FLUID MEASUREMENT / FLOW MEASUREMENT
All the fluid measurement devices are the practical application of Bernoulis equation.
Now they are classified as the following.
Flow measurement device in pressure conduit.
Orifice
Mouth Piece
Venturimeter
Nozzles
Pitot Static Tube
FLOW MEASUREMENT DEVICE IN OPEN CHANNEL
Notches
Wiers
Pitot tubes
1- ORIFICE
It is an opening at the side or bottom of container to discharge the liquid . it is used to measure the flow ratio. They are always running full (submerged). Standard orifice have generally of sharp edge. Discharge through orifice depends partly on the shape of orifice and head causing flow.
There are several reasons you might want to install a restrictive device or orifice in a piping system.
To create a false head for a centrifugal pump, allowing you to run the pump close to its BEP.
To increase the line pressure.
To decrease the flow through a line.
To increase the fluid velocity in a line.
TYPES OF ORIFICE
1. Classification According To Shape Of Orifice
Circular
Square
Rectangle
Triangle
2. Classification According To Size Of Orifice
Small orifice
Large orifice
3. Classification according to nature of discharge
Open orifice or simple orifice
Drowned or submerged orifice
The equation for flow through an orifice is a simple one to understand. Only the units are somewhat awkward.
Q = AV
Q = The flow in cubic feet per second (ft3/sec).
A = The area of the orifice in square feet (ft2).
V = The velocity of the liquid in feet per second (ft/sec).
Either the free discharge orifice or the submerged orifice can be modeled. The equations are the same for both cases. A pull-down menu allows you to select circular or square orifice geometry. For a circular orifice, B is orifice diameter. For a square orifice, B is orifice width and height. A pull-down menu allows you to select an orifice type. Discharge coefficients for the four orifice types are built into the calculation. User-defined discharge coefficients are permitted but be sure that Co= CcCv. The calculation only checks to see if inputs are positive; we do not check to see if Co= CcCv.
Built-in values for orifice discharge coefficients are:
Rounded Sharp-edged Short tube Borda Cc 1.0 0.62 1.0 0.52 Cv 0.98 0.98 0.8 0.98 The short tube C values are valid for L ~ 2.5 B. The Borda type is also known as a re-entrant since it juts into the tank. C values were obtained from Dally et al. (1993) for circular orifices. However, similar values for square orifices are given in Davis (1942), so our calculation uses the Dally values for both circular and square orifices.
Equations. These equations are valid for: H > 1.25 m (4.17 ft) and B > 2.54 cm (1 inch). Values will be computed even if H or B is too small, but a warning message will appear.
where: A = orifice area, B = orifice diameter or width and height, Cc = contraction coefficient, Cv = velocity coefficient, Co = orifice coefficient = CcCv, g = acceleration due to gravity = 32.174 ft/s2 or 9.8066 m/s2, H = head defined in diagrams above, Q = flowrate (discharge), V = horizontal velocity through orifice, X = horizontal trajectory, Y = vertical trajectory.
Solve for flow rate. Solve for discharge coefficient. Solve for orifice area. Solve for gravitational constant. Solve for center line head.
COEFFICIENT OF CONTRACTION
It is ratio between area of jet at vena contracta to area of orifice.
This Cc value varies slightly with head, size and shape of orifice. For sharp edge orifice it value is approximately is 0.64
CC = AC/A = DC/A = 0.64
COEFFICIENT OF VELOCITY
It is ratio of actual velocity of jet at vena contracta to theoretical velocity.
The value of coefficient of velocity is varies for different orifice and its average value is 0.97
EXPERIMENTAL METHOD TO DETERMINE COEFFICIENT OF VELOCITY
Coefficient of velocity Cv may be found experimentally for vertical orifice Cv may be found by vertical or horizontal coordinates of issuing jet. Consider water tank as shown in fig, having water head causing flow. Jet of liquid having horizontal velocity “V” but it is acted upon by gravity with downward acceleration.
COEFFICIENT OF DISCHARGE
It is the ratio between the actual discharge and theoretical discharge.
Average value of CD = 0.61---0.64
Values of CD varies with shape , size, and head over the orifice.
EXPERIMENTAL METHOD TO DETERMINE COEFFICIENT OF DISCHARGE
We'll consider here the case of zero initial velocity, as at the surface of a liquid in a container with an orifice in the side. We assume that a streamline starts at the surface, a distance h above the orifice, and neglect the pressure on the surface of the liquid, since it would cancel out anyway. The streamline then leads somehow to the orifice, and out into the jet that issues from it. We choose the point at which the streamlines are parallel a short distance from the orifice, and find that the velocity there is Vi = √2gh, as given by Torricelli's theorem.
