UNIVERSITI TENAGA NASIONAL

COLLEGE OF ENGINEERING

DEPARTMENT OF MECHANICAL ENGINEERING

ENGINEERING MEASUREMENTS AND LAB

(MESB 333)

PROJECT REPORT

RELATIONSHIP BETWEEN PRESSURE AND VELOCITY OF FLUIDS

GROUP MEMBERS:

1. ID: ME091513 NAME: PRAKASH A/L KRISHNAMURTI

2. ID: ME091512 NAME: NAVIN RAJ A/L K SAKARAN

3. ID: ME091515 NAME: THINNESH CHELVAM

4. ID: ME091919 NAME: PREMALA KRISHNAMOORTHY

5. ID: ME091751 NAME: NUR FARHANA AHMAD

SECTION : 04A GROUP : 01

INSTRUCTOR : PROF. DR.SAIFUDDIN BIN HJ. M. NOMANBHAY

Performed Date Due Date Submitted Date

19/08/2015 24/08/2015 24/08/2015

Page | 2

NO SUBJECT PAGE

1 STATEMENT OF OBJECTIVE 3

2 APPARATUS AND EQUIPMENT 3

3 ABSTRACT AND THEORY 3 – 6

4 PROCEDURE 7

5 DATA, OBSERVATION AND

RESULT

8 - 9

6 ANALYSIS AND DISCUSSION 10

7 CONCLUSION 11

8 REFERENCE 12

TABLE OF CONTENT

Page | 3

EXPERIMENT: VELOCITY OF FLUIDS

To study the relationship between area, velocity and flow rate of fluid and determine

the type of the flow.

1) 1500 ml bottle

2) Pail

3) 3 bottle cap with 5mm, 10mm and 15mm diameter

4) Bottle with measuring lines

5) Water

Relationship between flow rate and diameter

Flow Rate

Flow rate is a measurement of the volume of water that flows through a pipe in a given

amount of time. Generally, flow rate is recorded in terms of gallons per minute.

Effects of Pipe Size

If the pressure behind water flow in a pipe is kept constant, the size of the pipe will

directly affect the flow rate. If the diameter of the pipe is increased, the flow rate will

decrease. Also, If the length of the pipe is increased, the flow rate will decrease due

to friction.

Considerations

Flow rate is also affected by change in a pipe's elevation, bends or curves in a pipe,

and the roughness of a pipe's surface. So while the relationship between pipe size and

flow rate is constant, size is not necessarily the deciding factor in a pipe's flow rate.

OBJECTIVE

APPARATUS

SUMMARY OF THEORY

Page | 4

Relationship between velocity and area

A is the cross-sectional area and v is the average velocity. This equation seems logical

enough. The relationship tells us that flow rate is directly proportional to both the

magnitude of the average velocity (here after referred to as the speed) and the size of

a pipe. The larger the diameter, the greater its cross-sectional area.

Velocity of fluid in pipe is not uniform across section area. Therefore a mean velocity

is used and it is calculated by the continuity equation for the steady flow as:

Pipe diameter calculator

Calculate pipe diameter for known flow rate and velocity. Calculate flow velocity for

known pipe diameter and flow rate. Convert from volumetric to mass flow rate.

Calculate volumetric flow rate of ideal gas at different conditions of pressure and

temperature.

Pipe diameter can be calculated when volumetric flow rate and velocity is known as:

D - Internal pipe diameter;

q - Volumetric flow rate;

v - Velocity;

A - Pipe cross section area.

1) Flow rate can be expressed in either terms of cross sectional area and velocity, or

volume and time.

2) Because liquids are incompressible, the rate of flow into an area must equal the

rate of flow out of an area. This is known as the equation of continuity.

3) The equation of continuity can show how much the speed of a liquid increases if it

is forced to flow through a smaller area. For example, if the area of a pipe is halved,

the velocity of the fluid will double.

4) Although gases often behave as fluids, they are not incompressible the way liquids

are and so the continuity equation does not apply.

The flow rate of a fluid is the volume of fluid which passes through a surface in a given

unit of time. It is usually represented by the symbol Q.

Page | 5

Flow Rate

Volumetric flow rate is defined as:

Q= vA

Where Q is the flow rate, v is the velocity of the fluid, and A is the area of the cross

section of the space the fluid is moving through. Volumetric flow rate can also be found

with:

Q=Vt

Where Q is the flow rate, V is the Volume of fluid, and t is elapsed time.

Continuity

The equation of continuity works under the assumption that the flow in will equal the

flow out. This can be useful to solve for many properties of the fluid and its motion:

Flow in = Flow out

Using the known properties of a fluid in one condition, we can use the continuity

equation to solve for the properties of the same fluid under other conditions.

Q1=Q2

This can be expressed in many ways, for example:

A1∗v1=A2∗v2

The equation of continuity applies to any incompressible fluid. Since the fluid cannot

be compressed, the amount of fluid which flows into a surface must equal the amount

flowing out of the surface.

FIGURE 1

Page | 6

Applying the Continuity Equation

You can observe the continuity equation's effect in a garden hose. The water flows

through the hose and when it reaches the narrower nozzle, the velocity of the water

increases. Speed increases when cross-sectional area decreases, and speed

decreases when cross-sectional area increases. This is a consequence of the

continuity equation. If the flow Q is held constant, when the area A decreases, the

velocity v must increase proportionally. For example, if the nozzle of the hose is half

the area of the hose, the velocity must double to maintain the continuous flow.

Reynolds Number

Reynolds number is a number that indicates the type of flow that a fluid undergoes.

