4. System Design and Calculation

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					  4. System Design and Calculation
4.1 General
    In Hong Kong, plumbing design shall follow the requirements
    enforced by Water Supplies Department (WSD) and can make
    reference to the design guide published by institute. Details can
    make reference to:
•   “Hong Kong Waterworks Standard Requirements for Plumbing
    Installation in Buildings” - WSD
•   Waterworks Ordinance (Cap. 102)
•   Waterworks Regulations (Cap. 102A)
•   “Plumbing Engineering Services Design Guide” – The Institute of
    Plumbing (IOP)
•   “CIBSE Guides” – The Chartered Institution of Building Services
    Engineers


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  4. System Design and Calculation
4.2 Water Storage Capacity
•   In Hong Kong, the water storage capacity is governed by WSD.
    Potable Water
    Residential:
    First 10 Units,                        EACH 135L
    From 11th Unit and onward,             EACH 90L
    Commercial:
    Per Fitment,                           EACH 45L
    Flushing Water
    Per Fitment,                           EACH 45L
•   Storage capacity is the sum of sump tank and storage tank and the
    volume shall be in the ratio of 1 : 3 respectively.


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  4. System Design and Calculation
4.2 Simultaneous Demand
•   Simultaneous demand is widely adopted to determine the water flow
    rate for plumbing system design.
•   There is a few methods of determine the simultaneous demand but
    the mathematical model is originated from probability theory.
•   It is not mandatory for designer to adopt a single method for system
    design but due to convenience, method using Loading Unit to
    estimate the simultaneous demand is widely used in the field.
•   Two methods will be discussed in this section:
    - Binominal and Poisson Distribution Method.
    - Loading Unit Method.




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  4. System Design and Calculation
4.2 Simultaneous Demand
    Binominal and Poisson Distribution Method
•   The simultaneous demand can be estimated by:
    m = np + c [2np(1 – p)]0.5
    m = number of fittings subject to simultaneous use.
    n = total number of fittings connected
    p = t / T = usage ratio
    t = average time a demanding a fitting for each period of use.
    T = average time between occasions of use.
    c = coefficient representing an appropriate level of acceptability.
    [Choosing c = 1.8 will give a 98.9% acceptable service.]
•   The above expression for estimating simultaneous demand only
    applicable if all the fittings are of the same type.

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    4. System Design and Calculation
4.2 Simultaneous Demand
    Binominal and Poisson Distribution Method
•   Example
    System configuration:
     Appliance         No. of Fitting, n   Usage Ratio, p   Flow Rate, q (L/s)

     Wash Basin               30                0.2               0.15
     Sink                     20                0.4               0.30
•    Solution
     For Wash Basin
     m1 = 30  0.2 + 1.8  [2  30  0.2  (1 – 0.2)]0.5
        = 18.6 say 19
     Simultaneous demand of wash basin, q1 = 18.6  0.15 = 2.79L/s
     Equivalent number of sink subject to simultaneous use
                                                                            41
     m’1= 2.79 / 0.3 = 9.3 say 9
  4. System Design and Calculation
4.2 Simultaneous Demand
    Binominal and Poisson Distribution Method
•   Solution
    Equivalent number of sink that gives the same m’1= 9
    9 = n’1  0.4 + 1.8  [2  n’1  0.4  (1 – 0.4)]0.5
    n’1 = 11.80 (Solve by Iteration) say 12.
    Equivalent system configuration
     Appliance             No. of Fitting, n   Usage Ratio, p   Flow Rate, q (L/s)

     Equivalent Sink for          12                0.4               0.30
     Wash Basin
     Sink                         20                0.4               0.30

    m2 = 32  0.4 + 1.8  [2  32  0.4  (1 – 0.4)]0.5
       = 19.9 say 20
                                                                                42
    Simultaneous system demand, Q = 20  0.3 = 6.0L/s
  4. System Design and Calculation
4.2 Simultaneous Demand
    Loading Unit Method
•   It is the simplest way to determine the simultaneous demand
    published in Plumbing Engineering Services Designs Guide - IOP.
•   Loading Unit (LU) is a dimensionless figure to represent the
    associated water demand of each type of fitment, they are:
    Appliance                    Loading     Appliance                    Loading
                                 Units, LU                                Units, LU
    Wash basin domestic use          1.5     WC flushing cistern (9L)          2

