Jordan University of Science and Technology

Mechanical Engineering Department

Student Name: hussain salh alomary

Experiment Name: Flowrate Measurement
Experiment Number: 1
Student ID Number :126682
Abstract 5%

Introduction 10%

Theory 10%

Apparatus & procedure 10%

Data & calculations 40%

Tables & figures 10%

Discussion 10%

Conclusion 5%

Total 100%
:Abstracta
During this Experiment we are developing our knowledge on devices used to
measure the flow rate of fluids flowing through pipes by measuring them
experimentally and calculating the flow rate theoretically and comparing the two
.values

:Objectives
 To determine the calibration curve of venture meter, orifice meter and
Rotameter.
 Determine the discharge coefficient of venture meter, orifice meter as a
function of Re.
 To compare between the three types of flow meters from point of view of
pressure drop across them.

:Introduction
In physics and engineering, in particular fluid dynamics and hydrometry, the
volumetric flow rate (also known as volume flow rate, rate of fluid flow or volume
velocity) is the volume of fluid which passes per unit time; usually represented by
.the symbol Q (sometimes V̇ ). The SI unit is m3/s (cubic meters per second)
Volumetric flow rate can also be defined by:
Q=v*A
where:

 v = flow velocity
 A = cross-sectional vector area/surface

1. Actual Flow Rate has two types:

 Mass Flowrate (m)
 Volumetric Flowrate (Q)

2. Theoretical Flowrate
Devices used in our experiment for measuring Actual flow rate are:
1. Venturi
2. Orifice
3. Rotameter
 Figure 1.1: Venture meter Diagram

Figure 2.1: Orifice flow meter Diagram

 Figure 3.1: Rotameter used to calculate head losses

 Theory:
By controlling water in a weighting device for a given length of time, volume flow
rate can be determined from:
Q experimental = m / ρt [m³ /s]
Where: t = time in sec.
m = mass in kg.
ρ = density of water in kg / m
The basic theory used here is continuity equation (conservation of mass) which
states that:
A 1 V 1 = A n V n = Q = Q ideal
We must find relation for [Q exp ] using the weighing tank. This equation is :
Q exp= m/ρt [m^3/sec]
Using Bernoulli's Equation:
1 1
P1+ρgh1+ ρ v 12 = P2 + ρgh2+ ρ v 22
2 2
We obtain the equations used to calculate Q ideal for the venture meter which is:
A1
∗√ 2 g( h1−hn)
A 22
Q ideal =
√ An2
−1

The same equation is used to calculate Q ideal for the nozzle and orifice.
We know that these equations give us the [Q ideal ] and it is not identical
to [Q exp ] as there is some factor between them, this factor is (C)
(discharge factor), the relation is :
Q exp
C=
Qideal
The relation between flow rate and pressure difference and meter
area ratio are given as follows:

2∗(P 1−P 2)

∆pman = ρ g (∆hman) [Pa]

V =
√(
ρ[
A1 2
A2 )
−1]
(m/s)

∆pman = p2 – p1;
∆pLoss = p3 – p1
Qth = V1 * A1 [m3/s]
Qact = (accumulated water mass/∆t)/ρwater [m3/s]
CD = Qact /Qth
Cp = ∆ploss/(0.5ρV2)
Re = ρV1D1/μw

:Apparatus and Procedure

Water pumping table with weighting device to find the mass rate of flow
Venture tube with known area variation and manometer taps for finding the
pressure distribution. Venture pressure and flow is controlled by supply and out let
valves. Backpressure for the manometers is controlled by an air bleed valve on the
manifold

:Procedure
The Flow-Measuring Apparatus is connected to the hydraulic bench ,water supply
and the control value is adjusted until the rotameter is about at the mid-position in
.its calibrated tapered tube
Air is removed from manometric tubing by flexing it. The pressure within the
manometer reservoir is now varied and the flow rate decreased until with no flow
:and then
.Opening the outlet valve to fill the position to permit highest flow rate
Reading and recording the manometer high in all tubes
.Reading and recording the Rotameter scale reading
Measuring the flow rate by timing the collection of a known quantity of water in the
.bench weighing tank

;The diameter of the sections A, B, C, D, and the Orifice &amp

Reducing the flow rate by partially closing the outlet valve to produce
approximately five tests in the ranger of the maximum flow rate to the minimum
.flow rates and then repeating the measuring process

Figure 4.1: Apparatus used to conduct our flow measurement experiment.

