University of Bolton, Mechanical Engineering, AME5003 – Thermofluids and control systems

Venturi and orifice/ Engine Cycles

Assignment Number: 1

Author: Mohammed Rahman

Taught by: Dr Safa Alhakeem

Student Number: 1409201

ID: MMR1AES

DATE OF SUBMISSION: 25 April 2016

University of Bolton, Mechanical Engineering, AME5003 – Thermofluids and control systems

Abstract

This assignment is made up of two parts. The first part of the assignment will include a written report for a Laboratory experiment. This includes using a Hydraulics bench flowmeter demonstration apparatus, in which myself and 3 other members collectively obtained flow measurements in pipes using a Venturi meter and Orifice meter and Rotameter. In the process of this assignment I will be establishing the relationship between flowrate and pressure difference, and thereby determining the value for the coefficient of discharge.

The second part of the assignment is about engine cycles. For this will will describe different types of cycles and also state their purposes. I will also form calculations to elaborate on the performance of a Carnot cycle.

Contents

University of Bolton, Mechanical Engineering, AME5003 – Thermofluids and control systems

Apparatus

Hydraulics bench flowmeter demonstration apparatus

The apparatus is designed to measure the flowrate using the Venturi meter, Orifice meter and rotameter.

Venturi meter: Inlet pipe diameter, d1 = 31.75mm. Throat diameter, d2 = 15mm.

Orifice meter: Inlet pipe diameter, d1 = 31.75mm. Orifice diameter, d2 = 20mm.

University of Bolton, Mechanical Engineering, AME5003 – Thermofluids and control systems

Introduction

Venturi meter and orifice meters are the most commonly used flow meters for measuring mass/volumetric flow rate or velocity of a flowing fluid. We will observe the flow of water through a pipe, in which it is allowed to flow through the meter at different rates ranging from zero to the maximum.

Hydraulics Laboratory Experiment

Flow measurement in pipesVenturi and Orifice meters

purpose

To calibrate a Venturi and Orifice meter by establishing the relationship between flowrate and pressure difference, and thereby determining a value for the coefficient of discharge.

University of Bolton, Mechanical Engineering, AME5003 – Thermofluids and control systems

Venturi meter: Inlet pipe diameter, d1 = 31.75mm. Throat diameter, d2 = 15mm.

Orifice meter: Inlet pipe diameter, d1 = 31.75mm. Orifice diameter, d2 = 20mm.

Theory

The flowrate through a Venturi and Orifice meter can be found from the equation

Q=Cda1a2

√a12−a2

2√2 gH

where the cross-sectional areas are a1 for the inlet pipe and a2 for the throat or orifice.

The term

a1a2

√a12−a2

2is known as the meter coefficient, K.

Procedure

The apparatus has been adjusted to give a steady flowrate indicated as 20 on the Rotameter scale.

Record the manometer readings h1, h2, h6 and h7. Measure the flowrate by recording the time taken to collect a volume 10 litres. Adjust the flow control valve to obtain readings of 18, 16, 14,12 and 10 on the rotameter scale. Record manometer levels and measure flowrate for each rotameter reading.

University of Bolton, Mechanical Engineering, AME5003 – Thermofluids and control systems

Observations

H1 (mm) H2 (mm) H6 (mm) H7 (mm) Volume (liters) Time (sec)385 205 250 135 10 34.6365 184 210 115 10 40.27322 185 195 115 10 42.96305 185 180 120 6 28.79285 190 170 125 6 32.58260 190 160 128 6 40.18

Table of Results

1 2 3 4 5Hv = (h1 – h2) m Ho = (h6 – h7)

mQ

m³Hv½ Ho½

0.18 0.12 0.00028 0.424 0.3460.181 0.095 0.00024 0.425 0.3080.137 0.08 0.00023 0.370 0.2820.12 0.06 0.00020 0.346 0.244

0.095 0.045 0.00018 0.308 0.2120.07 0.032 0.00014 0.264 0.178

Q = Volume/time 1000 litres/s = 1 m3/s HV = Venturi head HO = Orifice head

Analysis

From the theory, Q∝H1/2. Verify this relationship Q

By plotting Q vs H1/2 for the venturi and orifice meters.

