Pump Tutorial. Pumping unit
Pumps- machines for creating a pressure flow of a liquid medium. When developing hydraulic systems and networks, the correct selection and use of pumps allows us to obtain the specified parameters for the movement of fluids in hydraulic systems. In this case, the designer needs to know design features of pumps, their properties and characteristics. In this section you can download for free and without registration books on centrifugal, vane, gear pumps and ventilators.
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Name:Pumps, fans, compressors: A textbook for thermal power engineering specialties at universities. |
| Cherkassky V. M. | |
| Description:Classifications, fundamentals of theory, characteristics, control methods, designs and operating issues of machines for supplying liquids and gases used in energy and other industries are considered. | |
| The year of publishing: 1984 | |
| Views: 36579 | Downloads: 6834 | |
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Name:Gear pumps for metal-cutting machines. |
| Rybkin E.A., Usov A.A. | |
| Description:The book contains an analysis of theoretical and experimental research methods of calculation and design of gear hydraulic pumps used in hydraulically powered metal-cutting machines. | |
| The year of publishing: 1960 | |
| Views: 35392 | Downloads: 893 | |
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Name:Pumps, fans and compressors. Study guide for colleges. | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Sherstyuk A.N. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Description:The book outlines the basics of the theory, calculation and operation of blade machines - pumps, fans and compressors. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| The year of publishing: 1972 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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Fittings, devices installed in branches |
General branch |
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1. Two-pipe heat exchanger (“pipe in pipe”) |
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2. Normal valve |
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3. Sharp turn |
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4. Smooth turn |
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5. Pipe entrance |
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6. Exit from the pipe |
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7. Sudden expansion |
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8. Sudden contraction |
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9. Confused |
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10. Diffuser |
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11. Coil |
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12. Shell and tube heat exchanger |
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13. Flow Q, m3/h |
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14. Branch length l, m |
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15. Markings for installation of receiving tanks, m |
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16. Free pressure at consumption points, H, m |
Characteristics of local resistances
Two-pipe heat exchanger (“pipe in pipe”): branch 3, length of heat exchange sections - 1.8 m, number of sections - 4.
Flip flop:
branch 1, angle 90º,
branch 1, angle 90º,
branch 2, angle 90º,
branch 3, angle 90º,
branch 3, angle 90º,
branch 3, angle 90º,
branch 3, angle 90º,
branch 3, angle 90º,
branch 3, angle 90º,
branch 3, angle 90º,
branch 3, angle 90º.
Pipe entrance:
common branch, entry angle 0°,
common branch, entry angle 0°,
branch 1, entry angle 0°,
branch 3, entry angle 0°.
Exit from the pipe:
common branch, exit angle 0°,
branch 1, exit angle 0º,
branch 2, exit angle 0º,
branch 3, exit angle 0º.
Sudden expansion:
common branch, expansion tank diameter dр = 0.6 m.
Sudden contraction:
branch 2, expansion tank diameter dр = 0.6 m.
Diffuser:
branch 2, opening angle α = 60º.
4. Calculation of hydraulic characteristics of the circuit
Calculation of the hydraulic parameters of the circuit is necessary to determine the energy costs for moving fluid and selecting a standard hydraulic machine (pump).
1 Calculation of pipeline diameters
The given technological scheme contains containers located at various elevations, a centrifugal pump and a complex branched pipeline with shut-off and control valves installed on it and including a number of local resistances. It is advisable to start the calculation by determining the diameters of the pipeline using the formula:
di = √ 4Qi /(πw) , (1)
where Qi is the medium flow rate for each branch, m3/s;
wi - fluid speed, m/s.
To find the flow rate of the common branch Q0, m3/h, use the following formula:
where Qi is the flow rate of the corresponding branch, m3/h.
Q0 = Q1 + Q2 + Q3 = 100 + 200 + 50 = 350 m3/h.
