Newton Force

F = m · g  [N]

m = weight           [Kg]
g = earths gravity   [m/s²]

Total Head

            u²
H = y + z + —  [m]
           2·g

y   = Pressure Head  [m]
z   = Potential Head [m]
 u²

 —  = Velocity Head  [m]

2·g
u   = Velocity       [m/s]
g   = Earths gravity [m/s²]

Reynolds Number, Laminar or Turbulent flow

     v·D             v·4·R   
Re = ——  [1] or Re = ————  [1]
           u                                 u


v = Average velocity          [m/s]
D = Hydraulic Diameter = 4·R  [m]
R = Hydraulic Radius = D/4    [m]
u   = Kinematic viscosity       [m²/s]
u  water 20°C       = 1,00·10^-6 [m²/s]


Turbulent flow     Re > 4000  
Laminar   flow     Re < 2000

Kinematic viscosity

        m
u =  —             [m²/s]
        r

m = Absolute viscosity    [kg/ms]
m  water 20°C  = 1,00·10^-3 [kg/ms]
r = Density of liquid     [kg/m³]

r fresh water     = 1000  [kg/m³]

r saltwater       = 1025  [kg/m³]

Discharge large orifice

$ \LARGE Q=\frac{2}{3}\cdot b\cdot \sqrt[2]{2g\cdot \left({h_{2}}^{\frac{3}{2}}-{h_{1}}^{\frac{3}{2}} \right )}$     [m³/s]
b  = Width orifice              [m]
g  = Earths gravity= 9,81       [m/s²]
h₁ = Pressure at top orifice    [m]
h₂ = Pressure at bottom orifice [m]

Discharge small orifice

Q = C_v·C_c·A₀·²Ö(2·g·h) [m³/s] 

C_v = Velocity coefficient (0,97-0,99)   [1]
C_c = Contraction coefficient (0,61-0,66)[1]
A₀ = Wetted  Area                       [m²] 
h =  Pressure just before orifice       [m]
g =  Earths gravity= 9,81               [m/s²]

Bernoulli's equation, expressed in head [m]

         u²₁            u²₂
y₁ + z₁ + —— = y₂ + z₂ + —— + DH_1-2 [m]
         2·g            2·g

y    = Pressure  Head      [m]
z    = Potential Head      [m]

 u²

 —   = Velocity  Head      [m]

2·g
g    = Earths gravity= 9,81[m/s²]

DH_1-2 = Head losses         [m]

Momentum equation, Force by flow

F = r·Q·(V₂-V₁)  [N]
r        = Density of liquid         [kg/m³]

r fresh water = 1000             [kg/m³]

r saltwater   = 1025             [kg/m³]

Q   = Discharge/ flow rate      [m³/s]

V₁  = Mean velocity before      [m/s]

V₂  = Mean velocity after       [m/s]

Force is negative, because it is a reaction force

Velocity Head

 u²

 —  = Velocity Head [m]

2·g

u = Velocity              [m/s]

g = Earths gravity= 9,81  [m/s²]

Pressure Head, distance point to free surface

           p
y = ——  [m]
        r·g


p = Pressure              [Pa=N/m²]
g = Earths gravity= 9,81  [m/s²]
r   = Density of liquid     [kg/m³]

r fresh water      = 1000  [kg/m³]

r saltwater        = 1025  [kg/m³]

General pressure intensity

    F
p = —  [Pa = N/²m]
    A

F = Newton Force                    [N]
A = Area on which the force acts    [m²] 

Colebrook-White and Darcy Weisbach combined

Calculate Velocity in pipe
Based on uniform flow, friction loss only. Suitable for turbulent and laminar flow.
$latex \fn_cm \color{red} \LARGE V=-2\cdot \sqrt[2]{2g\cdot D\cdot S_{f}}\cdot log\left ( \frac{k_{s}}{3,70\cdot D}+\frac{2,51\cdot \nu }{D\sqrt[2]{2g\cdot D\cdot S_{f}}} \right )$

with $latex \fn_cm \color{red} \LARGE S_{f}=\frac{h_{f}}{L} $

V  = Velocity                                    [m/s]
g  = Earths gravity= 9,81                        [m/s²]
D  = Hydraulic Diameter = 4·R                    [m]
S_f = Slope hydraulic gradient caused by friction [1]
h_f = Frictional head loss                        [m]
L  = Length                                      [m]
k_s = surface roughness                           [m]

u     = Kinematic viscosity                         [m²/s]

u  water 20°C       = 1,00·10^-6 [m²/s]

Basic formula Discharge

Q = u * A

Q  =  Discharge/ flow rate   [m³/s]
u  =  Velocity               [m/s]
A  =  Wetted Area            [m²]