Determine the slope of the graph, m, for each meter, m =1

where m=Q /H1/2H1/2

Determine a value of Cd for each meter from

Cd=1

K √2 gQH1/2

= 1K √2 g

⋅m

University of Bolton, Mechanical Engineering, AME5003 – Thermofluids and control systems

Conclusions

The experiment is carried out to experimentally verify the Bernoulli's Equation and to compare the pressure difference in venturi, orifice and variable area meter. The experiment is also carried out to calculate the head loss from experiment data for a rotameter. Based on the result that obtained, the pressure are varies according to the area that the fluid flow. Bernoulli's principle states that in a moving fluid, when the area decrease the velocity is increase and the pressure inside the fluid decrease. According to the laws governing fluid dynamics, a fluid's velocity must increase as it passes through constriction to satisfy the principle of continuity,

University of Bolton, Mechanical Engineering, AME5003 – Thermofluids and control systems

while its pressure must decrease to satisfy the principle of mechanical energy. In conclusion, the flow rate in venturi meter is higher than orifice meter. RECOMMENDATION In this experiment, there are few recommendations that can be applied to get better data and results, thus the experiment can be run properly and systematically. In order to get the accurate data, the experiment must be repeated at least two times and determined the average value of the data collected. When run the experiment, make sure that there is no air bubbles inside the equipment, because it will affect the results. Besides that, the water supply must be connected correctly and make sure that there is no any leakage inside the system. In taking the reading, the eyes must be parallel to the scale and the meniscus in order to prevent the parallax error and also to get accurate reading

Comment on the graphs, and compare the values you have obtained for Cd for each meter with expected values, as quoted in standard textbooks. Comment briefly on relevant choice of meter.

ENGINE CYCLES

University of Bolton, Mechanical Engineering, AME5003 – Thermofluids and control systems

Q1 Three (A-C) theoretical engine p-v cycles using air are described below. Each cycle comprises of 4 processes. Using the information supplied construct the general form of each cycle clearly labelling each cardinal state point (1-4) or (1-5) and name each cycle.

Cycle A

1-2 isentropic compression

2-3 Constant volume increase in pressure

3-4 isentropic expansion

4-1 Constant volume decrease in pressure

Cycle B

1-2 isentropic compression

2-3 Constant pressure increase in volume

3-4 Isentropic Expansion

4-1 Constant volume decrease in pressure

Cycle C

1-2 isentropic compression2-3 Constant volume increase in pressure

3-4 Constant pressure increase in volume

4-5 isentropic expansion

5-1 Constant volume decrease in pressure

Q2 Describe, with the aid of sketches, the four reversible processes that make up the Carnot Cycle. If a Carnot heat engine receives 500 kJ heat per cycle from

University of Bolton, Mechanical Engineering, AME5003 – Thermofluids and control systems

a high temperature source of 452oC and rejects heat to a low temperature sink at 15oC determine:

The Carnot cycle is composed of four totally reversible processes, these are:

Isothermal heat addition Isentropic expansion Isothermal heat rejection Isentropic compression

For both ideal and actual cycles: the thermal efficiency increases with an average increase in temperature at which heat is supplied to the system or with a decrease in the average temperature at which heat is rejected from the system.

Remind me later

Review

Isentropic means no change in entropy ( ). An adiabatic process is a process with no heat transfer ( ). We defined for reversible processes. So generally an adiabatic process is not necessarily isentropic -- only if the process is reversible and adiabatic we can call it isentropic.

