Experimental report fluid mechanic experiment 1 hydrostatics experiment 3a energy equation experiment 3d measurement of volumetric flow rate experiment 5a friction loss in pipe

- The state of static and compressed fluid is described by this equation: z+ p γ =constant 1 With z is the elevation of any point in the static fluid mass, constant specific weight γ and

EXPERIMENTAL REPORT

FLUID MECHANIC

Experiment 1: Hydrostatics Experiment 3A: Energy equation Experiment 3D: Measurement of volumetric flow rate

Experiment 5A: Friction loss in pipe

Semester:

Ho Chi Minh City,November,2022

I want to express my gratitude to Dr our lecturer, for his insightful comments,observations, and suggestions made throughout the Fluid Mechanics laboratory

His lectures provided me with a plethora of practical knowledge about chemistry as well

as the fundamental skills required to successfully carry out chemical experiments I'm overjoyed about that!

Author

EXPERIMENT 1: HYDROSTATICS

I Purpose and theory

- This experiment teaches students how to apply the primary hydrostatics equation toissues involving compressed fluid in a static state

- The state of static and compressed fluid is described by this equation:

z+ p γ =constant (1)

With z is the elevation of any point in the static fluid mass, constant specific weight γ and

p is the hydrostatic = constant is also called the water pressure measurement in meter.

From this equation, we can have some applications:

1 Isobaric surface:

- Isobaric surface is a surface on which the pressure is the same A specific image ofthe isobaric surface which we can see is atmospheric surface When the pressure atpoints on the atmospheric surface is equal, the height of them is equal, then

2 Fluid manometer

- Applying basic equation for calculating the pressure at any point in the static fluid

having the elevation z is:

p= ρ0+γ(z−z0)=ρ0+γh (2)

● Whereas surface 0-0 is a standard surface for comparison

● By measuring the height h, we can determine the pressure p

3 Calculating the specific gravity of fluid:

II Equipment

- The manometer has a collection of tubes with numbers ranging from 1 to 10 thatare placed on the board using an elevated ruler that is millimeter-accurate Thetubes' di (diameter) is 5 mm (except group of tubes 2 with the diameter equal toless than 3mm) These tubes contain:

● Tube 1 and 3 are used as fluid manometers to measure the atmosphericpressure in vessel T

● Group of tubes 2 containing tube 21, 22, 23 with diameters 1mm, 2mm, 3mmrespectively are used to observe the capillary phenomenon.

● 3 U-shaped tubes are couple tubes 4-5, 6-7, 8-9, containing fluids needed todetermine its specific gravity

- Tube 10 and 3 are used to observe acupressure surface The atmospheric pressure

of tube 1, 4, 6, 8 is the atmospheric pressure in vessel T The elevation of fluidlevel in tubes is creating pressure part contains static closed vessel T and un-staticopened vessel D, which is hang on block 12, have water Due to crank 11, we canchange the height of vessel D to differ the atmospheric pressure in vessel T

III Process

- Check the standard figure of the ruler (in millimeter), whether the rulers are in thehorizontal plane by reading the water level in tube 3 and tube 10 These 2 tubeneed to have the same water level

● Using the crank 11 to lift the vessel Ð to the pitch (the free surface of vessel

Ð must be higher than the free surface of vessel T about z0−zr = 15÷20cm)

● Start to measure the water level of tube 1 to 10 and record the result (alsothe group tube 2)

● Lower the vessel Ð to the average position (z0 − zr = 5 ÷ 7cm) and to thelow position (z0 − zr = −15 ÷ −20cm) Start to measure like above andrecord the result to the table

I Experiment results and observations

According to the three elevations of tank D in comparison with tank T, please record the measured values of 9 tubes, and Group Tube 2 in the following Table 1

Table 1a: The measured resulted (Unit: cm)

Table 1b: The measure result in type 2

II Step of Calculation and presentation of the experiment results

a) Calculate hydrostatic pressure of gas in the tank T

- From equation (1.2), the absolute pressure in the tank T is calculated:

p T = p a +γ H2O ( L3−L1 ) (1.4a)

- The specific weight of the water in the tank is determined by the temperature of surrounding environment If we take pa = 0, we can calculate the gauge pressure

p Td =γ H2O (L3−L1 ) (1.4b)With three positions of the tank D, we can calculate three values of the gas

pressure in the tank T

b) Calculate to the specific weight of the fluid in the U-tubes

- Consider to fluid has the specific weight γ, in static state in both i and i+ 1 of the

