NATIONAL UNIVERSITY OF SCIENCE & TECHNOLOGY
FACULTY OF INDUSTRIAL TECHNOLOGY
DEPARTMENT OF CHEMICAL ENGINEERING
CHEMICAL ENGINEERING LABOTORIES MANUALS
TCE 2109
ENGINEERING INSTRUCTOR: MISS L. TSHUMA
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3.0 EXPERIMENT 4: FLOW OVER WEIRS
3.1 AIM: To Characterise the flow of a fluid over a Rectangular notch.
3.2 THEORETICAL BACKGROUND
3.3 Weirs allow hydrologists and engineers a simple method of measuring the volumetric flow
rate in small to medium-sized streams or in industrial discharge locations. Since the geometry of
the top of the weir is known and all water flows over the weir, the depth of water behind the weir
can be converted to a rate of flow. The calculation relies on the fact that fluid will pass through the
critical depth of the flow regime in the vicinity of the crest of the weir. If water is not carried away
from the weir, it can make flow measurement complicated or even impossible. There are many
types of weirs and these are describe below.
5.0 Nomenclature
g
-acceleration due to gravity (9.81m/s)
z - height from horizontal datum
h - distances between crest and still water surface
v - Fluid velocity
P - Fluid pressure
ρ - Density
Qa - actual flow rate
Qt - theoretical flow rate
Cd - coefficient of discharge
Ө - angle of weir edge from vertical
W - Width of rectangular weir
Cd an experiment correction factor, which may be applied to the theoretical discharge value to
obtain the actual discharge, hence:𝑎𝑐𝑡𝑢𝑎𝑙𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑚𝑒𝑛𝑡 𝑑𝑖𝑠𝑐ℎ𝑎𝑟𝑔𝑒
𝐶𝑑 =
𝑇ℎ𝑒𝑜𝑟𝑒𝑡𝑖𝑐𝑎𝑙 𝐷𝑖𝑠𝑐ℎ𝑎𝑟𝑔𝑒
FOR RECTANGULAR WEIR
dQt = dAi.vi = dAj.vj
The total flow is found by integrating between zero and H (neglecting the lowering of the surface
of the water Qt =
2
3
. w. √2𝑔.H3/2
This equation may be written as Qt = k.H3/2
2
Where k may be called the Weir constant and it equals k = .w.√2𝑔
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Introducing the coefficient of Discharge (Cd) takes account of the following assumptions:2
a)
b)
c)
d)
Upstream of weir, the water is still.
Effect of drop down is neglected.
Pressure throughout the sheet of liquid (or nappe) is atmospheric.
The construction of the nappe due to curvature of streamlines.Actual..flow..rate..
Qa = Cd.k.H3/2
5.3 APPARATUS:
Fig 7 (a) : Rectangular Weir Picture
H
h
hhh
Fig (7) rectangular weir
6.0 METHOD
Ensure that the hydraulic bench is located on a level floor as the accuracy of the results will be
affected if the bench top is not level. Set up the equipment as shown in the diagram above.
Install the appropriate weir plate with the sharp edge of the weir facing downstream. Admit water
to the channel until the water discharges over the weir plate. Close the control valve and allow the
water level to stabilize. Set the Vernier Height Gauge to a datum reading using the top of the hook.
The datum is the apex of the Vee notch or the sill of the rectangular weir. In practice it is easier to
fill the channel with water and use the minimum water level as the datum – although not strictly
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accurate this method will prevent damage to the weir plate. Position the gauge about half way
between the notch plate and the stilling baffle. Admit water to the channel; adjust flow control
valves to obtain heads, H, increasing in steps of about 10mm. For each flow rate stabilize
conditions, measure and record H. Take readings of volume and time using the volumetric tank to
determine the flow rate.
7.0 RESULTS AND CALCULATIONS
(i)
Record breadth of notch.
(ii)
Tabulate volumes, times and heads
(iii)
Compute and tabulate:-Q, H, H3/2, log Q, log H
(iv)
Plot:- Log Q against log H , Q against H3/2
CONCLUSIONS:-
a) Is the Cd constant for this notch?
b) Estimate an average value of Cd for the range of the test.
c) Can the Q-H relationship be described by an empirical formula, if so write down the
formula and find the values of the constants?
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