LEVEL 3 ENGINEERING PRINCIPLES – FLUID SYSTEMS EQUATIONS Hydrostatics Equations Subject Fluid Density
Equation
ρ=
m V
Variables and Units ρ = density in kilograms per cubic meter (kg/m3) m = mass in kilograms (kg)
Relative Density
RD =
ρ ρ
Hydrostatic Pressure
P = ρgh
Hydrostatic Force
F = ρghA
V = volume in cubic meters (m3) RD = relative density (dimensionless) ρw = density of water in kilograms per cubic meter (kg/m3) P = hydrostatic pressure / pressure head in Pascals (Pa) g = gravity in meters per second squared (m/s2) h = fluid depth in meters (m)
Overturning Moment
F = thrust force in Newtons (N)
ρgℎ A M= 3
A = area of surface subjected to water pressure in meters squared (m2)
Equation
Variables and Units
Q = vA
Q = volume flow rate in cubic meters per second (m3/s)
Tubes, Pipes and Ducts Subject
Volume Flow Rate
v = fluid velocity in meters per second (m/s)
v A =v A
A = cross sectional area of pipe or duct in meters squared (m2) ṁ = mass flow rate in kilograms per second (kg/s)
Mass Flow Rate
ṁ = ρQ
ρ = density in kilograms per cubic meter (kg/m3)