    Wash basic public use             2      Shower                            3

    Wash basin concentrated           3      Sink tap nominal size 15mm        3
    use
    Bath tap nominal size 20mm       10      Sink tap nominal size 20mm       10

    Bath tap nominal size 25mm       22      Spray tap                        0.5

                                                                                      43
  4. System Design and Calculation
4.2 Simultaneous Demand
    Loading Unit Method
•   The simultaneous demand can be obtained from calculating the total
    LU from the pipe sizing chart Graph A1 in design guide issued by
    IOP.
•   Using the data of Flow Rate and LU from Graph A1, they can be
    represented by the following equation:
    Q = 0.0623LU0.681




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 4. System Design and Calculation
4.2 Simultaneous Demand
    Loading Unit Method
•   Example
    System Configuration
     Appliance                             Loading     Number of
                                           Units, LU   Appliance
     Wash basin concentrated use                3           30

     Sink tap nominal size 20mm                 10          20



    Total LU = 3  30 + 10  20 = 290
    Simultaneous demand, Q = 0.0623  (290)0.681 = 3.0L/s




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  4. System Design and Calculation
4.2 Simultaneous Demand
•   The simultaneous demand estimated by the same numbers of fitment
    of using Binominal and Poisson Distribution Method (6.0L/s) is double
    than that of using Loading Unit Method (3.0L/s).
•   It is due to the usage ratio used in Binominal and Poisson Distribution
    Method that is different in the assumption used in Loading Unit
    Method.
•   Designer shall pay special attention on making adjustment on the
    data utilized for determine the simultaneous demand to suit particular
    application.
•   In general, Loading Unit method give satisfactory estimation for
    residential and commercial buildings.




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  4. System Design and Calculation
4.3 Pipe Sizing
•   The objectives of pipe sizing is determine the size of pipe to convey
    certain amount of water such that
    i) No excessive pressure drop in pipe frictional loss.
    ii) No excessive flow velocity.
    Water Velocity
•   Water velocity within pipeline should be limited to avoid great
    pressure fluctuation thus causing water hammer effect.
•   The following table showing the recommended maximum velocity in
    pipeline:
           Pipe Bore Diameter (mm)   Maximum Water Velocity (m/s)
                      25                         1.0
                      50                         1.5
                     100                         2.0
                     >150                        3.0
                                                                      47
  4. System Design and Calculation
4.3 Pipe Sizing
    Frictional Loss
•   Pipe friction should be limited to avoid excessive pressure drop that
    cause insufficient water supply pressure at draw-off point.
•   Darcy Formula
           4fl V 2
     hf       
            d 2g
    hf is head loss to friction (m)
    f is friction coefficient and is function of Reynolds Number s for
    Laminar Flow.
    l is length of pipe (m)
    d is diameter of pipe (m)
    It is suitable for straight pipe loss calculation.

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  4. System Design and Calculation
4.3 Pipe Sizing
    Frictional Loss
•   Equivalent Length Method:
                          Δp 
    Pf   l  le  K n 
                            
                 n      l 
    Pf if total pressure loss in piping system
    K is friction factor.
    l is straight pipe length.
    le is equivalent length.
    ∆p/l is pressure drop per unit pipe straight length.
    ∆p/l & le can be obtained from tables in CIBSE Guide C. For copper
    pipe and water at 10 C, it can refer to page 4-40 & 4-41 of CIBSE
    Guide C.

