Hydraulics & Irrigation
Engineering (CE-4303)
Department of Civil Engineering
Flow Over Hump

Hump:
is a streamline construction provided at the bed of the channel. It
is locally raised bed.
Let’s examine the case of hump in a rectangular channel. We will neglect the
head loss.
Flow Over Hump

For frictionless two-dimensional flow,
sections 1 and 2 in Fig are related by
continuity and momentum:
v1 y1  v2 y 2
v21
v22
 y1   y2 Z
2g
2g
where
2
v
1
E2   y1  Z
2g
1
V1
y1
2
y2
Z
3
V2
y3
Flow Over Hump




The specific energy E2 is exactly Z
less than the approach energy E1,
and point 2 will lie on the same leg
of the curve as E1.
A sub-critical approach, Fr1 <1, will
cause the water level to decrease at
the bump. Supercritical approach
flow, Fr1>1, causes a water-level
increase over the bump.
If the hump height reaches
Zmax=Zc=E1-Ec, as illustrated in fig,
the flow at the crest will be exactly
critical (Fr=1).
If Z= Zmax, there are no physically
correct solutions to Eqn. That is, a
hump too large will “choke” the
channel and cause frictional effects,
typically a hydraulic jump.
1
2
Super-Critical
Approach
These hump arguments are reversed if the channel has a depression (Z<0):
Subcritical approach flow will cause a water-level rise and supercritical flow a fall in
depth. Point 2 will be |Z| to the right of point 1, and critical flow cannot occur.
Flow Over Hump
y2
y2
y3
y1
y3
y1
Z
Z<<Zc
Z
y1=yo, y2>yc, y3=yo
Damming
Action
Z<Zc
y1=yo, y2>yc, y3=yo
Afflux=y1-yo
yc
y1
Z
Z=Zc
y1=yo, y2=yc, y3=yo
y3
y1
yc
yo
Z
y3
Z>Zc y1>yo, y2=yc, y3=yo
Flow Over Hump

As it is explained with the help of E~y Diagram, a hump of any height “Z”
would cause the lowering of the water surface over the hump in case of
subcritical flow in channel. It is also clear that a gradual increase in the
height of hump “Z” would cause a gradual reduction in y2 value. That height
of hump which is just causing the flow depth over hump equal to yc is know
as critical height of hump Zc.

Further increase in Z (>Zc) would cause the flow depth y2 remaining equal yc
, thus causing the water surface over the hump to rise. This would further
cause an increase in the depth of water upstream of the hump which mean
that water surface upstream of the hump would rise beyond the previous
value i.e y1>yo. This phenomenon of rise in water surface upstream with
Z>Zc is called damming action and the resulting increase in depth upstream
of the hump i.e y1-yo is known as Afflux.
Hydraulic jump
Hydraulic jump formed on a spillway
model for the Karna-fuli Dam in
Bangladesh.
Rapid flow and hydraulic jump on a
dam
Hydraulics Jump or Standing Wave

Hydraulics jump is local non-uniform flow phenomenon resulting
from the change in flow from super critical to sub critical. In such as
case, the water level passes through the critical depth water surface
profile should be vertical. This off course physically cannot happen
and the result is discontinuity in the surface characterized by a
steep upward slope of the profile accompanied by lot of turbulence
and eddies. The eddies cause energy loss and depth after the jump
is slightly less than the corresponding alternate depth. The depth
before and after the hydraulic jump are known as conjugate depths
or sequent depths.
y
y1 & y2 are called
conjugate depths
y2
y2
y1
y1
Uses of Hydraulic Jump
Hydraulic jump is used to dissipate or
destroy the energy of water where it is not
needed otherwise it may cause damage to
hydraulic structures.
 It may be used for mixing of certain
chemicals like in case of water treatment
plants.
 It may also be used as a discharge
measuring device.

Equation for Conjugate Depths
Equation for head loss due to hydraulic jump
P=
Υ𝑄ℎ𝑙
550
ℎ𝑝
P=
Υ𝑄ℎ𝑙
1000
𝑘𝑤
L
Examples
Examples
Home Work
Solve Exercise Problems
(Chapter 10 Finnemore & Franzini)
• 10.23-10.34
• 10.56-10.60
• 10.65-10.72
Assignment 01: Submission Date 28-11-2022
Un-Steady Flow
Introduction
•
The flow conditions in the real-life systems usually vary with time
and thus the flows are unsteady.
• The unsteadiness may be due to natural processes, due to human
actions, or due to accidents and incidents.
• The analysis of unsteady flows is usually more complex than that of
steady flows because unsteady-flow conditions may vary with
respect to both space and time, i.e., they are function of both space
and time.
Partial differential equations describe unsteady flows since the
dependent variables (flow depth and flow velocity) are functions of
more than one independent variables (space and time).
Definition
•
A wave is defined as a temporal (i.e., with respect to time) or
spatial (i.e., with respect to distance) variation of flow depth
and rate of discharge. The wave length, L, is the distance
between two adjacent wave crests or troughs and the
amplitude, z, of a wave is the height of the maximum water
level above the still water level (Fig. 11-1).
Occurrence of Unsteady Flow
• Typical situations in which unsteady flows occur are as
follows:
1. Surges in power canals or tunnels produced by starting or
stopping of turbines or due to the opening or closing of
the turbine gates to meet the load changes
2. Surges in upstream or downstream channels produced by
starting or stopping of pumps and opening or closing of
control gates.
3. Waves in the navigation channels produced by the
operation of navigation locks.
4. Tides in estuaries, bays and inlets.
Occurrence of Unsteady Flow
5. Flood waves in streams, rivers, and drainage channels
due to rain-storms and/or snow-melt or produced by
the failure of dams, dykes, levees or other control
structures.
6. Waves generated by landslides and avalanches in rivers,
channels, reservoirs, and lakes.
7. Storm runoff in sewers and drainage channels.
8. Circulation in lakes and reservoirs produced by wind or
by temperature and density gradients.
9. Waves in lakes, reservoirs, estuaries, bays, inlets, and
oceans produced by wind storms, cyclones, and
earthquakes.