Water Resources Engineering

Open Channel Flow

Specific energy, critical depth, the Froude number and the hydraulic jump — the gravity-driven free-surface flows that dominate hydraulics questions.

PART 1

Topic Breakdown & Traps

In an open channel the flow has a free surface, so gravity and depth control behaviour. Specific energy

E = y + v^{2} /2 g

is minimum at the critical depth, where the Froude number

F r = 1

. Flow is subcritical (

F r < 1

, deep/slow) or supercritical (

F r > 1

, shallow/fast). A transition from super- to subcritical occurs abruptly through a hydraulic jump, dissipating energy.

Specific energy:

E = y + \frac{v ^{2}}{2 g} = y + \frac{q ^{2}}{2 g y ^{2}}

Critical depth (rectangular):

y_{c} = (\frac{q ^{2}}{g})^{1/3}, q = \frac{Q}{b}

Froude number:

F r = \frac{v}{g y}

;

F r = 1

critical

Hydraulic jump (sequent depth):

y_{2} = \frac{y _{1}}{2} (1 + 8 F r_{1}^{2} - 1)

Energy loss in jump:

Δ E = \frac{( y _{2} - y _{1} ) ^{3}}{4 y _{1} y _{2}}

⚠
Critical depth is independent of slope. It depends only on discharge per unit width $q$ (rectangular channel).
⚠
**Use unit discharge $q = Q / b$ ** in the critical-depth formula, not total $Q$ .
⚠
Jump only forms super→subcritical. Upstream must be supercritical ( $F r_{1} > 1$ ).

PART 2

Q1BASIC1 Mark · NAT

A rectangular channel

2 m

wide carries

8 m^{3} / s

. The critical depth is _____ m.

Q2MEDIUM1 Mark · NAT

Water flows

1 m

deep at

3 m/s

in a wide channel. The Froude number is _____.

Q3HARD2 Marks · NAT

A hydraulic jump has upstream depth

0.4 m

and upstream Froude number

2.5

. The sequent (downstream) depth is _____ m.