND = ρgALN * (h s + h d ) / 60 = K * L ( h s + h d ) = K * L (h s + h d ) α L ( h s + h d ) WHERE K = ρgAN/60 = CONSTANT α L (h s + h d ) WHERE K = ρgAN/60 = CONSTANT = AB * BC = AB * (BF + FC) = L ( h s + h d ) = AB * BC = AB * (BF + FC) = L (h s + h d ) THEREFORE, WORK DONE BY PUMP α AREA OF INDICATOR DIAGRAM