Hydraulics Flashcards
How are hydro-statics and hydro-dynamics different in terms of the variables involved?
Statics uses pressure only
Dynamics uses pressure and shear
What does steady flow mean?
dV/dt = 0
What does uniform flow mean?
dV/dx = 0
What is the condition for laminar flow?
Re < 2000
What is ideal flow?
The assumption of frictionless flow
What is the equation for hydraulic radius R?
Cross-sectional area/wetted perimeter
What is the shear equation in uniform flow?
τ = ρgRS
R is hydraulic radius
S is slope angle
What is the Manning’s discharge equation?
Q = a/n * A * R^2/3 * sqrt(S0)
How do you calculate discharge Q for a compound channel?
Split the channel into simple sections and calculate Q for each, then sum
How do equations for total energy and specific energy differ?
Total energy includes height, z, above reference height
What is the specific energy equation?
E = y + αv^2/2g
α is the energy coefficient, usually close to 1
What’s an important relationship to remember with flow variables?
V = Q/A
What is assumed to calculate the flow depth on the other side of a sluice gate to the depth given?
Energy is conserved (E1=E2)
What does the conservation of mass assumption mean?
Q1 = Q2
What is true of energy in critical flow?
dE/dy = 0
What is the equation for Froude Number?
Fr = U/sqrt(gy)
What are two naturally occurring instances of critical flow?
Change of bed surface slope from /mild to steep/
Free outfall past a /mild/ slope
For a constant total head H, how do changes in bed profile affect flow depth?
The specific energy decreases when the
channel bottom rises
How does increasing energy affect flow depth?
Increases depth in subcritical flow
Decreases depth in supercritical flow
In supercritical flow, how do changes to flow affect the rest of the waterway?
Changes only affect the downstream system as waves travel slower than flow and so cannot travel upstream
What 3 key changes occur at a hydraulic jump?
Flow goes from super to subcritical
Depth increases at the expense of velocity
Specific energy is lost irreversibly
What does the significant loss of energy at a hydraulic jump mean for continuity analysis?
Conservation of energy cannot be used, momentum must be used instead
What is the equation for energy loss at a hydraulic jump?
ΔE = (y2-y1)^3/(4y1y2)
What is the equation for power dissipated at a hydraulic jump?
P = ρgqΔE
What counts as rapidly varied flow (RVF)?
Sudden change in flow regime
Hydraulic jump
Flow around an obstruction
What is the equation for the slope of the free surface profile?
dy/dx = (S0-Sf)/(1-Fr^2)
How is the friction slope (Sf) defined?
The slope of the total head line
dH/dx = -Sf
What are the 5 bed slopes and their conditions?
Mild: yn > yc
Steep: yn < yc
Critical: yn = yc
Horizontal: S0 = 0
Adverse: S0 < 0
How does flow depth define the 3 zones in profile classification?
y > yn: Zone 1
yn > y > yc: Zone 2
yc > y: Zone 3
How does flow depth approach normal depth?
Asymptotically
How does flow depth approach critical depth?
Sharply, often almost vertically
How does flow depth trend in Zone 1 conditions?
It trends towards a horizontal flow surface
How do Zone 1 and Zone 3 profiles approach or diverge from the normal/critical depth on a critical slope?
Zone 1: Diverges sharply
Zone 3: Approaches asymptotically
What is different about a sluice gate on a steep slope compared to a mild one?
On a steep slope, the hydraulic jump occurs before the sluice, whereas for mild it occurs after
How does flow criticality affect the response of flow to a depression in the bed?
Subcritical flow will increase in depth
Supercritical flow will decrease in depth
How are the energy equations for subcritical normal flow and flow over a weir related?
En = Ew
yn + Vn^2/2g = yw + hw + Vw^2/2g
Why are hydraulic jumps often engineered to occur?
To reduce energy as a means of reducing speed, erosion etc.
What is a stilling basin and why is it used?
A series of blocks in the water flow that induce a hydraulic jump
The aim is to shorten the jump so as to reduce scour
From where do you start sketching flow profiles?
Locations of known flow depth
How do you check where a hydraulic jump occurs when comparing two possibilities?
Compare the height of the jump to the normal depth after the jump and check if this difference makes sense given the slope profile
How are the heights of two potential hydraulic jumps related?
yj1 = 1/2 yj2(sqrt(1+8Fr2^2)-1)
What does hL signify? What is it equivalent to?
Head loss due to friction
hL = Sf * L
How do you perform the direct step method?
Start from a known (y,V)
Proceed by solving for x assuming Δy is the same for each step
How do you perform the standard step method?
Start from a known (y,V)
Proceed by iteratively solving for y by changing Δx until the target y is met
What is an important part in the 2 step methods?
Finding the energy grade line using EGL = y + V^2/2g
What is the version of Manning’s formula used to find energy loss due to friction?
Sf = (n * V)^2/(R^4/3)
What is the equation of Δx in the direct step equation?
Δx = ΔE/(S0-Sfavg)
What values need to be calculated (and can be tabulated) for each depth in the direct step method?
A
P
R
V
EGL
Sf
Δx
What must be true of step size in the standard step method?
It must be small enough that changes in depth are small
What changes about equations in natural channels?
Z is used instead of y, where Z is the distance from a datum to the water surface
How do you know if your guess of y2 in the standard step method is correct?
E2 = E1 + (S0-Sfavg)Δx
What must you do if discharge is one of the required outputs but slope profile is unknown?
Assume profile to calculate discharge
What can R be assumed to be equivalent to in a very wide channel?
depth, y
What is the area of a trapezium?
1/2 (a+b) * h
What is the mnemonic for direct step method
YAPRR has Very HeaVy HeEps rolling down the Mean Slope
What is the mnemonic for standard step method?
Start Deep, ZAPR’s Very HeaVy HEAD Sloped over and the Sloping Distance changed his HEAD too much
What is the equation for normal depth of a wide channel?
yn = (Qn/(B * sqrt(S0)))^3/5
How does the uniform flow assumption help with finding normal flow depth?
At normal depth, all variables are assumed to be constant rather than changing
