HYDRAULIC STRUCTURES
Hydraulic structures form part of most major water engineering schemes e.g. irrigation, water
supply, drainage, sewage networks and treatment, hydropower etc. Hydraulic structures are
classified as follows:
a) Flow measuring structures e.g. weirs and flumes
b) Regulation structures e.g. gates and valves
c) Discharge structures e.g. spillways
1. Rectangular sharp crested weir
The primary purpose of a weir is to measure discharge.
A
y1
U12/2g
P1/ρg h1
crest
Z1
1
A
nappe
Z2
2
The simplest method of developing a numerical model which represents a weir is to use the
Bernoulli equation as the starting point applied along one streamline (due to uneven
distribution of volume)
Total energy of streamline A-A at 1
At section 2, the liquid passes over the weir and forms an over spilling jet whose lower nappe
is exposed to the atmosphere.
Total energy at 2
Assumptions


Velocities upstream are uniform and steady therefore pressure there varies according to
the hydrostatic equation
Pressure throughout nappe is atmospheric therefore P2 = 0

Effects of viscosity and surface tension are negligible
From the energy principle H1 = H2
The ideal discharge through an elemental strip of width b and depth δZ is;
δQideal =
Assumptions
i.
ii.
Elevation of water surface at section 2 is the same as that at1 (elevation of free surface is
horizontal)
Datum is raised to crest of weir
Thus integrating to obtain Q at weir
Integrating with respect to Z2
For practical purposes h1 >>>>
therefore equation 1.4 reduces to:
The streamlines approaching the weir converge downstream of the weir. This causes a
contraction or venacontracta which implies that actual discharge is less than Q ideal and
account must be taken of this by the coefficient of discharge Cd. Hence;
2. Triangular / Vee – Notch weir (sharp crested)
Rectangular weirs have the disadvantage of loss of accuracy at low flows. The vee – notch
weir overcomes this problem since b varies with height and therefore offers greater
sensitivity. However the vee – notch weir is inappropriate for large flows because its
construction would be very uneconomical. The theory and assumptions for the vee – notch
weir are the same as for the rectangular sharp crested weir.
δQideal =
b
θ
Z
δZ
b is not constant
b = f (θ, Z)
b = 2 Z2 tan (
Integrating;
The approach velocity, U1 is almost always negligible for vee – notch weirs in view of the
smaller discharges for which they are designed. Therefore:
From which;
3. Broad Crested Weir
The broad crested weir is an obstacle and the water upstream of the weir needs to gather just
enough specific energy to overcome the obstacle. Thus given a sufficient weir height ∆Z the
flow over the weir will be critical.
For the derivation of the equation of flow over a broad crested weir, refer to earlier notes on
open channel hydraulics; section 1.19.1.
4. Venture Flume
This refers to a device in which the flow is locally accelerated due to a streamlined lateral
contraction within the channel sides. Flumes are usually designed to achieve critical flow in
the narrowest section (throat). Flumes are especially applicable where depositions of solids
must be avoided e.g. in sewage works and irrigation canals. Deposition at weirs results in
gradual change of the weir coefficients. Additionally the use of weirs results in a relatively
large head loss.
For the derivation of the equation of flow in a venture flume, refer to earlier notes on open
channel hydraulics; section 1.19.3.
5. DAMS
Dams are interruptions in the flow of rivers, streams etc. that result in impounded reservoirs.
There are 4 main types of dams;
Gravity Dam: usually made from concrete and masonry and depends on its weight for
stability.
Arch Dams: transmit most of the horizontal thrust of the water behind them to the abutments
by arch action and have thinner cross-sections compared to gravity dams.
Buttress Dam: consists of a sloping membrane which transmits the water load to a series of
buttresses at right angles to the axis of the dam. There are several types of buttress dams; the
most important being the flat slab and the multiple arch.
Earth Dams: These are embankments of suitable rock or earth with provision for controlling
seepage by means of an impermeable zone and an upstream blanket. These earth dams are
common in dry areas.
6. SPILLWAYS
The majority of impounding reservoirs are formed as a result of construction of a dam. There
are times when the reservoir is full and the stream flow exceeds the demand. The excess
water must therefore be discharged safely from the reservoir. In most cases, to allow the
water to simply overtop the dam would result in failure of the structure. For this reason,
carefully designed overflow passages are incorporated as part of the design. The spillway
must be sufficient to accommodate large flood discharges likely to occur in the life of a dam.
Because of the high velocities of flow often attained on spillways, some form of energy
dissipation and a scour prevention system at the base of the spillway must be provided for.
This often takes the form of a stilling basin.
Gravity (Ogee) Spillways
The discharge relationship for a spillway is of the same form as other weirs.
L
Hd
h + Hd
Where;
Q = discharge
Cw = coefficient
L = Length of crest
h = head on spillway (vertical distance from crest of spillway to reservoir level)
Vo = approach velocity
Hd = height of spillway related to the downstream floor level
Siphon Spillway
Head Water
Datum
1
3
Crown/prime
2
Tail Water
If a large capacity is not necessary and space is limited; the siphon spillway could be a
practical selection. A siphon spillway is a structure in which the flow is below atmospheric
pressure
Applying Bernoulli’s equation to points 1, 2 and 3 in the above figure
But P1 = P2 = 0 (pressure is atmospheric)
From (i);
But V2 = V3 (same cross-sectional area of conduit)
Q = A2V2 = A3V3
Negative pressure
The Stilling Basin
Stilling basin and check weir
The flow discharged from the spillway outlet is usually highly supercritical. If this were left
uncontrolled, severe erosion at the toe of the dam would be experienced. This flow is
controlled by a dissipating or stilling device. A typical device of this nature is the stilling
basin. It consists of a short level apron at the foot of the spillway. It must be constructed of
concrete to resist scour. The function of the basin is to decelerate the flow sufficiently to
ensure the formation of a hydraulic jump within the basin. The jump dissipates much of the
energy and returns the flow to the subcritical state.
7. FLOW UNDER A VARYING HEAD
Q1(t)
A
∆h
h1
h(t)
Q(t)
a
Q = a. Velocity. Cd
From Torricelli; velocity Vt =
Thus Q(t) = a. Cd.
(i)
Volume of water in the tank; V = Ah
Change in volume; dV = Adh
Velocity in tank; Vtank =
Q(t) = A. Vtank =
Equating (i) to (ii)
If there is an inflow Q1(t) then
dV = - Adh + Q1(t)
In general;
(ii)
HOMEWORK
1. A pipeline 1000m long, 100mm diameter with a roughness coefficient 0.0186
discharges water from a tank having a cross-sectional area of 1000m2. Find the time
taken for the water level to fall from 20m to 15m above the pipe inlet (minor losses
are 1.5 )
2. A pyramidal vessel has a 15cm orifice at the bottom. If the water level in the vessel is
1.8m at the beginning, find the time taken for the level to fall to 90 cm given that C d =
0.62. Assume a square cross-section.