To carry out calculations, the flow rate Qi is converted from m3/h to m3/s:
Q0 = 350 m3/h = 350/3600 = 0.097 m3/s,
Q1 = 100 m3/h = 100/3600 = 0.028 m3/s,
Q2 = 200 m3/h = 200/3600 = 0.056 m3/s,
Q3 = 50 m3/h = 50/3600 = 0.014 m3/s.
In practice, for media pumped by pumps, it is recommended to take an economic speed value of ≈ 1.5 m/s.
The diameters of pipelines along branches are calculated using formula (1):
d1= (4 0.028)/(π 1.5) = 0.154 m = 154 mm,
d2= (4 0.056)/(π 1.5) = 0.218 m = 218 mm,
d3= (4 0.014)/(π 1.5) = 0.109 m = 109 mm,
d0= (4 0.097)/(π 1.5) = 0.287 m = 287 mm.
Based on the calculated values of di, the nearest standard pipe diameter dсti is selected according to GOST 8732 - 78 for seamless hot-rolled steel pipes.
For the first branch, a seamless hot-rolled steel pipe with an outer diameter of 168 mm, with a wall thickness of 5 mm, made of steel 10, manufactured according to group B of GOST 8731 - 74:
Pipe 168x 5 GOST 8732 - 78
B10 GOST 8731 - 74
For the second branch, a seamless hot-rolled steel pipe with an outer diameter of 245 mm, with a wall thickness of 7 mm, made of steel 10, manufactured according to group B of GOST 8731 - 74:
Pipe 245x 7 GOST 8732 - 78
B10 GOST 8731 - 74
For the third branch, a seamless hot-rolled steel pipe with an outer diameter of 121 mm, with a wall thickness of 4 mm, made of steel 10, manufactured according to group B of GOST 8731 - 74:
Pipe 121x5 GOST 8732 - 78
B10 GOST 8731 - 74
For the general branch, a seamless hot-rolled steel pipe with an outer diameter of 299 mm, with a wall thickness of 8 mm, made of steel 10, manufactured according to group B of GOST 8731 - 74:
Pipe 299x 8 GOST 8732 - 78
B10 GOST 8731 - 74.
Calculations of internal diameters di, mm, are made according to the formula:
di = Di - 2 b, (3)
where Di is the outer diameter of the corresponding pipeline, m;
b - wall thickness, m.
d0 = 299-2 8 = 283 mm = 0.283 m,
d1 = 168-2 5 = 158 mm = 0.158 m,
d2 = 245-2 7 = 231 mm = 0.231 m,
d3 = 121-2 4 = 113 mm = 0.113 m.
Since the internal diameters of standard pipes differ from the values calculated using formula (1), it is necessary to clarify the fluid flow speed w, m/s, using the formula:
wi = 4·Qi/(π·d2сti), (4)
where dсi is the calculated standard internal diameter for each pipeline branch, m;
Qi is the flow rate of the medium for each branch, m3/s.
w0 = (4 · 0.097)/(π · (0.283)2) = 1.54 m/s,
w1 = (4 · 0.028)/(π · (0.158)2) = 1.43 m/s,
w2 = (4 · 0.056)/(π · (0.231)2) = 1.34 m/s,
w3 = (4 · 0.014)/(π · (0.113)2) = 1.4 m/s.
2 Pressure loss in the pipeline
Head losses are divided into friction losses along the length and local losses. Friction losses Δhi, m, occur in straight pipes of constant cross-section and arise proportionally to the length of the pipe. They are determined by the formula:
Δhtrain i = λi · (li/di) · (wi2/2g) (5)
where λi is the dimensionless friction loss coefficient along the length (Darcy coefficient);
g - free fall acceleration, m/s2.
The Darcy coefficient λi is determined by the universal formula of A. D. Altshul:
λi = 0.11 (Δi /di + 68/Rei)0.25, (6)
where Δi is the absolute equivalent roughness, depending on the condition of the pipes;
Rei - Reynolds number.
