Hydraulics Lab (ECIV 3122) Islamic University – Gaza (IUG) Instructors : Dr. Khalil M. Alastal Eng. Mohammed Y. Mousa 1 Experiment (4): Flow measurement Introduction: The flow measuring apparatus is used to familiarize the students with typical methods of flow measurement of an incompressible fluid and, at the same time demonstrate applications of the Bernoulli's equation. The flow is determined using a sudden enlargement, venturi meter, orifice plate, elbow and a rotameter. The pressure drop associated with each meter is measured directly from the manometers. Purpose: To investigate the flow rate using particular flow measuring apparatus. Apparatus: 1. Water flow measuring apparatus (Figure 1). 2. Hydraulic bench. Figure 1: Water flow measuring apparatus
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Hydraulics Lab (ECIV 3122) Islamic University – Gaza (IUG)
Instructors : Dr. Khalil M. Alastal Eng. Mohammed Y. Mousa 1
Experiment (4): Flow measurement
Introduction:
The flow measuring apparatus is used to familiarize the students with typical methods of flow
measurement of an incompressible fluid and, at the same time demonstrate applications of the
Bernoulli's equation.
The flow is determined using a sudden enlargement, venturi meter, orifice plate, elbow and a
rotameter. The pressure drop associated with each meter is measured directly from the
manometers.
Purpose:
To investigate the flow rate using particular flow measuring apparatus.
Apparatus:
1. Water flow measuring apparatus (Figure 1).
2. Hydraulic bench.
Figure 1: Water flow measuring apparatus
Hydraulics Lab (ECIV 3122) Islamic University – Gaza (IUG)
Instructors : Dr. Khalil M. Alastal Eng. Mohammed Y. Mousa 2
Figure 2: Schematic diagram of water flow measuring apparatus
Water flow measuring apparatus is designed as a free-standing apparatus for use on the hydraulics
bench, although it could be used in conjunction with a low pressure water supply controlled by a
valve and a discharge to drain. Water enters the apparatus through the lower left-hand end and
flows horizontally through a sudden enlargement into a transparent venturi meter, and into an
orifice plate, a 90° elbow changes the flow direction to vertical and connects to a variable area flow
meter, a second bend passes the flow into a discharge pipe which incorporates an atmospheric
break.
The static head at various points in the flow path may be measured on a manometer panel. The
water flow through the apparatus is controlled by the delivery valve of the hydraulics bench and
the flow rate may be confirmed by using the volumetric measuring tank of the hydraulics bench.
Hydraulics Lab (ECIV 3122) Islamic University – Gaza (IUG)
Instructors : Dr. Khalil M. Alastal Eng. Mohammed Y. Mousa 3
Theory:
(1) Pressure drop at sudden enlargement
Figure 3: Schematic diagram of sudden enlargement
The test section consists of a 10mm diameter bore with a sudden enlargement to 20mm diameter.
Two manometer are provided.
Consider a sudden enlargement in pipe flow area from area A1 to area A2.
Applying Newton’s second law, the net force acting on the fluid equals the rate of increase of
momentum.
Where is the mean pressure of the eddying fluid over the annular area of the expansion. It is
known from experimental evidence that , since the jet issuing from the smaller pipe is
essentially parallel.
From Bernoulli equation:
Since the flow direction is horizontal .
And substituting from Newton’s second law:
Using Bernoulli equation:
Hydraulics Lab (ECIV 3122) Islamic University – Gaza (IUG)
Instructors : Dr. Khalil M. Alastal Eng. Mohammed Y. Mousa 4
But by continuity equation then:
Where is the coefficient of discharge.
Hydraulics Lab (ECIV 3122) Islamic University – Gaza (IUG)
Instructors : Dr. Khalil M. Alastal Eng. Mohammed Y. Mousa 5
(2) The venturi meter
Figure 4: Schematic diagram of venture meter
The venturi is manufactured from transparent acrylic materials and follows the classic 21°-10°
convergent-divergent design which forms the basis of most engineering standards for venturi flow
meters.
From consideration of continuity between the mouth of the venturi of area A1 and the throat of area
A2:
And on introducing the diameter ratio then:
Applying Bernoulli’s theorem to the venturi meter between section 1 and section 2, neglecting
losses and assuming the venturi is installed horizontally:
Rearranging
And solving for :
The volumetric flow rate is then given by:
Hydraulics Lab (ECIV 3122) Islamic University – Gaza (IUG)
Instructors : Dr. Khalil M. Alastal Eng. Mohammed Y. Mousa 6
The actual discharge will be less than this due to losses causing the velocity through the throat to be
less than that predicted by Bernoulli’s theorem, therefore it is necessary to introduce an
experimentally determined coefficient of discharge . The actual discharge will then be given by:
The coefficient of discharge varies with both the Reynolds number and area ratio. Typical values for
a machined venturi meter are between 0.975 and 0.995.
(3) Orifice plate
Figure 5: Schematic diagram of orifice plate
The orifice flow meter consists of a 20mm bore tube with an orifice of 12mm. The downstream
bore of the orifice is chamfered at 40° to provide an effective orifice plate thickness of 0.35mm.
Manometer tappings are positioned 20mm before the orifice and 10mm after the orifice plate.
Due to the sharpness of the contraction in flow area at the orifice plate, a vena contracta is formed
downstream of the throat in which the area of the vena contracta is less than that of the orifice.
Applying the continuity equation between the upstream conditions of area A1 and the vena
contracta of area Ac:
Where suffix denotes the vena contracta.
Applying Bernoulli’s equation, neglecting losses and assuming a horizontal installation:
Hydraulics Lab (ECIV 3122) Islamic University – Gaza (IUG)
Instructors : Dr. Khalil M. Alastal Eng. Mohammed Y. Mousa 7
Rearranging
And solving for :
The volumetric flow rate is then given by:
The flow area at the vena contracta is not known and therefore a coefficient of contraction may be
introduced so that
The coefficient of contraction will be included in the coefficient of discharge and the equations
rewritten in terms of the orifice area with any uncertainties and errors eliminated by the
experimental determination of the coefficient of discharge. The volumetric flow rate is then given
by:
The position of the manometer tappings has a small effect on the values of the discharge
coefficients which also vary with area ratio, with pipe size and with Reynolds number. The
variations of with Reynolds number is tabulated below for orifice plates with .
Reynolds
Number 2 x 104 3 x 104 5 x 104 7 x 104 1 x 105 3 x 105 1 x 106 1 x 107