A jet surrounded only by air (or another fluid of small density) is called a free jet, and is acted upon by gravity. A jet surrounded by fluid is called a submerged jet. If the fluid is the same as that of the jet, then buoyancy eliminates the effect of gravity on it. A submerged jet is also subject to much greater friction at its boundary. We shall consider here only free jets of water, and neglect the viscosity of water, which is small, but finite.
A cross section of a circular orifice of diameter Do is shown. The thickness of the wall is assumed small compared to the diameter of the orifice. Because of the convergence of the streamlines approaching the orifice, the cross section of the jet decreases slightly until the pressure is equalized over the cross-section, and the velocity profile is nearly rectangular. This point of minimum area is called the vena contracta. Beyond the vena contracta, friction with the fluid outside the jet (air) slows it down, and the cross section increases perforce. This divergence is usually quite small, and the jet is nearly cylindrical with a constant velocity. The jet is held together by surface tension, of course, which has a stronger effect the smaller the diameter of the jet.
The area A of the vena contracta is smaller than the area Ao of the orifice because the velocity is higher there (converging streamlines). For a sharp-edged, or "ideal" circular orifice, A/Ao = Cc = π/(π + 2) = 0.611. Cc is called the coefficient of contraction. For a sharp orifice, is usually estimated to be 0.62, a figure that can be used if the exact value is not known. For an orifice that resembles a short tube, Cc = 1, but then there are turbulence losses that affect the discharge.
The average velocity V is defined so that it gives the correct rate of discharge when it is assumed constant over the vena contracta, or Q = VA. Then, we can write V = CvVi, where Cv is the coefficient of velocity. The coefficient of velocity is usually quite high, between 0.95 and 0.99. Combining the results of this paragraph and the preceding one, the discharge Q = VA = CvViCcAo = CdAoVi. Cd, the coefficient of discharge, allows us to use the ideal velocity and the orifice area in calculating the discharge.
Discharge through small orifice
When depth D of orifice is less then one fifth of average head over the orifice, Then orifice is called as a small orifice.
D < H / 5 small orifice
D > H / 5 large orifice
Q = CD A Vth
FLOW THROUGH MOUTHPIECE
It is short tube of length equal to two or three times the diameter of tube fitted to and orifice of same diameter provided in tank containing the liquid. Or A mouthpiece is a short tube of length not more than two to three times its diameter, which is fitted to a tank for measuring discharge of the flow from the tank. By fitting the mouthpiece, the discharge through an orifice of the tank can be increased. Mouthpieces are classified on the basis of their shape, position and discharge conditions.
Types Of Mouthpiece
According To Position Of Mouthpiece
External mouth piece
Internal mouth piece
According To Shape Of Mouthpiece
Cylindrical mouthpiece
Converging mouthpiece
Diverging mouthpiece
According To Nature Of Discharge
Mouthpiece running full
Mouthpiece running free
External mouthpiece
If mouthpiece connected to orifice outside the tank, then it is called external mouthpiece.
Internal mouthpiece
If a piece of pipe is connected inside the tank to orifice is called internal mouthpiece.
Mouthpiece Running Full
When a jet of liquid touches the whole internal surface of mouthpiece at outlet then mouthpiece is called running full.
Mouthpiece Running Free
When a jet of liquid is running in such a way that it does not touching the whole internal surface of mouthpiece at outlet then such type of mouthpiece is called running free.
Qact = CD Qth
Qact = Cc Cv Qth
Cc = AC/A
CC = 0.64
Advantages To Use Mouthpiece
As liquid entered in to mouth piece firstly it will contract and then expand.. at section c-c cross sectional area of liquid bend minimum and beyond this stream line will become parallel. This will increase CD (coefficient of discharge). Therefore actual discharge will be more in mouth piece.
VENTURI METER
Venturi Meter are used to measure the velocity of flow of fluids in a pipe. They consist of a short length of pipe shaped like a vena contracta, which fits into a normal pipe-line
The converging tube is an efficient device to converging velocity head to pressure head, while diverging tube converge velocity head to pressure head. The tube may be combined to form venturi tube named after venturi meter. An Italian investigate its principle about 1791.
It is applied to measurement of water by Clamens Herschil in 1886.
Parts Of Venturi meter
Converging Tube
Throat Section
Diverging Tube
Venturi Meters have the following characteristics:-
Theoretically there is no restriction to the flow down the pipe.
They can be manufactured to fit any required pipe size.
The temperature and pressure within the pipe does not affect the meter or its accuracy.
There are no moving parts.
Unfortunately the accurate shape required of the inside of the meter makes them relatively expensive to manufacture.
Difference of pressure is used to measured discharge in pipes
Venturi effect is produced in pipe lines of cross sectional area.
It is easily measured by connect these two section by different manometer.