:Data and Calculations

 Figure 5.1: Data collected during our flow measurement experiment.
P1 P2 P3 P4 P5 P6 P7 P8 H Time for
mm mm mm mm mm mm mm mm Rotameter flowrate
H2O H2O H2O H2O H2O H2O H2O H2O floater 6kg
height (mm) (s)
256 230 250 250 224 230 228 128 53 50
284 228 270 274 212 222 220 120 87 30.91
332 224 304 318 190 210 206 104 125 20.9
388 218 342 362 164 196 192 86 155 16.47

 P 1 – P 2 for venturi meter to calculation flow rate.

 P 1 – P 3 for venturi meter to calculation head loss.
 P 4 – P 5 for orifice meter to calculation flow rate.
 P 4 – P 6 for orifice meter to calculation head loss.
 P 7 – P 8 for rotameter to calculation head loss.
Where:-
 Diameter at P 1 26 mm.
 Diameter at P 2 16 mm.
 Diameter at P 3 26 mm.
 Diameter at P 4 51.9 mm.
 Diameter at P 5 orifice hole 20 mm.
 Diameter at P 6 51.9 mm.
  Mass (m) = 6 Kg.

:Tables and Figures

 Calculations:
Table 1.1: Calculations for Actual Q
Number Of Trial Time (s) Q ACTUAL = m / ρt [m³ /s]
1 50 0.00012
2 30.91 0.000194112
3 20.9 0.000287081
4 16.47 0.000364299

The pressure at any point = ρg(Δh)

Table 2.1: Calculations for Pressure in pascals
P1 (Pa) P2 (Pa) P3 (Pa) P4 (Pa) P5 (Pa) P6 (Pa) P7 (Pa) P8 (Pa)
2511.36 2256.3 2452.5 2452.5 2197.44 2256.3 2236.68 1255.68

2786.04 2236.68 2648.7 2687.94 2079.72 2177.82 2158.2 1177.2

3256.92 2197.44 2982.24 3119.58 1863.9 2060.1 2020.86 1020.24

3806.28 2138.58 3355.02 3551.22 1608.84 1922.76 1883.52 843.66

To Calculate Area we use :

A= 3.14*{ (D/2000)^2} (m^2)
Table 3.1:calculations for area from diameters given.
D1(mm) 26 A1 (m2) 0.00053066
D2 (mm) 16 A2 0.00020096
D3(mm) 26 A3 0.00053066
D4(mm) 51.9 A4 0.002114484
D5 (mm) Orfice hole 20 A5 0.000314
D6 (mm) 51.9 A6 0.002114484

Table 4.1:Calculations for Velocity.

V1 V2 V4 V5
0.270495839 0.714278075 0.10606357 0.71423473
0.396979361 1.048273625 0.163785485 1.102935549
0.551297207 1.455769188 0.235333932 1.584744579
 0.691669102 1.826438722 0.292692882 1.971001184

To find the discharge for the Venturi meter we use :-

Q th = A 1 *V 1 [m³ /s]
C D = Q act / Q th
C D : discharge coefficient ( if C=1 then Q act. =Q th. )

Table 5.1: Cd for orifice and venturer as functions of reylond numbers

Q1 Q2 Re Q4 Q5 Re CD1 CD4
THEORETICAL THEORETICAL THEORETICAL THEORETICAL
0.000143541 0.000143541 4657.54424 0.00022427 0.00022427 3645.49620 0.83599620 0.535070039
7 4 2
0.000210661 0.000210661 6835.40621 0.000346322 0.000346322 5629.44812 0.92144191 0.560495929
4 6
0.000292551 0.000292551 9492.53469 0.00049761 0.00049761 8088.62983 0.98130230 0.576920593
5 8 5
0.000367041 0.000367041 11909.5342 0.000618894 0.000618894 10060.1063 0.99252835 0.588628272
1 4 6

Table 6.1:Calculations for delta P loss and Cp for venturi meter.

TIME P1 P3 Delta P loss Cp1
50 256 250 58.86 1.60890009
30.91 284 270 137.34 1.742975098
20.9 332 304 274.68 1.807529731
16.47 388 342 451.26 1.886514223

Table 7.1:Calculations for delta P loss and Cp for orifice meter.

