202
P. Liu
between its velocity and microwave velocity will determine the flow pattern
in the channel. According to the Froude number (Fr ), it can be divided into
three flow patterns: subcritical flow, supercritical flow, and critical flow. For
rectangular channels, Fr defined by the average velocity V of the section and
the water depth h is
Fr =
V
√
gh
When Fr < 1, the water flow is a subcritical flow. In this case, the perturbation wave propagates throughout the flow field, that is, it can propagate up
against the current. When Fr > 1, the water flow is a supercritical flow. In a
supercritical flow, disturbance waves can only propagate downstream. When
Fr = 1, the water flow is a critical flow. In that case, the disturbance wave
can only propagate downstream. From the perspective of the force on the
moving water body, the Fr number represents the ratio of the inertia force
of the water to the gravity. Therefore, when Fr is less than 1, it means that
the inertia force of the water is less than the gravity force. When Fr is greater
than 1, it means that the inertial force of the water is greater than gravity and
the inertial force plays a leading role in the water flow. If Fr = 1, the effect
of inertial force on the water is equal to the effect of gravity and the water
flow is in a critical flow.
(2) Section specific energy and critical water depth
In 1911, B.A. Bakhmeteff (1880–1951, as shown in Fig. 3.29), the Russian
hydraulician, proposed the unit time unit weight water mechanical energy as
an important physical quantity to study the flows of open channels, which
is expressed by the lowest particle of any cross-section as a base particle, as
shown in Fig. 3.30. For the case of a small slope, the expression of section
specific energy is as follows:
E s = h cos θ +
αV 2
2g
≈ h +
V 2
2g
In rectangular channel, if q (= Q /b) is used to represent unit width
discharge, then v = q/h. In this way, E s can also be expressed as
E s = h +
q 2
2gh 2
P. Liu
between its velocity and microwave velocity will determine the flow pattern
in the channel. According to the Froude number (Fr ), it can be divided into
three flow patterns: subcritical flow, supercritical flow, and critical flow. For
rectangular channels, Fr defined by the average velocity V of the section and
the water depth h is
Fr =
V
√
gh
When Fr < 1, the water flow is a subcritical flow. In this case, the perturbation wave propagates throughout the flow field, that is, it can propagate up
against the current. When Fr > 1, the water flow is a supercritical flow. In a
supercritical flow, disturbance waves can only propagate downstream. When
Fr = 1, the water flow is a critical flow. In that case, the disturbance wave
can only propagate downstream. From the perspective of the force on the
moving water body, the Fr number represents the ratio of the inertia force
of the water to the gravity. Therefore, when Fr is less than 1, it means that
the inertia force of the water is less than the gravity force. When Fr is greater
than 1, it means that the inertial force of the water is greater than gravity and
the inertial force plays a leading role in the water flow. If Fr = 1, the effect
of inertial force on the water is equal to the effect of gravity and the water
flow is in a critical flow.
(2) Section specific energy and critical water depth
In 1911, B.A. Bakhmeteff (1880–1951, as shown in Fig. 3.29), the Russian
hydraulician, proposed the unit time unit weight water mechanical energy as
an important physical quantity to study the flows of open channels, which
is expressed by the lowest particle of any cross-section as a base particle, as
shown in Fig. 3.30. For the case of a small slope, the expression of section
specific energy is as follows:
E s = h cos θ +
αV 2
2g
≈ h +
V 2
2g
In rectangular channel, if q (= Q /b) is used to represent unit width
discharge, then v = q/h. In this way, E s can also be expressed as
E s = h +
q 2
2gh 2