Class notes
Hydrology: Chapter 1
- Course
- GLY5827
- Institution
- Florida State University
Florida State University: Hydrology (Ming Ye) Chapter 1: Water Budget
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Chapter 1: Water BudgetHydrological cycle and water budget
Precipitation on land (flows down 100)
Evapotranspiration (flows up 61)
Ocean moisture (flows left 39)
Surface discharge (flows right 38)
Groundwater discharge (flows right 1)
Evaporation from oceans (flows up 424)
Precipitation into oceans (flows down 385)
Conservation of Mass
The law of conservation of mass/matter (also known as the lomonosov-lavoisier law) says that the mass of a
closed system will remain constant, regardless of the processes acting inside the system
An equivalent statement is that matter cannot be created/destroyed, although it may be rearranged
Nova’s program on NPR
E = mc^2 (einstein’s big idea)
Water budget
Mass change = inflow-outflow
Dividing everything by time over which the change occurs gives
Mass change rate = mass inflow rate - mass outflow rate
delta(m) = inflow-outflow
delta(m) = change/storage
delta(t) = time
delta(m)/delta(t) = inflow/delta(t)-outflow/delta(t) = i’-o’
Time rate of mass change = mass inflow rate (inflow mass rate) - mass outflow rate
How much water/mass flows in and flows out
Example:
(min/time) x delta(t) - (mout/time) x delta(t)
(5 gallons/day) x 5 days - (3 gallons/day) x 5 days = 10 gallons
delta(m)/delta(t) = (min/t) - (mout/t)
Mass change rate = mass inflow rate - mass outflow rate
Principle of conservation of mass (water budget): for any particular compartment (usually referred to as a
control volume), the time rate of change of mass stored within the compartment is equal to the difference
between the inflow rate and the outflow rate
dm/dt = i’-o’ (mass) if density is constant dv/dt=i-o (volume)
Unit of each item? (mass) steady state: no change in storage over time i-o = 0 (volume)
Control volume: is a volume in space (a geometric entity, independent of mass) through which fluid may flow
, Example:
delta(m)/delta(t) = dm/dt = i’-o’
mass/time
Units and dimensions
We can separate hydrological units into two classes:
Basic measurements that can be directly measured
Length [l] (meter and foot)
Mass [m] (gram and pound)
Time [t] (second and day)
Temperature [q] or [k] (celsius and fahrenheit)
Derived quantities that are not directly measured but are calculated from measured variables using an
equation representing a relationship between variables using an equation representing a relationship
between variables
Velocity ([l/t]
Mass flow rate [m/t]
Volumetric flow rate [l^3/t]
[] stands for dimension; there are a variety of units that correspond to each dimensional quantity
Every quantity should have a unit!
The water budget: an example
dv/dt = i-o
A reservoir, inflow and outflow of every unit time [t] is 2 and 1 unit volume [l^3], respectively
I-o = 2 l^3t^-1 - 1 l^3t^-1 = 1 L^3
The most common system of units employed today is the international system of units (abbreviated si)
We will use SI units in this course; not the english system (e.g. ft and lbs)
A simple unit conversation
Precipitation is typically measured as a volume [l^3] per unit area [l^2] which has dimensions of length [l]
It is more convenient to use depth rather than total volume, because the volumes can be quite large
We are probably more familiar with the statement “20mm of precipitation was recorded at smith airport” than
“smith airport received 20,000m^3 of water”
In the US, the average annual precipitation varies from a minimum at death valley, CA (1.6 inches), to a
maximum on mt. waialeale on the island of Kauai in Hawaii (460 inches). What is the average annual
precipitation (in mm) at each of these locations?
Death valley, CA = 40.64mm
Mt. Waialeale, HI = 11684mm
The global water budget
dv/dt = i’-o’
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