Canal effect. Figure 14-45 shows an anchored barge that...

Canal effect. Figure $14-45$ shows an anchored barge that extends across a canal by distance $d=30 \mathrm{m}$ and into the water by distance $b=12 \mathrm{m} .$ The canal has a width $D=55 \mathrm{m},$ a water depth $H=14 \mathrm{m},$ and a uniform water-flow speed $v_{i}=1.5 \mathrm{m} / \mathrm{s} .$ Assume that the flow around the barge is uniform. As the water passes the bow, the water level undergoes a dramatic dip known as the canal effect. If the dip has depth $h=0.80 \mathrm{m},$ what is the water speed alongside the boat through the vertical cross sections at (a) point $a$ and (b) point $b$ ? The erosion due to the speed increase is a common concern to hydraulic engineers.

Canal effect. Figure $14-45$ shows an anchored barge that extends across a canal by distance
$d=30 \mathrm{m}$ and into the water by distance $b=12 \mathrm{m} .$ The canal has a
width $D=55 \mathrm{m},$ a water depth $H=14 \mathrm{m},$ and a uniform water-flow
speed $v_{i}=1.5 \mathrm{m} / \mathrm{s} .$ Assume that the
flow around the barge is uniform. As the water passes the bow, the water
level undergoes a dramatic dip known as the canal effect. If the dip has depth $h=0.80 \mathrm{m},$ what is the water speed alongside the boat
through the vertical cross sections at (a) point $a$ and (b) point $b$ ?
The erosion due to the speed increase is a common concern to hydraulic engineers.

Key Concepts

Flow Contraction (Venturi Effect)

When the effective cross-sectional area of a channel is reduced by an obstruction, the fluid must flow faster through the constricted section to conserve mass. This acceleration is analogous to the Venturi effect, where a decrease in cross-sectional area leads to an increase in velocity and a corresponding drop in pressure.

Hydraulic Erosion

The increased water speed resulting from the contraction of flow can enhance the erosive forces acting on the channel’s bed and banks. Hydraulic engineers are particularly concerned with these accelerated flows because they can lead to significant erosion, which may compromise the stability of hydraulic structures and the surrounding terrain.

Continuity Equation

This principle states that for an incompressible fluid, the mass flow rate must remain constant along a streamline. In the context of canal flow, when an obstruction like a barge reduces the effective cross-sectional area, the fluid velocity increases to maintain the same volumetric flow, which explains the acceleration of water alongside the boat.

Bernoulli's Principle

Bernoulli’s principle relates pressure, velocity, and elevation in a flowing fluid. As the water speeds up around the obstruction, the pressure decreases, which can lead to a drop in the water surface level (the canal effect). This principle helps in understanding why a dip in the water level accompanies an increase in velocity.

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