1. Basic Hydraulics: Hydraulic continuity concepts

2. Balance Principles Water not created or destroyed as it moves.
What is put into system eventually comes out of system
Principle of conservation of mass
Water flows downhill
Flow from higher energy to lower energy
Principle of conservation of energy (which includes accounting for energy losses)
Moving water can exert forces on objects
Analyzing forces associated with water flow allow us to solve hydraulic problems.
Principle of conservation of momentum.

3. Mass conservation
The law of conservation of mass/matter states that mass of system substances will remain constant, regardless of processes acting inside system
Matter changes form, but cannot be created or destroyed
For any chemical process in a closed system, mass of reactants must equal mass of products

4. Mass conservation For water typically called the continuity equation
When flow is steady, the storage term vanishes

5. Conservation of mass (continuity)
Example: Initial volume= 20 gallons, outflow=0.2 gal/min, inflow=0.1 gal/min. What’s volume after 30 min?

6. Area, Velocity, and Discharge
Discharge (Q) is the product of the cross sectional flow area A and the mean section velocity V
Sometimes cross sections are divided and the total discharge is the sum of individual area-velocity products

7. Continuity Even if pipe size changes: Qin = Qout
Branching pipe: Q1 = Q2 + Q3

8. Velocity of flow Average velocity = v = Q/A
What happens if size changes and no storage? Q1 = Q2 = A1v1 = A2 v2 v2/v1 = A1/A2

9. Velocity of flow
Sometimes cross sections are divided and the total discharge is the sum of individual area-velocity products A1 A2 V1 A3 A4 V4 V2 V3

10. Geometric Properties Natural Cross Section Engineered Cross Section
Cross Sections
Natural Cross Section
Engineered Cross Section

11. Geometric Properties
Although typically used for open channels, these properties are also defined for closed conduits.
Flow area (all the “blue”), A
Wetted perimeter, P
Topwidth, T
Flow depth, y
Hydraulic Depth, A/T
Hydraulic Radius, A/P

12. Energy of flow 2 Three kinds of energy gradients cause flow
Elevation (called potential energy)
Pressure (another kind of potential)
Kinetic (related to how fast water is moving)
p1, v1
Elevation 1
p2, v2
Elevation 2 1 2

13. Pressure Pressure at point = p = g h
For US customary units, g = 62.4 lb/ft3
Example:
At point 1, p1 = g h1
At bottom of tank, pbottom = g hbottom
Pressure energy = h h1
hbottom 1

14. Energy losses Due to Boundary resistance (friction losses)
Effects of changes in flow geometry (local losses)
Local losses often expressed as hL = K v2/2g in which K = the head loss coefficient
Friction losses commonly computed using empirical equation, such as Manning’s equation, Chezy equation, Darcy-Weisbach equation or Hazen-Williams (water only!)

15. Total energy Express energy in consistent units.
Elevation (h) has units of ft.
Pressure has units of lb/ft2. If we divide p by g (62.4 lb/ft3), we get units of L for the pressure term.
Velocity has units of ft/sec. Energy related (velocity)2. Measure of velocity energy consistent with other energy units is v2/2g where g = gravitational acceleration.
These energy terms referred to as “head”.
Total energy (head) = h + p/g + v2/2g

16. Conservation of energy
Total energy at a point = E = h + p/g + V2/2g
Between any two points in the flow E1 = E2 + hL1-2
where hL1-2 = energy “loss” between locations
So h1 + p1 /g + V12/2g = h2 + p2 /g + V22/2g + hL1-2