The range of Reynolds number corresponds to the flow type is as below:

Re<2000 – Laminar Flow

2000<Re<4000 – Transition Flow

Re> 4000 – Turbulent Flow

Formula to calculate Reynolds Number,

𝑹𝒆 =𝒗𝑫

𝝊

Page | 7

1) Set the apparatus as shown in figure above.

2) Close the outlet of the bottle with the bottle cap with 5mm diameter in size.

3) Make sure it is tightly closed to avoid any leakage.

4) Measure 1000 ml of water using a measuring bottle.

5) Pour the 1000 ml water into the bottle through the inlet.

6) Use a finger to close the hole at the outlet of the bottle before start pouring

water into the bottle.

7) Make sure there is no water leakage at the outlet and surrounding the bottle

cap.

8) Remove the finger once the 1000 ml of water has been poured into the bottle.

9) Start the stop watch immediately after the finger is removed.

10) Measure the time required for the 1000 ml of water to flow out from the bottle

through the 5 mm outlet.

11) Record the time taken in Table 1.

12) Repeat step 2 to step 11 by using outlet with diameter 10 mm and 15 mm.

13) Dismiss the apparatus once the experiment is completed.

PROCEDURE

Page | 8

Diameter,

d

(mm)

Volume,

v

(m³)

Time, t

(s)

Flow rate,

Q

(x 10-6)

Velocity

(m/s)

Kinematics

Viscosity

(m2/s)

Re Type of

flow

5 0.001 56.0 17.8571 0.9095 0.8 X 10-6 5684 Turbulent

10 0.001 11.9 84.0336 1.0699 0.8 X 10-6 13336 Turbulent

15 0.001 5.2 192.3077 1.0882 0.8 X 10-6 20404 Turbulent

Sample Calculation:

For Diameter 5mm;

a) Flow rate, Q

𝑄 =𝑉

𝑡=

0.001

56= 17.8571 × 10−6 𝑚3𝑠−1

b) Velocity, v

𝑣 =𝑄

𝐴=

17.8571 × 10−6

𝜋4 (0.005)

= 0.9095 𝑚𝑠−1

c) Reynolds Number, Re

𝑅𝑒 =𝑣𝐷

𝜐=

(0.9095)(0.005)

0.8 × 10−6= 5684

DATA, OBSERVATION AND RESULTS

Page | 9

Graph 1

Graph 2

0.00E+00

5.00E-05

1.00E-04

1.50E-04

2.00E-04

2.50E-04

0.00E+002.00E-034.00E-036.00E-038.00E-031.00E-021.20E-021.40E-02

Flo

w R

ate

(m

³/s)

Area (m²)

Flow Rate Against Area

9.00E-01

9.20E-01

9.40E-01

9.60E-01

9.80E-01

1.00E+00

1.02E+00

1.04E+00

1.06E+00

1.08E+00

1.10E+00

0.00E+002.00E-034.00E-036.00E-038.00E-031.00E-021.20E-021.40E-02

Velo

cit

y (

m/s

)

Area (m²)

Velocity Against Area

Page | 10

1. The flow rate increase when the area of the outlet increase. This is due to the

time taken for the 1 litter fluids to flow decrease when the area increase.

2. Reynolds number depends on the velocity of the fluids, the diameter of the

pipe, and the kinematic viscosity of the fluid. In this experiment, the velocity

increase as the diameter increase. Thus the Reynolds number also increase.

3. The flow rate increase as the time taken for the fluid to flow decrease. The

results obtained obeys the flowrate equation.

4. From the graph of flowrate against area, we can see that the flowrate increase

as the area increase, this is due to the decrease in time of flow when the area

increase. From the graph of velocity against area, we can see that velocity

increase as the area increase. This is due to the equation of flowrate where

V α 1/A.

5. Precaution

a) Make sure the hole of the outlet closed properly to avoid any leaks.

b) Pour the water inside the bottle properly and avoid any splash of water, it

can reduce the total volume of water.

Errors

a) The time taken for the liquid to completely flow maybe be not accurate

because of the stopwatch may not started on the same time as the liquid

starts to flow.

b) The volume of the water inside the bottle may not be as accurate as 1 litter

because there is some drops of water left in the bottle after the

experiment.

c) The flowrate may be affected by the slight elevation of the bottle because

it was hold by using hand and human hand may vibrate due to heavy

weight.

ANALYSIS AND DISCUSSION

Page | 11

The aim of this experiment is to determine the velocity of a fluid flow that corresponds

to diameter of the outlet. In this experiment the velocity of the flow calculated using

flow rate equation Q=AV and the Reynolds number calculated using equation Re =𝑢𝑑

𝑣.

From the results, we can see that the velocity of flow increase as the diameter of the

outlet becomes bigger. With the increment of velocity, the Reynolds number of the

flow also increases. As from the experiment that conducted, all flows are considered

as turbulent flow because the Reynolds number that obtained is more than 4000. The

objective of the experiment is achieved.

CONCLUSION

Page | 12

1) https://en.wikipedia.org/wiki/Bernoulli%27s_principle

2) http://physics.stackexchange.com/questions/95620/relation-between-pressure-

velocity-and-area

3) http://francesa.phy.cmich.edu/people/andy/physics110/book/Chapters/Chapter9

.htm

4) http://www.researchgate.net/post/Could_anyone_please_tell_about_pressure_a

nd_velocity_relationship10

5) http://www.princeton.edu/~asmits/Bicycle_web/Bernoulli.html

REFERENCE