We select the absolute roughness of pipes as 0.2 mm for steel pipes that have been in use with slight corrosion.
The Reynolds number Re is calculated using the following formula:
Rei = (wi · di · ρ)/μ = (wi · di)/ν, (7)
where wi is the fluid flow speed through the corresponding pipeline, m/s;
di is the internal diameter of the corresponding pipeline, m;
ρ - liquid density, kg/m3;
μ - dynamic viscosity, Pa s,
ν - kinematic viscosity, m2/s.
Local losses are caused by local hydraulic resistance, that is, local changes in the shape and size of the channel, causing flow deformation. These include: sharp turns of the pipe (elbow), smooth turns, inlets and outlets of pipelines, sharp (sudden) expansions and contractions, confusers, diffusers, coils, heat exchangers, valves, etc.
Local pressure loss Δhм.с. i, m, are determined by the Weisbach formula as follows:
Δhм.с.i = ∑ξi (wi2/2g), (8)
where ξi is the resistance coefficient for various types of local resistance.
After calculating the components of pressure losses, the total losses Δhi, m, are determined by branches according to the formula:
Δhi = Δhtrain i + Δhm.s. i, (9)
where Δhtrain i - friction losses, m;
Δhм.с. i - losses due to local resistance, m.
Nfull i = Δho + Δhi + Hi + zi, (10)
where Hi is the free pressure at points of consumption, m;
zi - marks for installation of receiving tanks, m.
3 Calculation of hydraulic resistance along the common branch
3.1 Head loss due to friction
For the general branch of the pipeline, the Reynolds number is determined by formula (7):
Reо = (1.54 · 0.283)/(1.01 · 10-6) = 431505.
λо = 0.11 · (0.0002/0.283 + 68/431505)0.25 = 0.019.
Δhtrain = 0.019 · (1.5/0.283) · (1.54)2/(2 · 9.81) = 0.012 m.
pump hydraulic pipeline pressure
4.3.2 Calculation of losses due to local resistance
Two entrances to a pipe with sharp edges: ξin = 0.5.
Two valves are normal when fully open, with an internal diameter (taken as nominal diameter) of 283 mm. Since GOST does not indicate this conditional diameter and, accordingly, the valve resistance coefficient ξvent, interpolation is used to find it. In this case, ξvent = 5.234.
Pipe outlet: ξout = 1.
Sudden expansion.
The resistance coefficient is selected depending on the ratio of the cross-sectional areas of the expansion tank and pipeline and the Reynolds number.
The ratio of the found cross-sectional areas is found through the ratio of the squares of the corresponding diameters:
F0/Fр = (d0/dр)2 = (0.283/0.6)2 = 0.223.
With a Reynolds number of 431505 and an area ratio of 0.223, the drag coefficient
ξext = 0.65.
For the general branch, the total pressure loss due to local resistance Δhм.с.о, m, is calculated using formula (8):
Δhм.с.о = (2 · 0.5 + 2 · 5.234 + 1+ 0.65) · (1.54)2/(2 · 9.81) = 1.59 m.
Total losses Δho, m, in the common branch according to formula (9):
Δho = 0.012 + 1.59 = 1.602 m.
4 Calculation of hydraulic resistance for 1 branch
4.1 Head loss due to friction
For the first branch of the pipeline, the Reynolds number is determined by formula (7):
Re1 = (1.43 · 0.158)/(1.01 · 10-6) = 223704.
λ1 = 0.11 · (0.0002/0.158 + 68/223704)0.25 = 0.022.
Friction losses are calculated using formula (5):
Δhtrain1 = 0.022 · (4/0.158) · (1.43)2/(2 · 9.81) = 0.058 m.
4.2 Calculation of losses due to local resistance
Let us determine the resistance coefficients ξ for a number of types of local resistances.
2. Two sharp turns of the pipe (elbow) with a rotation angle of 90°: ξkol= 1.
3. Two normal valves when fully open, with an internal diameter (taken as nominal bore) of 158 mm. Since GOST does not indicate this conditional diameter and, accordingly, the valve resistance coefficient ξvent, interpolation is used to find it. In this case, ξvent = 4.453.
