GVF - profile classification

describe the main features of the GVF profile of water surface

• it joins 2 normal depths

• it crosses critical depth

• it is gradual, the curve is possibly over a few hundred meters long

how can the different situations which cause GVF be identified and classified?

• examine the slope and the resulting normal and critical depths

what is the critical slope (S_c)?

in uniform flow, for a given Q there will be a slope which normal depth=critical depth, this is the critical slope

what is the critical slope given by for a wide channel (b»»y)

S_c = (gn²)/(y_c^1/3)

what are the different classifications for open channels in GVF studies?

• mild

• steep

• critical

• horizontal

• adverse

what are the classifications derived from?

whether the normal depth in uniform flow is sub-critical, super-critical or critical

• or by comparing the critical slope

define S₀ for horizontal and adverse channels

• horizontal channel → S₀=0

• adverse channel → S₀<0

what 3 things does the GVF equation tell us regarding depth change

1. S₀ - S_f > 0 if y is greater than normal depth

2. 1 - Fr² > 0 if y is greater than critical depth

3. dy/dx < 0 (depth increasing) if y lies between normal and critical depths

the depth space is divided into 3 regions by the normal and critical depths, what are the regions defined by (letter + digit)?

mild slope:

• M1 (above normal depth)

• M2 (between normal depth and critical depth)

• M3 (below critical depth)

steep slope

• S1 (above critical depth)

• S2 (between critical depth and normal depth)

• S3 (below normal depth)

describe the M1 profile

• y increases along the channel

• y is greater than y_n so S_f<S₀

• y is greater than y_c so Fr<1

• flow is subcritical

describe the M2 profile

• y decreased along channel

• y is less than y_n so S_f>S₀

• y is greater than y_c so Fr <1

• flow is subcritical

describe the M3 profile

y increases along channel

• y is less than y_n so S_f>S₀

• y is less than y_c so Fr >1

• flow is supercritical

describe the S1 profile

• y increases along channel

• y is greater than y_n so S_f<S₀

• y is greater than y_c so Fr < 1

• flow is subcritical

describe the S2 profile

y decreases along channel

• y is greater than y_n so S_f<S₀

• y is less than y_c so Fr >1

• flow is supercritical

describe the S3 profile

y increases along channel

• y is less than y_n so S_f>S₀

• y is less than y_c so Fr >1

• flow is supercritical

what is a control point?

a location where there is a known relationship between water depth and discharge

• provide a location to start a GVF calculation

what are the general rules for supercritical and subcritical flow

• supercritical is controlled by upstream conditions

• subcritical is controlled by downstream conditions

given a long enough stretch of channel, what will flow try to do?

revert to normal flow

where does a hydraulic jump occur?

between 2 regions of GVF at a point where the jump conditions for the sequent depths is correct

what can be assumed about a hydraulic jump where the slope is mild?

if there is no influential downstream control, a hydraulic jump can be assumed to jump directly to normal depth