Fluid Mechanics assignment 21248974 PDF

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The assignment is about pumps and piping network for an RO plant...

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Fluid Mechanics assignment By: Thato Mokemane Student number: 21248974 Date: 11 October 2018

Introduction The aim of the present research is to design and propose a piping and pump network to produce 0.0115740741 m3 / s from sea water. The pumps used have their own characteristics relative to the power required, the efficiency and the total pump head. Pump curves are therefore needed in combination with the total head curves to select appropriate pumping and pump network equipment for pumping water from the sea. (WASTE DISTRIBUTION NETWORKS, 2018)A pump is carefully chosen so that the effective functioning point is also close to efficiency.

1. The piping network overview The choice of the pumps and pipes is affected by the properties of the fluid to be pumped and the quantity of the fluid required. For sea water we shall assume that the temperature is between 293K and 298K. The properties of sea water under this conditions will be used as adapted from Seawater thermophysical properties library by Kishor G. Nayar in order to compute the calculations of Total head loss.

2. Head loss calculation and discussion Important information to take note of:      

𝑅𝑒 =

Steel pipes with well-rounded pipe inlets and pipe exit and the flow is fully developed Inner diameter of 1.2m. All the valves are fully open 4 × 90° smooth elbows are flanged The fluid is incompressible 2 × tee (line flow) branch is flanged

𝜌𝑉𝐷

Equation 1

𝜇

𝐿

𝐻𝐿 = (∑ 𝑓 𝐷 + ∑ 𝐾𝐿 ) 1

√𝑓

= −2.0𝑙𝑜𝑔10 (

𝜀⁄ 𝐷 3.7

+

𝑉2

Equation 2

2𝑔

2.51

𝑅𝑒√𝑓

)

Equation 3

Table 1: tabulated results of calculation of head loss from the ocean reservoir to the storage tank (Q)FLOW RATE(m3/s) dynamic viscosity(Pa.s) kinematic viscosity diameter velocity density Reynold's number(Re) Acceleration due to gravity SUM OF KL

HEAD LOSS(HL)

0.038580247 0.00108 0.00000105 1.2m 0.034112428m/s 1027kg/m3 11677.82114 9.81m/s2 2.95 0.000461847m

𝜺 𝜺/D length f

0.00015 0.000125 110m 0.02985849

Equation 2 was used for the calculation of total head loss. Firstly, the Reynold’s number had to be computed to find out if the flow was in the laminar or turbulent regime and the flow was found out to be turbulent because the Reynolds number ≥ 4000. Having calculated the Reynold’s number we could in turn calculated the friction factor using Colebrook equation 3. It should be noted that for 90° smooth bend elbows the loss coefficient is 0.3 as stated in fluid Mechanics 3rd Edition textbook by YUNUS A and John M. Cimbala. The loss coefficient of the pipe inlet and outlet used are adapted from the fluid Mechanics textbook. The pump head is computed using equation 4 below. 𝑃1

+𝛼 𝜌𝑔

𝑉2

2𝑔

+ 𝑍 + ℎ𝑝𝑢𝑚𝑝 =

𝑃2

𝜌𝑔

+ 𝛼2

𝑉22

2𝑔

+ 𝑍2 + 𝐻𝐿

Equation 4

Assumptions:    

P1 =P2 = Patm Velocity at the free surfaces can be neglected. V22 = V

α2 = 1.05 for fully developed turbulent flow

ℎ𝑝𝑢𝑚𝑝,𝑢 = 𝑍2 − 𝑍 + 𝛼2

2

𝑉2 + 𝐻𝐿 2𝑔

Equation 5

ℎ𝑝𝑢𝑚𝑝,𝑢 = 3 − 0 + 5.60047731 ∗ 10−6 + 0.000461847 = 3.000047167𝑚

𝑊𝑝𝑢𝑚𝑝 = ℎ𝑝𝑢𝑚𝑝,𝑢 × 𝑄 × 𝜌𝑔 ×

1

𝑛𝑝𝑢𝑚𝑝

Equation 6

𝑊𝑝𝑢𝑚𝑝,𝑢 = 349.8219 𝑊𝑎𝑡𝑡𝑠

NB: pump head for the pump used to increase pressure for the RO plant can be calculated in the same manner: Assumptions taken when performing calculations:     

