← Fluid Mechanics & Hydraulics · RRB JE Civil CBT-2

Chapter 2 of 12

Open Channel Flow

In the RRB JE Civil CBT-2 syllabus under Fluid Mechanics & Hydraulics · 3 parts

Open Channel Flow — Uniform Flow & Most Economical Sections · Specific Energy & Critical Flow · Hydraulic Jump

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📑 Contents (26 sections)

Part 1 of 3

Open Channel Flow — Uniform Flow & Most Economical Sections

Last reviewed 16 Sept 2026 · 6 min read

Open channels

An open channel is a conduit in which liquid flows with a free surface at atmospheric pressure — rivers, canals, flumes, and sewers or culverts flowing partly full. The driving force is gravity (component of weight along the slope), not pressure.

Pipe flow	Open-channel flow
Flows full, under pressure	Free surface at atmospheric pressure
Driven by pressure gradient	Driven by gravity (bed slope)
HGL is above the pipe	HGL coincides with the water surface
Cross-section fixed	Flow area varies with depth

Types of channels

Prismatic — constant cross-section and bed slope (most artificial canals); non-prismatic — natural rivers.
Rigid boundary (lined) and mobile boundary (alluvial, erodible).

Types of flow

Steady / unsteady — depth at a section constant / changing with time.
Uniform / non-uniform (varied) — depth constant / changing along the channel.
Gradually varied flow (GVF) — depth changes slowly over a long distance (backwater).
Rapidly varied flow (RVF) — abrupt change over a short distance (hydraulic jump, flow over a weir).
Subcritical ( $F r < 1$ ), critical ( $F r = 1$ ), supercritical ( $F r > 1$ ), with $F r = V / g D$ .
Laminar / turbulent — based on $R e = V R / ν$ (laminar below about 500; open-channel flow in practice is almost always turbulent).

In uniform flow the depth, velocity and area are constant along the channel, and the bed, water surface and energy line are parallel ( $S_{0} = S_{w} = S_{f}$ ). The depth of uniform flow is the normal depth $y_{n}$ .

Geometric elements

Element	Definition
Flow area $A$	Cross-sectional area of flow
Wetted perimeter $P$	Length of boundary in contact with liquid
Hydraulic radius $R$	$A / P$ (hydraulic mean depth)
Top width $T$	Width of free surface
Hydraulic depth $D$	$A / T$
Section factor (critical flow)	$Z = A D$
Section factor (uniform flow)	$A R^{2/3}$

For a trapezoid (bottom width $b$ , depth $y$ , side slope $m$ H : 1V): $A = (b + m y) y$ , $P = b + 2 y 1 + m^{2}$ , $T = b + 2 m y$ .

For a wide rectangular channel ( $b ≫ y$ ): $R \approx y$ .

Velocity distribution

Velocity is zero at the bed and banks and increases towards the surface; the maximum velocity usually occurs slightly below the free surface (about 0.05–0.25 of the depth), because of air resistance and secondary currents.
Mean velocity in a vertical ≈ velocity at 0.6 depth below the surface, or the average of velocities at 0.2 and 0.8 depth (current-meter practice).
Surface velocity ≈ 1.1–1.25 × mean velocity (float measurements use a reduction factor).

Uniform flow formulas

FormulaChezy and Manning

Chezy: $V = C R S$ ( $C$ has dimensions $L^{1/2} T^{- 1}$ )

Manning: $V = \frac{1}{n} R^{2/3} S^{1/2}$ (SI units)

Relation: $C = \frac{R ^{1/6}}{n}$ ; also $C = 8 g / f$

Discharge: $Q = A V = \frac{1}{n} A R^{2/3} S^{1/2} = K S$ , where the conveyance $K = \frac{1}{n} A R^{2/3}$

Other formulas for Chezy's $C$ :

Bazin: $C = \frac{87}{1 + K / R}$ ( $K$ depends on surface roughness).
Ganguillet–Kutter: a longer expression in $n$ , $S$ and $R$ (historically used for Indian canals).

Typical Manning's $n$ (indicative): smooth cement/glass about 0.010–0.011; concrete about 0.013–0.015; brickwork about 0.015; unlined earth canals in good condition about 0.020–0.025; natural streams 0.025–0.035 and higher with weeds.

Normal depth is found by solving $A R^{2/3} = \frac{n Q}{S}$ — by trial, charts or iteration.