Pipe outlet: ξout = 1.
For the first branch, the total pressure loss due to local resistance Δhм.с.1, m, is calculated using formula (8):
Δhм.с.1 = (0.5 + 2 1 + 4.453+ 1) (1.43)2/(2 9.81) = 0.829 m.
We determine the total losses Δh1, m, in the first branch using formula (9):
Δh1 = 0.058 + 0.829 = 0.887 m.
We determine the total pressure Nfull i, m, required to supply liquid through the branch using formula (10):
Nfull 1 = 1.602 + 0.887 + 3 + 2 = 7.489 m.
5 Calculation of hydraulic resistance for 2 branches
5.1 Head loss due to friction
For the second branch of the pipeline, the Reynolds number is determined by formula (7):
Re2 = (1.34 · 0.231)/(1.01 · 10-6) = 306475.
λ2 = 0.11 · (0.0002/0.231 + 68/306475)0.25 = 0.02.
Friction losses are calculated using formula (5):
Δhtrain 2 = 0.02 · (8/0.231) · (1.34)2/(2 · 9.81) = 0.063 m.
5.2 Calculation of losses due to local resistance
Let us determine the resistance coefficients ξ for a number of types of local resistances.
Sudden contraction.
The resistance coefficient is selected depending on the ratio of the cross-sectional areas of the expansion tank and pipeline, as well as the Reynolds number.
F2/Fр = (d2/dр)2 = (0.0231/0.6)2 = 0.148; Re = 306475>10000: ξin narrowing = 0.45.
The valve is normal when fully open, with an internal diameter (taken as nominal bore) of 231 mm. Since GOST does not indicate this conditional diameter and, accordingly, the valve resistance coefficient ξvent, interpolation is used to find it. In this case, ξvent = 4.938.
3. Sharp turn of the pipe (elbow) with a rotation angle of 90°: ξkol = 1.
Diffuser.
The diffuser resistance coefficient ξdiff is calculated using the following formula:
ξdif = λi/(8 sin(α/2)) [(F2′/F2)2 - 1]/ (F2′/F2)2 + sinα [(F2′/F2) - 1]/ (F2 ′/F2), (11)
where F2 is the cross-sectional area of the pipeline before expansion, m2;
F2′ - cross-sectional area of the pipeline after expansion, m2;
α - diffuser opening angle;
λi - Darcy coefficient. Calculated for a pipeline section with a smaller cross-section F2 (before expansion).
We accept the diameter of the pipeline after expansion independently, selecting the required standard diameter from GOST.
We accept a seamless hot-rolled steel pipe with an outer diameter of 273 mm, with a wall thickness of 7 mm, from steel 10, manufactured according to group B of GOST 8731-74:
Pipe 237x7 GOST 8732-78
B10 GOST 8731-74.
d2′ = 273 - 2 7 = 259 mm = 0.259 m.
Replacing the value F1/F0 equal to it (d1/d0)2, we get:
ξdif = λ2 /(8 sin(α/2)) [ (d2′ /d2)4 - 1]/(d2′ /d2)4 + sin(α) [(d2′ /d2)2 -1 ]/(d2′ /d2)2 = 0.02/(8 sin(60°/2)) ((0.259/0.231)4 - 1)/(0.2590/0.231)4 + sin(60° )·((0.259/0.231)2 - 1)/ 0.259/0.231)2 = 0.18.
5. Output from the pipe: ξout = 1.
For the second branch, the total pressure loss due to local resistance Δhм.с. 2 are calculated using formula (8):
Δhм.с.2 = (0.45 + 4.938 + 1 + 0.18 + 1) · (1.34)2/(2 · 9.81) = 0.69 m.
The total losses Δh2, m, in the second branch are determined according to formula (9):
Nfull2 = 1.602 + 0.756 + 4+ 3 = 9.358 m.
