orifice and mouthpieces
TRANSCRIPT
SONG Layheang
Hydraulic Structures
Mobile : +855 (0) 92 79 64 66E-mail: [email protected]
Department of Rural Engineering, Institute of Technology of CambodiaPO Box 86, Bvld of Russian, Phnom Penh, Cambodia
Institute of Technology of CambodiaPO Box 86, Bvld of Russian, Phnom Penh, Cambodia
Hydraulic Principles of Structures
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There are a large variety of hydraulic structures to serve the many
purposes for which water resources are used.
A classification is based on the function performed by the
structure.
SONG Layheang
Orifice and Mouthpieces
Mobile : +855 (0) 92 79 64 66E-mail: [email protected]
Department of Rural Engineering, Institute of Technology of CambodiaPO Box 86, Bvld of Russian, Phnom Penh, Cambodia
Institute of Technology of CambodiaPO Box 86, Bvld of Russian, Phnom Penh, Cambodia
Orifices and mouthpieces
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An orifice is a hole or an opening in a barrier placed in a stream
through which water discharges under pressure. An orifice also
can be made in the side or bottom of a tank or vessel or in a plate
placed between the flanges of a pipeline to measure flow through
these structures.
Orifices are classified according to size (small and large), shape
(circular, rectangular, triangular), and the shape of the upstream
edge (sharp edged or round cornered).
Some orifices contain a mouthpiece, which is a cylindrical
extension of an orifice. An orifice may discharge free or may be
submerged under a downstream level.
Orifices and mouthpieces
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Stream jet through an orifice
Flow through a Small Orifice
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When the area of an orifice is sufficiently small with respect to the
size of the container, the velocity of flow can be considered
constant throughout the orifice. For the orifice section shown in
the previous slide, apply Bernoulli’s theorem at points 1 and 2
with the datum at the center of the orifice.
The approach velocity , v1, is very small compared to v2 and can
be disregarded. Hence
0v2g h 0
v2g 0
v 2gh
Flow through a Small Orifice
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The actual velocity is slightly less, due to the viscous shear effect
between water and orifice edge. Hence, including a coefficient of
velocity, we have
The size of the jet is narrowest at a distance of about one-half the
orifice diameter. At the narrowest section, the vena contracta, the
streamlines are parallel and perpendicular to the orifice. At the
vena contracta, discharge
In terms of the orifice area,
v C 2gh
Q a C 2gh
Q C C A 2gh
Flow through a Small Orifice
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Where Cc is the ratio of the area of jet at the vena contracta to the
area of the orifice, known as the coefficient of contraction. The
two coefficients are combined into a single coefficient of
discharge, Cd. Thus
Q: discharge (m3/s)
Cd: coefficient of discharge
A: area of the orifice (m2)
g: gravitational acceleration (m/s2)
h: height from the water surface to the center of the orifice (m)
Q C A 2gh L T
Flow through a Large Orifice
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When the head over the orifice is less than five times the size
(diameter or height of opening) of the orifice, it is a large orifice
for which equation in small orifice is not true because the stream
lines of the jet are not normal to the orifice plane and the velocity
is not constant throughout the orifice.
In the rectangular orifice under the low head shown in the next
slide, the velocity of flow through an elemental strip a depth of h
from the free surface is 2 , and the discharge is
dQ Bdh 2gh
Flow through a Large Orifice
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For the total discharge, integrating between the limits of H1 and H2
and introducing a coefficient
Where B: length of the orifice (m) H1 and H2: height from the free surface to the upper & loweredge of the orifice
Q23C 2gB H ⁄ H ⁄ L T
Flow through a Large Orifice
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Example of Flow through a Small & a Large Orifice
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In a stream of 5 ft width and 3 ft depth, a plate is placed that has a
rectangular orifice 3 ft in length and 1.2 ft in height. The upper
edge of the orifice is 9 in. below the water surface. Determine the
orifice discharge (a) treating it as a small orifice and (b) using the
large orifice approach. Cd=0.6.
Solution
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Example 2
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Discharge from an orifice of 75 mm diameter is 0.02 m3/s under a
constant head of 3 m. An external mouthpiece of the same
diameter is installed that raises the coefficient of contraction from
0.63 to 1.0. The coefficient of velocity is not known and remains
unchanged. Determine discharge from the mouthpiece.
Solution of Example 2
15
Time to Empty
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In the case of a tank or vessel, if the water level is not kept
constant by an inflow, the level will drop due to discharge from
the orifice. The rate of flow through the orifice will vary with the
change in head. Consider that at any instant the head over the
orifice is h, and in time dt it falls by dh. If the volume of water
leaving the tank is equated to the volume of flow through the
orifice, then
Time to Empty
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By expressing the water surface area in the tank, At, by a suitable
formula for a specified shape and by integrating between two
levels, the time needed to lower the water surface can be
determined. Simultaneously with orifice discharge, if an inflow at
a constant rate of Qi takes place into the vessel, the term Qidt
should be subtracted from the right side of the equation.
Example 3
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A vessel has the shape of a cone as shown in Figure. The orifice at
the bottom has a diameter of 100 mm. How long will it take the
cone to become one-half empty from its full depth? Cd=0.6.
3 m
3.5 m
Example 3
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Solution
Problems
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Problems
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Reference
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Gupta, R. S. (2001). Hydrology and hydraulic systems (p. 59). Long Grove, Ill: Waveland Press.
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