Types of Venturi meter
Horizontal venturi meter
Vertical Venturi meter
Inclined Venturimeter
Measurement Of Flow.
For a meter with the above arrangements of manometers, the quantity flowing is given by:-
(1)
(2)
Applying Bernoulli's equation at stations 1 and 2
(3)
(4)
(5)
(6)
(7)
where
(8)
(9)
Which can be written as
(10)
In practice, because of fluid resistance, the actual velocity and consequently actual discharge is LESS than that given by the above equations. A coefficient of discharge is therefore introduced, which usually lies between 0.96 to 0.99.
In an actual meter it is not be practical for the tubes to be taken straight up as shown, since the pressures would require the use of long tubes. A more practical arrangement is to measure the difference in pressure rather than the absolute values. This is achieved as shown in the following diagram.
For the above arrangement the Quantity flowing is given by.
(11)
Where the constant K is specific to a particular meter and will include an allowance for a coefficient of discharge.
The Nozzle
A nozzle is short converging tube connected at end of pipe. It is a diverging discharge cone of venture tube, the result of flow nozzles as shown in fig
It is simplest then venturitube and can install between flanges of pipe line. It will answer the same purpose, those at expense of increase friction loss at pipes.
Functions
To measure rate of flow
For servicing the vehicle
Use in impulse turbine
Discharge Coefficient - cd Diameter Ratio d = D2 / D1 Reynolds Number - Re 104 105 106 107 0.2 0.968 0.988 0.994 0.995 0.4 0.957 0.984 0.993 0.995 0.6 0.95 0.981 0.992 0.995 0.8 0.94 0.978 0.991 0.995 The flow nozzle is recommended for both clean and dirty liquids
The rangeability is 4 to 1
The relative pressure loss is medium
Typical accuracy is 1-2% of full range
Required upstream pipe length is 10 to 30 diameters
The viscosity effect high
The relative is medium
NOTCHES AND WEIRS
A weir is a small dam that regulates the flow of water in an open channel, lake, reservoir, etc. Weirs have been used to power mills, raise or maintain water levels, create impoundments and to measure flow. Perhaps the most common use of weirs today is as outlet control structures on detention ponds.
A measuring weir is an overflow structure built perpendicular to an open channel axis to measure the rate of flow of water. A properly built and operated weir of a given shape has a unique depth of water at the measuring station in the upstream pool for each discharge. The crest overflow shape governs how the discharge varies with head measurement
What is weir contraction?
The overflow section shape, usually cut with a sharp upstream corner into a thin plate, is the weir notch, sometimes called the overflow section. When the distances from the sides of the weir notch to the sides of the weir pool are greater than two measurement heads, the water will flow relatively slowly along the bulkhead face toward the overflow opening. As the water from the sides of the channel nears the notch, it accelerates and has to turn to pass through the opening. This turning cannot occur instantaneously, so a curved flow path or side contraction results in which the water springs free to form a jet narrower than the overflow opening width. This effect is also known as an end contraction. The term vertical contraction includes both crest contraction and drawdown at the weir plate. When approach conditions allow full contractions at the ends and at the bottom, the weir is a contracted weir. For full contraction, the ends of the weir should not be closer to the sides and bottom of the approach channel than a specified distance. If the specified distances are not met, then the weir is partially contracted
What is velocity of approach?
Velocity of approach is equal to the discharge divided by the flow section area at the head measuring station. Velocity of approach is important because it can change weir calibrations by effectively reducing the crest length and/or measuring head. In addition, a variable discharge coefficient results as increasing velocity changes the curvature of flow springing from the weir plates.
The sheet of water flowing through a notch or over a weir is known as nappe or vein. The bottom edge of the notch or the top of a weir over which water flows is known as sill or crest. The height above the bottom of the tank or channel is known as crest height. Notches and weirs can be classified based on the followings;
According to the shape of the openings, notches/weirs may be classified
Rectangular type
Suppressed Rectangular Weir
Rectangular weir with end contraction
Cipoletti weir
Triangular Weir / V notch
Broad Crested Weir OR Free Fall
Triangular Weir / V notch
What is a V-notch (triangular) weir?
As the name suggests, a V-notch or triangular weir has a triangular opening through which discharge occurs. Regarded as highly accurate, these types of weirs are suitable for low discharges because the head increases more rapidly on a triangular section. V-notch weirs are not noticeably affected by the velocity of approach.
Example of a V-notch weir
The discharge from a V-notch weir can be determined using:
For fully contracted weirs with a notch angle between 20 and 100 degrees the coefficient of discharge ranges from 0.57 to 0.59.