U-tube Pressure in the tank T can also be calculated:

c) Calculate the error of the method of pressure measurement method

- Applying the theory of error, from the formula (1.4b) we determine the relative error δ p of the gauge pressure measurement:

δ L3−1=∆ L3+∆ L1

|L3−L1|

Thus δ p =δ γ H2O +δ L3−1 (1.7)

Usually we take: δ γ H2O=0.12 % and ∆ L3=∆ L1=0.5mm

III Answer the question and the results

1 Which tubes or tanks have equal water level in the hydrostatic experiment set? Why?

In the hydrostatic experiment, tubes 3 and 10 have the same water level becausetheir free surfaces are in contact with the air and experience atmosphericpressure as a result Since they interact with the same fluid and feel the samepressure on tank T, tube 1, which is the free surface, they also share the samehorizontal plane

2 Which tubes have water level that do not according to hydrostatic law in the hydrostatics experiment set? Why?

According to capillarity, which arises because tubes 21, 22, and 23 have varyingvalues for their diameters (all are less than 3 cm), the water level in tube 2deviates from the law of fluid static (depending on the surface tension) Thewater levels in tubes 21, 22, and 23 vary as a result of capillarity As the waterlevel rises, the tube's diameter decreases

3 Calculate the absolute pressure, gauge pressure of the gas in the tank T and the relative error of this pressure in the measured cases The results fill in table 2.

4 Calculate the specific weight of three fluids in pairs of tubes: 4 - 5, 6- 7, 8 –

9 and the relative error of these specific weights for the cases The results fill in table 2.

Table 2: The calculated results

EXPERIMENT 3D: MEASUREMENT OF VOLUMETRIC FLOW RATE

- The fan inlet is a duct 149 mm diameter provided with pressure tapings whereby the

static pressure may be measured simultaneously at each of 4 sections

- All four pressure tapings are connected to a bank of pressurized manometer tubes

(1,2,3,4) Two flow measurement devices are:

● 65mm orifice plat (1)

● 65mm – 149mm diameter venturi nozzle (2)

Figure: Experimental map

of density ρ1 is used to indicate ∆ p, the pressure difference may be expressed

in terms of the manometric head differential ∆ hby:

- The discharge coefficients of the orifice plat and the venturi nozzle can bedetermined by empirical formula

For the orifice plate:

C=0.5959+0.0312 β2.1−0.184 β2+0.0029 β2.5(10 6

ℜ )0.73

+0.0039 β4(1−β4)−0.0158 β3

(2.3)

1 Check that there are no obstructions in the air intake and outlet openings.

2 Turn on the fan switch

3 Adjust the number of revolutions of the inverter in the range of 400 - 450 rpm

4 Read the height of the water level in the two pressure gauge tubes 1 and 2, record

in Table 1, the first row below the column “pressure gauge tubes 1, 2” Read thereadings on the left manometer, record it in Table 1, the first row below the

“barometer” column

5 Read the height of the water level in the two pressure gauge tubes 3 and 4, record

in Table 2, On the first row below the column “pressure gauge tubes 3, 4” Readthe readings on the right manometer, record it in Table 2, first row below the

“barometer” column

6 Repeat steps 3 to 5 for 3 more rpm values on the inverter: 650-700 rpm, 900 – 950rpm and 1150 - 1200 rpm Record the corresponding values in tables 1 and 2

EXPERIMENT 3D: MEASUREMENT OF VOLUMETRIC FLOW RATE

I Derive the formula (2.1) in case of C = 1

- The Work-Energy equation written between cross-section 1 in the approach fluid flowand cross-section 2 in the constricted area of flow is shown below:

● A2 is the constricted cross-sectional area perpendicular to flow

● P1 is the approach pressure in the pipe

● P2 is the pressure in the meter.

● β is the diameter ratio = D d

● ρ is the flow density

The volumetric flow rate calculated from this equation is calledQ ideal,which doesn’tinclude the effects of frictional losses In practice, there are always friction losses andother non-ideal factors, so we need to add a discharge coefficient C into the equation for

Q but in this question, it assumes that C = 1, So C is not necessary in this formula

Furthermore, we need to add the expandability factor, which is also detailed in the codeand allows for the effects of density change in gas flows where a high-pressure reductionoccurs For liquid flows and gas flows with moderate variation in pressure at the meter ε ≈1

II.Derive the formula (2.2)

- We call A, B as the free surface of tube 1 and 2 respectively

- The pipe is on horizontal plane so Z1 = Z2

- Applying the fluid statics, we can get

Then, we find the difference of pressure measured by pressure gauge and measuring tube

by applying following formula:

(p1− p2)−The value of¿gauge The value of¿gauge

To calculate C value in orifice plate, we will use iteration method:

Step 1: We assume C = 1 to calculate Q by the function (2.1):

Step 4: After getting value of C, we will replace C = 1 with this new value of Cand calculate Q again by formula (1).