University of Bolton, Mechanical Engineering, AME5003 – Thermofluids and control systems

University of Bolton, Mechanical Engineering, AME5003 – Thermofluids and control systems

. If a Carnot heat engine receives 500 kJ heat per cycle from a high temperature source of 452oC and rejects heat to a low temperature sink at 15oC determine

a) The thermal efficiency of the engineb) The amount of heat rejected to the sink per cycle

University of Bolton, Mechanical Engineering, AME5003 – Thermofluids and control systems

Bibliography

https://www.google.co.uk/search?q=the+four+reversible+processes+that+make+up+the+Carnot+Cycle&biw=1920&bih=960&site=webhp&source=lnms&tbm=isch&sa=X&ved=0ahUKEwj_m7_H-5rMAhVMLcAKHQ38C3cQ_AUIBigB#imgrc=ILeXTPe14XOgPM%3A

https://www.youtube.com/watch?v=9X0WTOqlmCI

http://www.engineeringtoolbox.com/orifice-nozzle-venturi-d_590.html

efficiency (= useful energy out / total energy in). Clearly without the word “useful” the efficiency would be 100% in all systems. (Why? Because ‘energy is conserved’)

http://hazeldorothy03orificevsventurimeter.blogspot.co.uk/

http://www.oberlin.edu/physics/dstyer/P111/Carnot.pdf

http://ffden-2.phys.uaf.edu/webproj/212_spring_2014/Keanu_Paikai/Keanu_Paikai_2/EfficiencyofEngines.html

University of Bolton, Mechanical Engineering, AME5003 – Thermofluids and control systems

Objectives:

1. To find the coefficient of discharge for venturi meter. 2. To find the coefficient of discharge for orifice meter.

Theory:

Venturi meter and orifice meter are the commonly used flow meters for measuring mass/volumetric flow rate or velocity of the flowing fluid. These flow meters are also known as variable head meters. They are categorized as full-bore meter as measurement of the fluid takes place when it flows through a conduit or channel.

Venturi meter:

The venturi meter has a converging conical inlet, a cylindrical throat and a diverging recovery cone. It has no projections into the fluid, no sharp corners and no sudden changes in contour. The following figure shows the venturi meter with uniform cylindrical section before converging entrance, a throat and divergent outlet.

Convergent Cylindrical inlet

Entrance

Throat

Divergent outlet

D

d

University of Bolton, Mechanical Engineering, AME5003 – Thermofluids and control systems

Pressure taps

Figure 1. Venturi meter

The converging inlet section decreases the area of the fluid stream, causing the velocity to increase and the pressure to decrease. The low pressure is measured in the center of the cylindrical throat as the pressure will be at its lowest value, where neither the pressure nor the velocity will be changing. As the fluid enters the diverging section the pressure is largely

recovered lowering the velocity of the fluid. The major disadvantages of this type of flow detection are the high initial costs for installation and difficulty in installation and inspection.

The Venturi effect is the reduction in fluid pressure that results when a fluid flows through a constricted section of pipe. The fluid velocity must increase through the constriction to satisfy the equation of continuity, while its pressure must decrease due to conservation of energy: the gain in kinetic energy is balanced by a drop in pressure or a pressure gradient force. An equation for the drop in pressure due to Venturi effect may be derived from a combination of Bernoulli’s principle and the equation of continuity.

The equation for venturi meter is obtained by applying Bernoulli equation and equation of

continuity assuming an incompressible flow of fluids through manometer tubes. If V

1

and V

2

are the average upstream and downstream velocities and ρ is the density of the fluid, then using Bernoulli’s equation we get,

........................... (1)

University of Bolton, Mechanical Engineering, AME5003 – Thermofluids and control systems

where

1

and

2

are kinetic energy correction factors at two pressure tap positions. Assuming density of fluid to be constant, the equation of continuity can be written as:

............................. (2) where D

1

and D

2

are diameter of pipe and throat in meters respectively.