Weirs are typically installed in open channels such as streams to determine discharge (flowrate). The basic principle is that discharge is directly related to the water depth above the crotch (bottom) of the V; this distance is called head (h). The V-notch design causes small changes in discharge to have a large change in depth allowing more accurate head measurement than with a rectangular weir. Equations
Rectangular Weir
The rectangular weir is the most commonly used thin plate weir. Weirs are typically installed in open channels such as streams to determine discharge (flowrate). The basic principle is that discharge is directly related to the water depth (h) in the figure above; h is known as the "head."
What is a suppressed weir?
When the sides of the flow channel act as the ends of a rectangular weir, no side contraction exists, and the nappe does not contract from the width of the channel. This type of weir is a suppressed weir. The falling sheet of water springing from the weir plate is the nappe. It can be "suppressed," "partially contracted," or "fully contracted." Suppressed means there are no contractions. A suppressed weir's notch width (b) is equal to the channel width (B); thus, there really isn't a notch - the weir is flat all the way along the top. For a weir to be fully contracted, (B-b) must be greater than 4hmax, where hmax is the maximum expected head on the weir (USBR, 1997). A partially contracted weir has B-b between 0 and 4hmax. Weir contractions cause the water flow lines to converge through the notch.
Equation The Kindsvater-Carter rectangular weir equation (ISO, 1980): The sum b+Kb is called "effective width"
the sum h+Kh is called "effective head."
value for g is 9.8066 m/s2
Kh=0.001 m.
Ce is a function of b/B and h/P,
Kb is a function of b/B.
Our "Solve for Flowrate" calculation is analytic, but our "Solve for Head" and "Solve for Notch Width" calculations require numerical solutions since Ce and Kb cannot be computed directly, as they are functions of h and/or b.
Cipoletti / Trapezoidal Weir
Introduction Weirs are typically installed in open channels such as streams to determine discharge (flowrate). The basic principle is that discharge is directly related to the water depth (h) in the figure above; h is known as the "head." The Cipoletti (or trapezoidal) weir has side slopes in the vertical to horizontal ratio of 4 to 1. Cipoletti weirs are considered fully contracted and have the installation requirements shown below. The discharge coefficient for Cipoletti weirs is 3.367 (in English units), and it does not depend on L or P like it does for a rectangular weir.
What is a trapezoidal weir?
A trapezoidal weir has an opening comprised of a rectangle bounded by two triangles. The discharge through this type of weir is determined by summing the discharge over the rectangular section with end contractions with the discharge from the triangular or V-notch section.
What is a Cipoletti weir?
A Cipoletti weir is a trapezoidal weir with a side slope of 1 horizontal to 4 vertical.
The discharge through a Cipoletti weir can be determined using the following formula:
Equation The Cipoletti weir equation is shown below for Q in cfs (ft3/s) and head and length in feet units (USBR, 1997). Our calculation allows you to work in a variety of units. Note that L is measured along the bottom of the weir (called the crest), not along the water surface.
Weir Design
What is a broad-crested weir?
A weir in the form of a relatively long raised channel control crest section is a broad-crested weir. The flow control section can have different shapes, such as triangular or circular. True broad-crested weir flow occurs when the upstream head above the crest is between the limits of about 1/20 and 1/2 the crest length in the direction of flow.
Discharge over a broad-crested weir is determined as follows:
This equation can be modified to account for end contractions and the velocity of approach following the form of the rectangular sharp-crested weir equation. The coefficient of discharge is generally between 0.85 and 1.1. Because of the wide variety in broad crested weir shapes, it is recommended that the coefficient of discharge be calibrated in the field
What is a long-crested weir?
Long-crested weirs provide more weir crest length by installing the weir at some configuration other than perpendicular to the channel. They are used in open channel irrigation systems to minimize water surface elevation fluctuations. The thickness of the water layer over the crest is directly related to the length of the weir crest. A longer crest length produces a thinner water layer which in turn creates smaller variations in the upstream water levels. It is important to note that long-crested weirs are not intended as hydraulic measurement devices.
What is a sharp-crested weir?
If the notch plate is mounted on the supporting bulkhead such that the water does not contact or cling to the downstream weir plate or supporting bulkhead, but springs clear, the weir is a sharp-crested or thin-plate weir. The top thickness of the crest and side plates should be between 0.03 and 0.08 inches.
Example of a sharp-crested weir (Food and Agricultural Organization 1993)
For a rectangular sharp-crested weir that takes end contractions and the velocity of approach into account the discharge is determined by:
where
Q Cd g L n H vo discharge (cfs) coefficient of discharge gravity (ft/s2) crest length (ft) number of end contractions head (ft) velocity of approach (ft/s)
By neglecting the velocity of approach the rectangular sharp-crested weir equation reduces to:
If we assume that the head is not greater than one-third the weir length, the value of the discharge coefficient is between 0.6 to 0.62. If end contractions are also neglected the rectangular sharp-crested weir equation further reduces to a form known as the Francis formula.