The pipe inlet and outlets are well rounded Isolation valves(ball valves) are fully open 2× tee( line flow) are flanged Fluid is incompressible and fully developed The pipe outlet at the bottom of the storage tank, point 1 and the pipe exit to the RO- plant, point 2 are the two points taken as basis for the calculation of pump head. This makes the elevation equal to zero but the pressure is greater that the atmospheric pressure since pressure increases with depth.

The energy equation simplifies to:

ℎ𝑝𝑢𝑚𝑝,𝑢 =

𝑃2 −𝑃1 𝜌𝑔

+ 𝛼2

2

𝑉2 2𝑔

+ 𝐻𝐿

Equation 7

Table 2: tabulated results of calculation of head loss from the storage tank to the RO - plant 0.00015 𝜺 0.000125 𝜺/D 30m length 0.02985849 f

0.038580247 m3/s 0.00108 Pa.s 0.00000105 1.2m 0.034112428m/s 1027kg/m3 11677.82114

FLOW RATE (Q) dynamic viscosity kinematic viscosity diameter velocity density Reynold's number SUM OF KL

1.58

HEAD LOSS

0.000137982m ( Computed using equation 2)

ℎ𝑝𝑢𝑚𝑝,𝑢 =

𝑉2 (75 ∗ 105 ) − (101325 + 3𝜌𝑔) + 𝛼2 2 + 𝐻𝐿 2𝑔 𝜌𝑔 ℎ𝑝𝑢𝑚𝑝,𝑢 = 731.3692952𝑚 𝑊𝑝𝑢𝑚𝑝,𝑢 = 111.625 𝐾𝑊

3. Net positive suction Head calculations (NPSH)

𝑁𝑃𝑆𝐻 = (

𝑃𝐼𝑁𝐿𝐸𝑇 𝜌𝑔

+

𝑉2

2𝑔

𝑃

) − 𝜌𝑔𝑣

Equation 8

The vapour pressure of sea water at 20ºC used is adapted from the Seawater thermophysical properties library by Kishor G. Nayar. The steady state equation 4 is used to calculate the pressure at the inlet of the pump. Assumptions for pump used to deliver water to storage tank:   

The free surface velocity of the sea water is neglected. P1 = Patm For turbulent flow 𝛼2 = 1.05

Assumptions for pump used to increase pressure of water to the RO -plant:  

P1 = Patm + 𝜌𝑔ℎ For turbulent flow 𝛼2 = 1.05

𝑃𝑖𝑛𝑙𝑒𝑡 = (

𝑃1

− 𝛼2 𝜌𝑔

𝑉22

2𝑔

− 𝑍2 − 𝐻𝐿) ∗ 𝝆𝒈

Equation 9

Table 3: tabulated value of the NPSH of the pump to the storage tank and the pumps to the RO plant

65.054kPa Pressure INLET 2153.3pa Vapour Pressure acceleration due to gravity 9.81m/s2 1027kg/m3 density velocity 0.010233728m/s NPSHPUMP TO STORAGE TANK

6.243385526m

131549.61Pa Pressure INLET 2153.3pa Vapour Pressure acceleration due to gravity 9.81m/s2 1027kg/m3 density velocity 0.010233728m/s NPSHpumps to RO-PLANT

12.84353124m

4. Pump curves and discussion

Operating point Figure 1: PUMP CHARACTERISTIC CURVE (Bell & Gossett, 2018)

