Engineering Dimensions and Units
Fundamental dimension A unique quantity that describes a basic characteristic, such as force (F) mass (M) length (L) time (t)
Systems of units SI system Systeme International d’ Unites
Based on meter for length, second for time, kilogram for mass and Kelvin for temperature. Force is expressed in Newtons.
English (now American) system Feet, pounds (mass), seconds, pounds (force) cgs system
Density The density of a substance is defined as its mass divided by a unit volume ρ=M/V where ρ=density M=mass V=volume
In the SI system the base unit for density is kg/m^3, whereas in the American engineering system density is commonly expressed as (lb_M)/(ft^3 ) (lb_M=pounds(mass)). Density of water
SI system: 1 x 103kg/m3 = 1 g/cm3 American engineering system: 62.4 lbM/ft3.
Concentration derived dimension and is usually expressed gravimetrically as the mass of a material A in a unit volume consisting of a material A and some other materials B.
Concentration of A in a mixture of A and B:
where CA = concentration of A M¬A = mass of material A VA = volume of material A V¬B = volume of material B
Basic unit for concentration is kg/m3
Most widely used concentration term in environmental engineering is milligrams per liter, written as mg/L.
Sample Problem Plastic beads with a volume of 0.04 m+3+ and a mass of 0.48 kg are placed in a container and 100 liters of water are poured into the container. What is the concentration of plastic beads in mg/L?
C_A=M_A/(V_A+V_B ) where A represents the beads and B represents the water
C_A=3.43 kg/m^3 =3430 mg/L
If the plastic beads with a volume of 0.04 m3 are placed in a 100-liter container and the container is filled to the brim with water, the total volume is
VA + VB = 100 L
Therefore, the concentration of beads is
CA = 4800 mg/L.