MECHANICS of FLUIDS LABORATORY - Mechanical Engineering

At any upstream (of the hump) location, say
h 1 , we see that the corresponding specific energy
head is E 1 . The vertical line that locates E 1 also
locates the energy E 2 which is downstream of the
hump. A vertical line drawn at E 1 intersects the
line at h 1 and h 2 , which are the upstream and
downstream liquid heights, respectively. Note
that the minimum specific energy head is at the
highest point of the hump z c , and the energy
head there is E c .
As water flows over the hump, the initial
specific energy head E 1 is reduced to a value E by
an amount equal to the height of the hump. So at
any location along the hump, the specific energy
head is E 1 - z, where z is the elevation above the
channel bed. At the point where the flow is
critical, the critical depth h c is given by
Q 2
1/3 2E
h c = ⎛ ⎞ = c
⎝ b 2 g⎠
3
Flow Over a Hump
(15.2)
Equipment
Open Channel Flow Apparatus (Figure
12.1)
Installed hump
The open channel flow apparatus is described
in Experiment 12 and illustrated schematically in
Figure 12.1. Adjust the channel so that it is
horizontal. Make every effort to minimize
leakage of water past the sides of the hump.
Start both pumps and adjust the valves to give a
smooth water surface profile over the hump. For
one set of conditions, take readings from the
manometers to determine the volume flow rate
over the hump.
The open channel flow apparatus has a
depth gage attached. It will be necessary to
measure the water depth at certain specific
locations on or about the hump. These locations
are shown in Figure 15.3 (dimensions are in feet).
There are 8 water depths to be measured. So for
one flow rate, two manometer readings and 8
water depths will be recorded. Gather data for
the assigned number of flow rates.
Results
Although the data taken in this experiment
seem simple, the calculations required to reduce
the data appropriately can occupy much time.
With the data obtained:
Determine the flow rate using the manometer
readings. This value will be referred to as the
actual flow rate Q AC (subscript AC will refer
to an actual value, while TH refers to a
theoretical value).
Calculate the flow rate using a rearranged
form of Equation 15.2. This value will be
referred to as the theoretical flow rate Q TH .
Compare the two flow rates and find % error.
Use Equation 15.2 to find the value of the
critical depth using Q AC. Compare this value
to the measured value, and find % error.
Calculate the theoretical and actual values
of the minimum energy E c using Equation 15.2.
Compare the results.
Calculate the actual specific energy head E AC
at each measurement station using Equation
15.1. Determine also the total energy head
H AC (= E AC + z) for all readings.
Compose a chart using the column and row
headings shown in Table 15.1.
1 2 3 4 5 6 7 8
flow
direction
hump
2
0.276
0.313
0.313 0.313 0.313
1
FIGURE 15.3. Water depth
measurement locations
for flow over a hump.
(Dimensions in feet.)
37