TIME P4 P6 Delta P loss Cp4
50 250 230 196.2 34.88160977
30.91 274 222 510.12 38.03220678
20.9 318 210 1059.48 38.26076572
16.47 362 196 1628.46 38.01743125

Table 8.1: Calculations for delta P loss for the rotameter

TIME P7 P8 Delta P loss
50 228 128 981
30.91 220 120 981
20.9 206 104 1000.62
16.47 192 86 1039.86

Calculations Sample:
  Q act = m / ρt
Where:-
m = 6Kg
ρ = 1000 (kg/m 3 )
Then for trial #1 Q = 6/(1000*50) = 0.00012 [m³ /s].

 The pressure at any point = ρg(Δh)

Where:-
ρ = 1000 (kg/m 3 )
g = 9.81 m/s 2
Then for h = 256 mm
P=1000*9.81*0.23=2511.36 pa

 The Area
A = pi *[(D/2)^2] [m 2 ].
A 1 = 3.14 * [(26/2000)^2]= 0.00053066 m^2
For Velocity calculations we use the following equation:

2∗( P 1−P 2)
V =
√(
ρ[
A1 2
A2 )−1]
(m/s)

And V2= V1*(A1/A2)

 The discharge for the Venturi meter

Q th = A 1 *V 1 [m³ /s]
Q th = 0.00053066 * 0.270495839 = 0.000143541
[m³ /s]

 The discharge for the Orifice meter

Q th = A 4 *V 4 [m³ /s]
Q th = 0.002114484* 0.10606357
=0.00022427 [m³ /s]
  C D = Q act / Q th
C D for Venturi meter at Time = 50 sec
C D = 0.00012 / 0.000143541
= 0.835996202

 Δp Loss :-
Δp Loss = (P 1 – P 3 )*g*ρ [pa]
Δp Loss = (256- 250)*9.81*1000*0.001 = 58.86[pa]
 C p :-
C p =2* Δp Loss /(ρ*V ^2 ) =( 58.86 *2)/(1000*(0.270495839^2)) =
1.60890009

Cp Versus Re

45

40

35

30
Venturi
25 e
Cp

20 Orifice

15

10

0
3000 4000 5000 6000 7000 8000 9000 10000 11000 12000 13000

Re

Figure 6.1: Diagram of Cp versus Reynold's Number

 Cd Versus Re
1.2

0.8

0.6 Ventur
Cd

ie
0.4 Orifice

0.2

0
3000 4000 5000 6000 7000 8000 9000 10000 11000 12000 13000
Re

Figure 7.1: Diagram of Cd Versus Reynold's Number

Rotameter Q actual Vs H

0
Q actual

0
40 60 80 100 120 140 160 180

H (mm)

Figure 8.1: Diagram of Q actual for a rotameter Vs. Height

 Q actual Vs Sqrt Delta Pressure

0
Venturi
Q actual

0 Orifice

0
0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Sqrt( Delta Presure)

Figure 9.1: Diagram for Actual Q vs Square root of change in pressure

:Discussion
- It is clearly shown in Table 1 that there is a large decrease in pressure in the
rotameter indicating a great head loss in it. On the other hand, the decrease in
pressure in the venture and orifice is relatively smaller indicating a smaller head loss.
In addition to that, the pressure drop in the orifice is greater than it is in the venture.
Head losses and friction losses impose higher load on the pump, so it is important to
choose the best volumetric flow meter that is suitable to the specified application
- It is also obvious from the results in Tables 4 and 6 that as the
pressure decreases, the velocity increases.
- Figure 3 shows that the C D for the venture is higher than the orifice
whereas the behavior is the opposite in the case of Cp in figure 8.
- Figures 9 and 10 are the calibration curves for the venture, orifice,
and rotameter which will make it easier for the experimentalist to
take the readings and convert them directly in flow rates.

:Conclusion
The volume flow rate is constant at any point along the venture tube, or in other
words when the cross-section area decreases the velocity of flow increases and the
pressure decreases (according to Bernoulli’s equation) in the same ratio at any
section.
The energy balance equation for a steady state in compressible flow is known as the
Bernoulli equation. The pressure decreased across the venture is recoverable while
in the orifice is not from the result & the graph above we conclude that the
discharge is different about the system where the inlet discharge is almost equal to
discharge for venture, but it is less than discharge for Orifice this is because different
inlet diameter for all component. And we also conclude that the kinetic head is
different for component because the velocity increase with less diameter so the
kinetic head for Orifice is larger than venture & inlet pipe.