Hydrology BC ENV 3025

# Units, dimensions, and conversions

## Hydrological quantities

• basic measurements (e.g. velocity of water in a stream, mass of water in a raingage)
• derived quantities (discharge in a stream)

## Units and dimensions

• precipitation has the dimension length [L] and the unit cm or mm or inch
• many quantities have a dimension that is some combination of these fundamental dimensions
• in equations, the dimensions on both sides have to match
• the most common system of units employed today is the SI (System International d'Unites)
 Quantity Dimension Unit SI Symbol Formula Base units: length [L] meter m mass [M] kilogram kg temperature [Q] kelvin K time [T] second s Derived units: area [L2] square meter m2 volume [L3] cubic meter m3 velocity [L T-1] meter per second m s-1 acceleration [L T-2] meter per second squared m s-2 density [M L-3] kilogram per cubic meter kg m-3 force [M L T-2] newton N kg m s-2 pressure [M L-1 T-2] pascal Pa N m-2 stress [M L-1 T-2] pascal Pa N m-2 energy [M L2 T-2] joule J N·m quantity of heat [M L2 T-2] joule J N·m work [M L2 T-2] joule J N·m power [M L2 T-3] watt W J s-1 viscosity, dynamic [M L-1 T-1] pascal-second Pa·s viscosity, kinematic [L2 T-1] square meter per second m2 s-1 specific heat [L2 Q-1 T-2] joule per kilogram-kelvin J kg-1 K-1

## Significant figures and precision

• no more digits than justified by the precision of a measurement should be presented
• derived quantities should reflect the number of significant digits of the least relatively precise number involved in the calculation

## Unit Conversions

• how to perform unit concersions
• for a list of the most common unit conversions, see this Table

### Resources

• Hornberger G.M. et al. (1998) Elements of Physical Hydrology, Appendix 1.

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