6 Calculation of hydraulic resistance for 3 branches
6.1 Head loss due to friction
For the third branch of the pipeline, the Reynolds number is determined by formula (7):
Re3 = (1.4 · 0.113)/(1.01 · 10-6) = 156634.
λ3 = 0.11 · (0.0002/0.113 + 68/156634)0.25 = 0.024.
Let us determine the Reynolds number at ν = 1.31·10-6 m2/s using formula (7):
Ret = (1.4 0.113)/(1.31 10-6) = 120763.
λt = 0.11 · (0.0002/0.113 + 68/120763)0.25 = 0.0242.
Friction losses are calculated using formula (5):
Δhtrain3 = 0.024 · (10/0.113) · (1.4)2/(2 · 9.81) + 0.0242 · (1/0.113) · (1.4)2/(2 · 9.81) = 0.234 m.
6.2 Calculation of losses due to local resistance
Let us determine the resistance coefficients ξ for a number of types of local resistances.
Entrance to a pipe with sharp edges: ξin = 0.5.
2. Eight sharp turns of the pipe (elbows) with a rotation angle of 90°: ξkol = 1.
2. The valve is normal when fully open, with an internal diameter (taken as nominal bore) of 113 mm. Since GOST does not indicate this conditional diameter and, accordingly, the valve resistance coefficient ξvent, interpolation is used to find it. In this case, ξvent = 4.243.
A “pipe-in-pipe” heat exchanger with liquid flowing through an internal pipe.
Resistance is calculated using the formula:
Δhт = λт · (Ltr/dtr) · (w2tr/2g) · m1 + ξ1 · (w2tr/2g) · m2, (12)
where the first term is friction losses,
where m1 is the number of direct heat exchange sections; second - losses due to local resistance due to smooth turns, ξ1 - resistance coefficient smooth turn 180°; m2 - number of turns.
The resistance coefficient for a smooth 180° turn ξ1 is calculated by the formula:
ξ1 = ξ1′ α°/90°, (13)
where ξ1′- is taken depending on the ratio d3/2 R0 = 0.6: ξ1′ = 0.44.
ξ1 = 0.44 180°/90°=0.88.
We calculate the resistance of the heat exchanger using formula (12):
Δhт = 0.0242 · (1.8/0.113) · ((1.4)2/(2 · 9.81)) · 4 + 0.88 · ((1.4)2/(2 · 9, 81)) 3 = 0.418 m.
Pipe outlet: ξout = 1.
For the third branch, the total pressure loss due to local resistance Δhм.с.3 is calculated using formula (8):
Δhм.с.3 = (0.5 + 8 1+ 4.243) (1.4)2/(2 9.81) + 0.418 = 1.691 m.
The total losses Δh3, m, in the third branch are determined according to formula (9):
Nfull3 = 1.602 + 1.925 + 2 + 6 = 11.53 m.
4.7 Selecting a standard hydraulic machine
To select a centrifugal hydraulic machine (pump), it is necessary to establish the performance and pressure that it must provide.
To ensure specified liquid flow rates to all points of consumption, the pump performance must meet the condition
Qus = ∑ Qi , (14)
us = max (Nfull). (15)
Total productivity Q = 350 m3/h.
To comply with condition (15), it is necessary to select the area with the highest required pressure by comparing various options, based on the mandatory supply of the necessary flow rates and the required free pressures. The area with the highest required pressure is taken as the base one, and it will determine the pump pressure. The pressure required to select a pump is Hpump = Hmax = Hfull 3 = 11.53 m.
The remaining branches can be converted to smaller pipe diameters in order to optimize the pipeline in terms of its cost, based on the condition:
Nfull1 = Nfull2 =...= Nfull. (16)
In most cases, such recalculation is not carried out, and the fulfillment of condition (16) is achieved by creating additional local resistance at the input of the corresponding section, as a rule, by installing a control valve.