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  4. System Design and Calculation
4.3 Pipe Sizing
    Frictional Loss
•   K-Factors for Common Pipe Fittings:
                        Reductions                                 Enlargement
       Diameter Ratio                  K           Diameter Ratio                K
             3/2                       0.3               3/2                     0.4
             2/1                       0.4               2/1                     0.7
             3/1                       0.4               3/1                     0.9
             4/1                       0.5               4/1                     1.0

                   Copper Pipe Elbow                                 Valves
        Pipe Diameter                  K                Type                     K
         10 – 25mm                     1.0           Gate Valve                  0.2
         32 – 50 mm                    0.8           Angle Valve                 5.0
         65 – 90 mm                    0.5         Tap or Stopcock               10

                                             Tee
            Type                       K                Type                     K
       Straight Through                0.2             Branch                    0.5
                                                                                       50
  4. System Design and Calculation
4.3 Pipe Sizing
•   The pipe sizing shall ensure the total pressure loss in water pipe
    distribution system that the required minimum pressure at draw-off
    point can be maintained.
•   Ps = Pf + Pd + Pz
    Ps is water pressure at source
    Pd is minimum discharge pressure at draw-off point
    Pz is the static head gain or loss. = gH
•   Remark:
    Pipe friction dominants in sizing small diameter pipeline whereas
    water velocity dominants in sizing large diameter one.




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  4. System Design and Calculation
4.3 Pipe Sizing
•   Example
    Water pressure at                         Sink       Wash    Bath
                                                         Basin
    upstream of main gate
    valve is 1.5 bar            Gate
                                Valve
    The draw-off point is 1m
    above floor level.
    Tap is installed at sink,           25m          8m           6m

    wash basin and bath.                 A           B            C

    Water flow:
    Sink, 0.3L/s
    Wash Basin,. 0.15L/s
    Bath, 0.3L/s
    Minimum pressure at
    draw-off point is 1bar
                                                                        52
  4. System Design and Calculation
4.3 Pipe Sizing
•   Solution
    Ps = 1.5bar, Pd = 1.0bar, Pz = 0.0981bar
    Allowable pressure drop in the piping system,
    Pf = Ps – Pd – Pz = 1.5 – 1.0 – 0.0981 = 0.4019 bar = 40,190Pa




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    4. System Design and Calculation
4.3 Pipe Sizing
•   Solution
Section      Mass     Pipe   Pressure   le     K-Factor            Pipe        l + leK     Pf
             Flow     Size   Drop                                  Length, l               (Pa)
             (kg/s)   (mm)   Gradient                              (m)
                             (Pa/m)



    A         0.75     28       900      1.1   Gate Valve = 3,        25        28.52     25,668
                                               Tee = 0.2
    B         0.45     28       375      1.0   Tee = 0.2               8         8.20     3,075
    C         0.30     22       650      0.7   Elbow = 1.0             6         15.8     10,270
                                               Gate Valve = 3.0,
                                               Tap = 10
                                                                                  Total   39,013


•         Total pressure drop of piping system = 39,013Pa < 40,190 Pa, the
          pipe size is OK.
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  4. System Design and Calculation
4.4 Design Consideration
•   Minimum pressure at draw-off point should be maintained at 10m
    head such that most water using equipment can operate properly
    such as domestic type instantaneous water heater.
•   Pneumatic booster pump system should be adopted for water supply
    in topmost floors if water tank close to the topmost floor that
    minimum 10m head cannot be achieved at draw-off point.
•   For flushing water supply, it may not necessary to use pneumatic
    booster pump system for the top most floors because even 5m head
    could refill the cistern as well. Alternatively using separate down
    pipe for the topmost floors can minimize the pressure fluctuation by
    minimizing the simultaneous demand of the whole down pipe.
•   Space and elevation of water tank could reduce unnecessary upfeed
    and/or booster system.


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  4. System Design and Calculation
4.4 Design Consideration                                                            Elevated
                                                                                    Storage
    Pressure Zoning in High Rise Building                                           Tank

•   Maximum pressure at draw-off point
    should limit to 60m head to avoid                                Intermediate
                                                                     Storage/
    excessive pressure.                                              Sump Tank
•   Building height in the range of 150 to        Intermediate                            Draw-off
                                                  Upfeed Pump                             Point
    200m can consider using cascade
    upfeed system thus minimize energy
    wastage on pressure reducing as well
    as lower pressure requirement on
    piping accessories.                            Lot Boundary

•   If break tank is practically infeasible to
                                                          Water
    be provided, pressure reducing valve                  Meter          Upfeed
                                                                         Pump
    is required to regulate the system                    m
    pressure zoning.                                          Sump
                                                              Tank
                                                 Supply                                  56
                                                 Main