1


2

 Know the difference between units and dimensions
 Understand the SI, USCS, and AES systems of units
 Know the SI prefixes from nano to giga
 Understand and apply the concept of dimensional homogeneity

3

 What is the difference between an absolute and a gravitational system of
units?
 What is a coherent system of units?
 Apply dimensional homogeneity to constants and equations.

4

 Dimension  abstract quantity (e.g. length)
 Unit  a specific definition of a dimension based upon a physical
reference (e.g. meter)

5


6


7


8


9

 An equation is said to be dimensionally homogeneous if the dimensions on
both sides of the equal sign are the same.

10


11


12


13


14


15

 A Datum is a reference point used when making a measurement (in this
case, it is the ground).
 Suppose we wish to find the difference in height between the third floor
and fifth floor of a building.
H= h_{5} – h_{3 }= 50 ft.30 ft. = 20 feet

16


17


18


19


20


21


22


23


24


25

 The force of wind acting on a body can be computed by the formula:
 F = 0.00256 C_{d} V^{2} A
 where:
 F = wind force (lb_{f})
 C_{d}= drag coefficient (no units)
 V = wind velocity (mi/h)
 A = projected area(ft^{2})
 To keep the equation dimensionally homogeneous, what are the units of
0.00256?

26

 Pressure loss due to pipe friction
 Dp = pressure loss (Pa)
 d = pipe diameter (m)
 f = friction factor (dimensionless)
 r = fluid density (kg/m^{3})
 L = pipe length (m)
 v = fluid velocity (m/s)
 (1) Show equation is
dimensionally homogeneous
 (2) Find D p (Pa) for
 d = 2 in, f = 0.02, r = 1 g/cm^{3}, L = 20 ft, & v = 200
ft/min

27


28

 Some formulas have numeric constants that are not dimensionless, i.e.
units are hidden in the constant.
 As an example, the velocity of sound is expressed by the relation,
 where
 c = speed of sound (ft/s)
 T = temperature (^{o}R)

29

 Convert this relationship so that c is in meters per
 second and T is in kelvin.
 Step 1  Solve for the constant
 Step 2  Units on left and right must be the same

30

 Step 3  Convert the units
 So
 where
 c = speed of sound (m/s)
 T = temperature (K)

31

 The flow of water over a weir can be computed
 by:
 Q = 5.35LH^{3/2}
 where: Q = volume of water (ft^{3}/s)
 L = length of weir(ft)
 H = height of water over
weir (ft)
 Convert the formula so that Q is in gallons/min and L
 and H are measured in inches.

32