When choosing a pump, it is also taken into account that the required operating modes of the pump (flow and pressure) must be within the operating range of its characteristics.
Based on the calculation of the hydraulic parameters of the technological scheme, the selected pump according to these characteristics is a horizontal cantilever pump with a support on the body of the grade K 200 - 150 - 250. Using the graphic characteristics, we clarify the correctness of the choice of the pump.
For this pump:
The K 200 - 150 - 250 pump provides a flow of 315 m3/h, its productivity will be slightly higher - 20 m. A solution to this problem can be the use of the regulating effect of shut-off valves (valves installed on the pipeline) or the installation of additional (reserve) tanks, which due to the additional pressure of the liquid column, they will smooth out or completely eliminate the discrepancy between the required pressure and the pressure provided by the pump. Cantilever pumps K Purpose Centrifugal cantilever single-stage pumps of type K with a horizontal axial supply of liquid to the impeller are designed for pumping clean water (except sea water) with pH = 6-9, temperature from 0 to 85 ° C in stationary conditions (using a double gland seal with supply to it water up to 105°C) and other liquids similar to water in density, viscosity and chemical activity, containing solid inclusions by volume of no more than 0.1% and up to 0.2 mm in size. Used in water utility systems, for irrigation, irrigation and drainage. Description The cantilever pump is, from a hydraulic point of view, a characteristic type of centrifugal pump, the working element of which is a centrifugal wheel. A centrifugal wheel consists of two disks, between which, connecting them into a single structure, there are blades that are smoothly curved in the direction opposite to the direction of rotation of the wheel. When the wheel rotates, each particle of liquid located inside the wheel is subject to a centrifugal force, directly proportional to the distance of the particle from the center of the wheel and the square of the angular speed of rotation of the wheel. Under the influence of this force, the liquid is ejected into the pressure pipeline from the impeller, as a result of which a vacuum is created in the center of the wheel, and increased pressure is created in its peripheral part. The movement of liquid through the suction pipeline occurs due to the pressure difference above the free surface of the liquid in the receiving tank and in the central region of the wheel, where there is a vacuum. In K-type pumps, torque is supplied from the electric motor shaft to the pump shaft through an elastic coupling. The design of the pump according to the seal assembly is determined by the water temperature and pressure at the pump inlet. The single gland seal is not supplied with barrier fluid. When the water temperature is above 85°C or when the absolute pressure at the inlet is below atmospheric, barrier water is supplied to the double gland seal at a pressure exceeding the liquid pressure before the seal by 0.5-1 kgf/cm2. The barrier fluid (water) is supplied to a dead end into the double gland seal. The normal amount of external water leakage is up to 3 l/h; liquid must leak through the seal to lubricate the sealing surface. The group of cantilever pumps includes centrifugal single-stage cast iron pumps with a one-way liquid supply to the impeller. The wheel of such a pump is located at the end of a shaft (console) fixed in the bearings of the pump housing or electric motor. For the correct operation of centrifugal pumps and their selection when creating various pumping installations and stations, it is necessary to know how the main parameters of pumps change in different conditions their work. It is important to have information about changes in pressure H, power consumption N and pump efficiency η when its supply Q changes. The selection of a pump for a given technological scheme is made from catalogs based on the calculation of the hydraulic parameters of the technological scheme. When choosing a pump, take into account that the required operating modes of the pump (flow and pressure) must be within the operating range of its characteristics. Bibliography 1. Bashta T. M. Hydraulics, hydraulic machines and hydraulic drives. M.: Mechanical Engineering, 1982. Shlipchenko Z. S. Pumps, compressors and fans. Kyiv, Technika, 1976. Educational and methodological instructions for implementation course work in the discipline “Pumps and Compressors” for students of the specialty 05/17: Dzerzhinsk, 1995. Selection of a pump for a given technological scheme for students of the specialty 17.05.: Dzerzhinsk, 1995. Designation Name Documentation Assembly drawing Ring sealing Working wheel
