Gradually varied flow (introduction)

if the discharge is the same in the upstream channel and the downstream channel, how can the flow be described?

steady

if there is a sudden change in slope, how do the upstream and downstream flows adjust?

they vary gradually in space to meet each other at the transition in slope

when does a hydraulic jump occur?

if super-critical flow joins sub-critical flow causing a more dramatic profile

describe the slope for uniform flow

the bed slope or geometric slope is the same as the slope of the total energy line

what are the conditions for uniform flow?

dy/dx = 0 , y_u = y_d, S_f=S_w=S₀

how does depth change in gradually varied flow?

depth y changes with distance

what are the conditions for gradually varied flow?

dy/dx«1, y_u ≠ y_d, S_f≠S_w≠S₀

state the GVF equation

dy/dx = (S₀-S_f)/(1-Fr²)

what does the GVF equation assume?

• small slopes

• quasi 1D

• hydrostatic pressure

what does the GVF equation depend on?

• the difference between geometric and friction slopes

• sub or supercritical flow

what equations are used to derive the GVF equation?

the equation for total energy, H:

• H= z + y + V²/2g

the specific energy equation,:

• E_s=y + V²/2g

what assumption is made when calculating S_f?

the rate of energy loss is the same as uniform flow of the same depth (i.e. use the Manning or Chezy equation with S₀=S_f