University of Bolton, Mechanical Engineering, AME5003 – Thermofluids and control systems

Eliminating V

1

from equation (1) and equation (2) we get,........................... (3)

where β is the ratio of the diameter of throat to that of diameter of pipe.If we assume a small friction lose between two pressure taps, the above equation (3) can be

corrected by introducing empirical factor C

v

and written as,............................. (4)

University of Bolton, Mechanical Engineering, AME5003 – Thermofluids and control systems

The small effect of the kinetic energy factors α

1

and α

2

are also taken into account in the

definition of C

v

.

University of Bolton, Mechanical Engineering, AME5003 – Thermofluids and control systems

Volumetric flow rate Q

a

can be calculated as:

Q

a

= V

2

S

2

= ........................... (5)

University of Bolton, Mechanical Engineering, AME5003 – Thermofluids and control systems

where, S

2

is the cross sectional area of throat in m

2

. Substituting (P

1

– P

2

) = ρgH in above equation (5) we get,

Q

a

= V

2

S

2

= ............................... (6)where ΔH is the manometric height difference * (specific gravity of manometric fluid – specific

gravity of manometric fluid of water).

University of Bolton, Mechanical Engineering, AME5003 – Thermofluids and control systems

Orifice meter:

An orifice meter is essentially a cylindrical tube that contains a plate with a thin hole in the middle of it. The thin hole essentially forces the fluid to flow faster through the hole in order to maintain flow rate. The point of maximum convergence usually occurs slightly downstream from the actual physical orifice this is the reason orifice meters are less accurate than venturi meters, as we cannot use the exact location and diameter of the point of maximum convergence in calculations. Beyond the vena contracta point, the fluid expands again and velocity decreases as pressure increases.

Head loss

D 1

Figure 2. Orifice meter

Vena Contracta

D2

Variable distance

D 1

The above figure 2 shows the orifice meter with the variable position of vena contracta with respect to plate. Orifice meter uses the same principle of continuity equation and Bernoulli principle to calculate the volumetric flow rate, as shown above for venturi meter.

So,

Q

a

= V

2

S

2

= ............................... (7)

University of Bolton, Mechanical Engineering, AME5003 – Thermofluids and control systems

Here C

o

is the orifice discharge coefficient.

Procedure:

1. Check all the clamps for tightness. 2. Check whether the water level in the tank is sufficient such that the suction pipe of

pump

is completely immersed.

3. For measurement through venturi, open the outlet valve of the venturi meter and close the

valve of orifice meter.

4. For a good amount of variation in discharge also close the by-pass valve of pump. 5. Now switch on the pump. 6. Open the gate valve and start the flow. 7. If any air bubbles exist in U-tube manometer remove them through air cock valve.

Operate the air cock valve slowly and cautiously to avoid mercury run away through

water.

8. Wait for a while for stabilization of flow. 9. Close the gate valve of measuring tank and measure the time for discharge of five

liters

University of Bolton, Mechanical Engineering, AME5003 – Thermofluids and control systems

of water and the manometer difference. Before taking any measurements, make sure the

flow is stable.

10. Repeat the procedure by changing the discharge by slowly opening the by-pass valve and

take the six readings.

11. Repeat the same for orifice meter.

Given data:

For venturi meter:

Cross sectional area of throat in venturi meter (S

2

) = 1.76*10

-4

m

2

Ratio of diameter of throat to pipe (β) = 0.4848

University of Bolton, Mechanical Engineering, AME5003 – Thermofluids and control systems

For orifice meter:

Cross sectional area of throat in venturi meter (S

2

) = 1.54*10

-4

m

2

Ratio of diameter of throat to pipe (β) = 0.4904

http://www.academia.edu/18747069/Lab_Report_Flowmeter_Measurement_Apparatus_FM101_2015_

http://site.iugaza.edu.ps/mymousa/files/Experiment-4-Fluid-mechanics-lab.pdf

http://www.slideshare.net/jeufier/calibration-of-orifice-venturi-meter