Hydraulics

Question 1

How are hydro-statics and hydro-dynamics different in terms of the variables involved?

Answer 1

Statics uses pressure only
Dynamics uses pressure and shear

Question 2

What does steady flow mean?

Answer 2

dV/dt = 0

Question 3

What does uniform flow mean?

Answer 3

dV/dx = 0

Question 4

What is the condition for laminar flow?

Answer 4

Re < 2000

Question 5

What is ideal flow?

Answer 5

The assumption of frictionless flow

Question 6

What is the equation for hydraulic radius R?

Answer 6

Cross-sectional area/wetted perimeter

Question 7

What is the shear equation in uniform flow?

Answer 7

τ = ρgRS
R is hydraulic radius
S is slope angle

Question 8

What is the Manning’s discharge equation?

Answer 8

Q = a/n * A * R^2/3 * sqrt(S0)

Question 9

How do you calculate discharge Q for a compound channel?

Answer 9

Split the channel into simple sections and calculate Q for each, then sum

Question 10

How do equations for total energy and specific energy differ?

Answer 10

Total energy includes height, z, above reference height

Question 11

What is the specific energy equation?

Answer 11

E = y + αv^2/2g
α is the energy coefficient, usually close to 1

Question 12

What’s an important relationship to remember with flow variables?

Answer 12

V = Q/A

Question 13

What is assumed to calculate the flow depth on the other side of a sluice gate to the depth given?

Answer 13

Energy is conserved (E1=E2)

Question 14

What does the conservation of mass assumption mean?

Answer 14

Q1 = Q2

Question 15

What is true of energy in critical flow?

Answer 15

dE/dy = 0

Question 16

What is the equation for Froude Number?

Answer 16

Fr = U/sqrt(gy)

Question 17

What are two naturally occurring instances of critical flow?

Answer 17

Change of bed surface slope from /mild to steep/
Free outfall past a /mild/ slope

Question 18

For a constant total head H, how do changes in bed profile affect flow depth?

Answer 18

The specific energy decreases when the
channel bottom rises

Question 19

How does increasing energy affect flow depth?

Answer 19

Increases depth in subcritical flow
Decreases depth in supercritical flow

Question 20

In supercritical flow, how do changes to flow affect the rest of the waterway?

Answer 20

Changes only affect the downstream system as waves travel slower than flow and so cannot travel upstream

Question 21

What 3 key changes occur at a hydraulic jump?

Answer 21

Flow goes from super to subcritical
Depth increases at the expense of velocity
Specific energy is lost irreversibly

Question 22

What does the significant loss of energy at a hydraulic jump mean for continuity analysis?

Answer 22

Conservation of energy cannot be used, momentum must be used instead

Question 23

What is the equation for energy loss at a hydraulic jump?

Answer 23

ΔE = (y2-y1)^3/(4y1y2)

Question 24

What is the equation for power dissipated at a hydraulic jump?

Answer 24

P = ρgqΔE

Question 25

What counts as rapidly varied flow (RVF)?

Answer 25

Sudden change in flow regime Hydraulic jump Flow around an obstruction

Question 26

What is the equation for the slope of the free surface profile?

Answer 26

dy/dx = (S0-Sf)/(1-Fr^2)

Question 27

How is the friction slope (Sf) defined?

Answer 27

The slope of the total head line dH/dx = -Sf

Question 28

What are the 5 bed slopes and their conditions?

Answer 28

Mild: yn > yc Steep: yn < yc Critical: yn = yc Horizontal: S0 = 0 Adverse: S0 < 0

Question 29

How does flow depth define the 3 zones in profile classification?

Answer 29

y > yn: Zone 1 yn > y > yc: Zone 2 yc > y: Zone 3

Question 30

How does flow depth approach normal depth?

Answer 30

Asymptotically

Question 31

How does flow depth approach critical depth?

Answer 31

Sharply, often almost vertically

Question 32

How does flow depth trend in Zone 1 conditions?

Answer 32

It trends towards a horizontal flow surface

Question 33

How do Zone 1 and Zone 3 profiles approach or diverge from the normal/critical depth on a critical slope?

Answer 33

Zone 1: Diverges sharply Zone 3: Approaches asymptotically

Question 34

What is different about a sluice gate on a steep slope compared to a mild one?

Answer 34

On a steep slope, the hydraulic jump occurs before the sluice, whereas for mild it occurs after

Question 35

How does flow criticality affect the response of flow to a depression in the bed?

Answer 35

Subcritical flow will increase in depth Supercritical flow will decrease in depth

Question 36

How are the energy equations for subcritical normal flow and flow over a weir related?

Answer 36

En = Ew yn + Vn^2/2g = yw + hw + Vw^2/2g

Question 37

Why are hydraulic jumps often engineered to occur?

Answer 37

To reduce energy as a means of reducing speed, erosion etc.

Question 38

What is a stilling basin and why is it used?

Answer 38

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

Question 39

From where do you start sketching flow profiles?

Answer 39

Locations of known flow depth

Question 40

How do you check where a hydraulic jump occurs when comparing two possibilities?

Answer 40

Compare the height of the jump to the normal depth after the jump and check if this difference makes sense given the slope profile

Question 41

How are the heights of two potential hydraulic jumps related?

Answer 41

yj1 = 1/2 yj2(sqrt(1+8Fr2^2)-1)

Question 42

What does hL signify? What is it equivalent to?

Answer 42

Head loss due to friction hL = Sf * L

Question 43

How do you perform the direct step method?

Answer 43

Start from a known (y,V) Proceed by solving for x assuming Δy is the same for each step

Question 44

How do you perform the standard step method?

Answer 44

Start from a known (y,V) Proceed by iteratively solving for y by changing Δx until the target y is met

Question 45

What is an important part in the 2 step methods?

Answer 45

Finding the energy grade line using EGL = y + V^2/2g

Question 46

What is the version of Manning's formula used to find energy loss due to friction?

Answer 46

Sf = (n * V)^2/(R^4/3)

Question 47

What is the equation of Δx in the direct step equation?

Answer 47

Δx = ΔE/(S0-Sfavg)

Question 48

What values need to be calculated (and can be tabulated) for each depth in the direct step method?

Answer 48

A P R V EGL Sf Δx

Question 49

What must be true of step size in the standard step method?

Answer 49

It must be small enough that changes in depth are small

Question 50

What changes about equations in natural channels?

Answer 50

Z is used instead of y, where Z is the distance from a datum to the water surface

Question 51

How do you know if your guess of y2 in the standard step method is correct?

Answer 51

E2 = E1 + (S0-Sfavg)Δx

Question 52

What must you do if discharge is one of the required outputs but slope profile is unknown?

Answer 52

Assume profile to calculate discharge

Question 53

What can R be assumed to be equivalent to in a very wide channel?

Answer 53

depth, y

Question 54

What is the area of a trapezium?

Answer 54

1/2 (a+b) * h

Question 55

What is the mnemonic for direct step method

Answer 55

YAPRR has Very HeaVy HeEps rolling down the Mean Slope

Question 56

What is the mnemonic for standard step method?

Answer 56

Start Deep, ZAPR’s Very HeaVy HEAD Sloped over and the Sloping Distance changed his HEAD too much

Question 57

What is the equation for normal depth of a wide channel?

Answer 57

yn = (Qn/(B * sqrt(S0)))^3/5

Question 58

How does the uniform flow assumption help with finding normal flow depth?

Answer 58

At normal depth, all variables are assumed to be constant rather than changing