For pumping water from the sea to the storage tank, a 0.3429 m ID centrifugal pump Series 90 whose performance curve is shown in figure 1 is less heftier than the requirements. The NPSH

available tabulated in table 3 is larger than the NPSH required, (Cengel & Cimbala, 2014) in order to make sure that cavitation does not take place it is necessary for the NPSH available to be greater than the NPSH required. The pump head of 3.000047167m = 9.9426744324147 FEET is suitable for the pump conditions and the required flow rate. One pump is to be used to deliver water to the storage tank and is connected in parallel with a spare pump in case of malfunction. There are isolation valves fitted to allow the system isolation for repairs. The valves are spaced periodically as depicted in figure 3 so that small sections can be outof-the-way if there arises a problem requiring a shut-down of a pump. A check valve is also installed at the system’s high point to prevent back flow. Also it would be wise to install air relief valves at high points of the system to release air in order to maintain the required system flow.

Operation point

Figure 2:

pump curve for series pumps used to increase pressure at the RO (grundfos, 2018)

Figure 2 shows a pump performance curve of SP 125-15N centrifugal pump with the motor efficiency of 76.4%. The NSPH required is 6.52m, and in table 3 it is tabulated that the NSPH available is 12.84m which is larger than the NSPH required therefore cavitation will not take place. For the required flow rate of 38.5l/s the total head of the pump is 243.7m, so three pumps have to be connected in series to give a desired pump head of 731.3m. The operation point is observed in figure 2 to give a flow rate of 40.17l/s which is a bit larger than required, (Cengel & Cimbala, 2014) a valve or a damper can be installed in the line so that the flow rate can be decreased to the system requirements. There are isolation valves fitted to allow the system isolation for repairs. The valves are spaced periodically as depicted in figure 3 so that small sections can be out-of-the-way if there arises a problem requiring a shut-down of a pump. In cases of pump malfunctions, the pumps are connected to in parallel with another set of 3 of series pumps of the same type. The flow rate of water through the pumps is set to zero by the use of isolation valves.

S-3

S-2

Ø2

S-1

P-3

200m

10m

VV-1 V-5 V-14 V-9

P-1 V-8

E-4

V-1

3m

V-12 V-13

30m

Ø1.2m

104m

Equipment List Displayed Text E-2 E-4 E-5,E-9 P-1 V-1,V-5,V-8,V-9,V-12,V-13 S-1.S-2,S-3 VV-1 PP1 E-8 P-2 P-3

Description PUMPS STORAGE TANK RO -PLANT PIPE ISOLATION VALVES SIMPLE SUPPORT CHECK VALVE PUMP NET FOR FILTEFRING FRESH WATER PIPE PIPE TO SEA

E-9 E-5

P-2

E-2 PP1

E-8

-11

PP2

Material

MANUFACTURE series 90 centrifugal

STEEL

Figure 3: drawing design of the pipes, valves, tanks and pump network (drawn using Visio)

The issue pertaining to safety is dealt by with the use of a net at the pipe inlet in the sea to prevent aquatic life from entering the pipe line even though large fish may swing against the current produced. The pipes in sea have sacrificial anodes as prevention against extremely corrosive sea environment. The pipe line delivering water to the sea is 200m away from the pipe line that draws water from the sea to avoid the increase in salinity of the intake water. The pressure of water delivered to the sea is decreased by means of increasing the pipe line diameter and using supports to elevate the pipe so that the flow is against gravity, this means is much cheaper as no energy is required.

References (2018, OCTOBER 20). Retrieved from PUMPSTOP: http://webpages.uidaho.edu/larc380/lessonPumps/pumpCharts.htm Bell, & Gossett. (2018, october 22). Retrieved from http://www.researchairflo.com/wpcontent/uploads/2015/02/BG-Pumps-Series-90.pdf Cengel, Y. A., & Cimbala, J. M. (2014). Fluid Mechanics fundamentals and applications. New York: McGraw- Hill. grundfos. (2018, October 22). Retrieved from https://product-selection.grundfos.com/frontpage.html?qcid=451748341&sizeType=guided WASTE DISTRIBUTION NETWORKS. (2018, october 20 ). Retrieved from CE370: http://faculty.kfupm.edu.sa/CE/abukhari/Courses/CE370/Lectures/Water%20Distribution%2 0System.pdf...