Part 2 of 3

Specific Energy & Critical Flow

Last reviewed 16 Sept 2026 · 6 min read

Specific energy

Specific energy $E$ is the energy per unit weight of liquid measured with respect to the channel bed:

E = y + \frac{V ^{2}}{2 g} = y + \frac{Q ^{2}}{2 g A ^{2}}

For a rectangular channel with discharge per unit width $q$ :

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

Unlike total energy, specific energy can increase or decrease along a channel (bed level is the datum at each section).

Specific energy diagram

Plotting $y$ against $E$ for constant $q$ :

The curve approaches the line $E = y$ (45°) for large depths and the $E$ -axis for small depths.
For any $E$ greater than the minimum, there are two possible depths — alternate depths — one subcritical ( $y > y_{c}$ ) and one supercritical ( $y < y_{c}$ ).
At the minimum specific energy, the two depths coincide — the critical depth $y_{c}$ .

Critical flow

Critical flow is the state of minimum specific energy for a given discharge (equivalently, maximum discharge for a given specific energy).

FormulaCritical flow — general section

\frac{Q ^{2} T}{g A ^{3}} = 1 ⟺ \frac{V ^{2}}{g D} = 1, F r = \frac{V}{g D} = 1

Section factor: $Z = A A / T = \frac{Q}{g}$

Velocity head at critical flow = half the hydraulic depth: $\frac{V _{c}^{2}}{2 g} = \frac{D _{c}}{2}$

FormulaCritical depth for common sections

Section	Critical depth	$E_{min}$
Rectangular	$y_{c} = (\frac{q ^{2}}{g})^{1/3}$ ; $V_{c} = g y_{c}$	$\frac{3}{2} y_{c}$
Triangular (side slope $m$ )	$y_{c} = (\frac{2 Q ^{2}}{g m ^{2}})^{1/5}$	$\frac{5}{4} y_{c}$
Parabolic	—	$\frac{4}{3} y_{c}$

Subcritical, critical and supercritical flow

	Subcritical (tranquil)	Critical	Supercritical (rapid, shooting)
Froude number	$F r < 1$	$F r = 1$	$F r > 1$
Depth	$y > y_{c}$	$y = y_{c}$	$y < y_{c}$
Velocity	$V < g D$	$V = g D$	$V > g D$
Small surface waves	Travel upstream and downstream	Standing wave	Travel only downstream
Control	Downstream	—	Upstream

$g D$ is the celerity of a small gravity wave in shallow water.

Part 3 of 3

Hydraulic Jump

Last reviewed 16 Sept 2026 · 5 min read

What a hydraulic jump is

A hydraulic jump is the abrupt rise of the water surface when flow changes from supercritical to subcritical. It is a form of rapidly varied flow marked by a turbulent roller, air entrainment and a large loss of energy.

Jumps form, for example, at the foot of spillways, below sluice gates, and where a steep slope changes to a mild slope.

The depth before the jump $y_{1}$ (supercritical) and after it $y_{2}$ (subcritical) are sequent (conjugate) depths.
Because the energy loss is unknown, the analysis uses the momentum equation, not Bernoulli: specific force is the same on both sides (bed friction over the short length neglected).

Sequent depth ratio (horizontal rectangular channel)

FormulaHydraulic jump equations

Sequent depths:

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

with $F r_{1} = \frac{V _{1}}{g y _{1}}$ .

Equivalent form: $\frac{2 q ^{2}}{g} = y_{1} y_{2} (y_{1} + y_{2})$

Energy loss:

E_{L} = E_{1} - E_{2} = \frac{( y _{2} - y _{1} ) ^{3}}{4 y _{1} y _{2}}

Height of jump: $h_{j} = y_{2} - y_{1}$

Length of jump (horizontal apron, practical): $L_{j} \approx 5$ to $7 (y_{2} - y_{1})$ — commonly 6(y₂ − y₁)

Efficiency: $η = E_{2} / E_{1}$ ; relative loss $E_{L} / E_{1}$

Power lost: $P = ρ g Q E_{L}$

For a general (non-rectangular) section, sequent depths satisfy equal specific force: $\frac{Q ^{2}}{g A _{1}} + A_{1} \overset{z}{ˉ}_{1} = \frac{Q ^{2}}{g A _{2}} + A_{2} \overset{z}{ˉ}_{2}$ .

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