John S. Cooper - Consultancy Services

Volume of Cylinder

V  =  p r²h

- where  r  =  radius of cylinder
                h  =  height/length of cylinder

Volume of Cone

V  =  1/3p r²h

- where r = radius of base of cone
              h  =  height of cone

Volume of Pyramid

V  =  1/3Ah

- where  A  =  area of base
                h  =  height of pyramid

Volume of Sphere

V  =  4/3 p r³

- where r = radius of sphere

Area of Triangle

(i)    A  =  1/2Lh

- where   L  =  length of base
                 h  =  vertical height

(ii)    A  =  [s(s-a)(s-b)(s-c)]^0.5

- where a, b, c = length of sides
                        s = 1/2(a + b + c)

(iii)   A   =   (ab/2)SinC
             =   (ac/2)SinB
             =   (bc/2)SinA

-  where    a, b, c  =   length of sides
                  A , B, C  =   included angles

Area of Sector of Circle

A  =  (p r²/360)a

-  where    r   =   radius of circle
                  a   =   included angle

Area of Segment of Circle

A  =  (p r²/360)a - (c/2)(r - s)

-  where    r  =  radius of circle
                  a  =  included angle
                   c  =  length of chord
                   s  =  depth of segment

Discharge from An Orifice

Q  =  mA(2gH)^0.5

-  where   Q  =  discharge (m/s)
                  A  =  area of the orifice (m²)
                  H  =  head over orifice (m)
                  g  =  9.806 (m/s²)
                  m =  ~ 0.62 (sharp-edged plate)
                           ~ 0.62 (penstock)
                           ~ 0.86 (opening in wall of
                                        chamber)
                           ~ 0.81 (short length of pipe)

Flow over 90 Degree V-Notch Weir

Q = 1.4H^2.5 (approximate)

-  where   Q  =  flow (m³/s)
                  H  =  head over apex (m)

Flow over Half 90 Degree V-Notch Weir

Q  =  0.7H^2.5 (approximate)

-  where   Q  =  flow (m³/s)
                  H  =  head over apex (m)

Flow over a Rectangular Weir
(Fully Contracted)

Q = 1.84(L - 3.9H)H^1.5 (approximate)

- where    Q  =  flow (m³/s)
                   L  =  length of weir (m)
                   B  =  head over weir (m)

Flow through a Rectangular Standing
Wave Flume

Q = 1.706BH^1.5 (approximate)

- where    Q  =  flow (m³/s)
                   B  =  width of throat (m)
                   H  =  head over invert (m)

Manning Formula
(For Flow in Pipes)

V = (0.01/n)r^0.667s^0.5

- where     V  =  velocity of flow (m/s)
                    n  =  coefficient of friction
                    r  =  hydraulic mean depth (mm)
                    s  =  hydraulic gradient

Box Pipe Flow Formula
(For Flow in Horizontal Pipes)

Q = 1/5(d⁵H/L)^0.5

- where    Q  =  flowrate (l/s)
                  d  =  diameter (cm)
                  H  =  head (m)
                   L  =  length (m)

Parameter Loading Calculation

kg   =  Conc (mg/l) x Volume (m³)
                               1000

Mogden Formula

General formula frequently employed by the Water
Service Companies for the calculation of trade effluent charges.

C  =  R + V + B(O_t/O_s) + S(S_t/S_s)

- where    C  =  Charge per m³ trade effluent.
                  R  =  Cost per m³ of receiving and conveying
                            sewage through the sewerage system.
                  V  =  Cost per m³ of providing and operating
                            volumetric capacity at the sewage 
                            sewage treatment works.
                  B  =  Cost per m³ of providing and operating
                            biological treatment capacity at the
                            sewage treatment works.
                  S  =  Cost per m³ for the handling and
                           disposal of sludge at the sewage
                            treatment works.
                  O_t  =  Average COD/BOD concentration of
                             trade effluent after settlement for
                            1 hour.
                  O_s  =  Average COD/BOD concentration of 
                             sewage after settlement for 1 hour.
                  S_t  =  Average Settleable Suspended solids
                             concentration of trade effluent.
                  S_s  =  Average Settleable Suspended  Solids
                              concentration of sewage.

Accrued Capital Funds

Total Accrued Capital  =  P[1 + (r/100)]ⁿ

- where   P  =  Amount invested initially
                  r   =  Annual rate of interest (%)
                  n  =  No. of years of investment

Annual Capital and Loan Charge Repayments

Annual Repayment   =   Capital Sum                                        [1 - (1 + r)^-n]/r

- where    r  =  % Interest Rate/100
                  n  =  Period of loan (years)