Step 5: We keep doing this iteration method until: |Q1−Q2|

Difference(Pressuregauge-Measuringtube) (%)

IV Determine the volumetric flow rate in three experiments by using venturi nozzle

Then, we find the difference of pressure measured by pressure gauge and measuring tube

by applying following formula:

(p3− p4)−The value of¿pressure gauge The value of¿ ¿ pressure gauge¿

Next, calculating the value of C in the venturi nozzle by using the formula (2.5):

Answer the question

1) Explain the difference from the results of U tubes and pressure gauge.

The easiest way to identify between gauge pressure and absolute pressure is tocompare their respective zero points: gauge pressure utilizes atmosphericpressure as its zero point, whereas absolute pressure uses absolute zero Whilegauge pressure measurement is inaccurate owing to fluctuating air pressure,absolute pressure is always definite

2) Determine the air flow rater in 4 experiments by using orifice flat

0.05

0.06939

0.08661

Fan frequency - Flowrate relationship

4) Compare the computed results between the using of orifice plat and venturi nozzle, give the discussions.

- Using an orifice plate and a venturi nozzle always produces somewhat differentresults

- When calculating the Q value, using venturi nozzle is better It is because:

● The venturi nozzle's diverging portion is a specific part that is responsible forrestoring pressure lost during the measurement of the average velocity or flowrate of the flowing fluid

● The orifice plate's pressure loss is significantly greater than that of the venturimeter because it lacks a specific component designed for pressure recovery

As a result, the flow is disturbed and produces less stable results as it goesthrough the orifice plate because it expands quickly

● As a result of having smaller relative calculation errors than the orifice plate,the venturi nozzle is, in general, a more accurate measurement tool than thelatter

EXPERIMENT 5A: FRICTION LOSS IN PIPE

I Purpose

- To investigate the variation of friction head along a circular pipe with the mean flow

velocity in the pipe

- To investigate the friction factor against Reynolds number and roughness.

● V i ,V j: velocity at section i, j respectively

● P i ,P j:pressure at section i, j respectively

● Z i ,Z j: elevation at water surface section i, j

● Z ij: friction loss from section i to section j

- For this apparatus, Z i =Z j ;V i =V j, hence

h ij=P i −P j

∆ h ij: the difference of manometer reading at section i and section j

On the other hand, the friction factor can be determined by Darcy’s formula:

h ij = λ L D 2 g V2 (4.3)Where:

● λ: friction factor

● D : diameter of pipe

● V : velocity of pipe

- The friction coefficient depends upon the Reynolds number of flow and upon the ratio ∆ D the relative roughness of the pipe:

- Four test sections with interval of 3 m are connected to a bank of pressurizedmanometer tubes

- Water from the pipe flow into the concrete channel, and at the end of channel a notch, is installed to measure the flow rate in the channel, this flow rate is equal tothe flow rate in the pipe

vee Water level over the veevee notch is measured by a point gauge vernier mounted on asmall tank which is opened to the channel

- The flow rate over the vee-notch is calculated by formula as follow:

Q= 8

15tg(α

2)C D√❑ (1)Where:

The flow rate over the Vee-notch is regulated by a control valve of pump, and

an ampere meter mounted on an electric box will show the current intensity ofmotor corresponding to the flow rate in the pipe The difference of pressurebetween the test sections in the pipe are measured by reading the water level inthe tubes of manometer

IV Process

1) Before testing, check valves (1), (2) and locks Make sure they are closed andcheck the spindle of the pump and the motor by turning lightly to see whether it ishard or not, if it moves is well

2) On electric box, you press: POWER ON button and RUN / STOP button, ONbutton to start the pump Fully open the valve (1) by turning counterclockwise until

it is no longer rotatable Note: If valve 2 does not open fully, opening the valve 1will cause break the manometer tubes because of high pressure Slowly open thevalve (1) and see the change in current intensity to the value that you need of thetest And then open locks.

3) Measurements are made twice

4) Important note when you want to shut down Close valve (1), then switch off (pressthe OFF button of RUN / STOP and power OFF button) Then close the valve (2)immediately, to keep the water in the pile

♦ The first measurement:

o Open the locks of the manometer tubes at the section (1) and (2)

o Adjust the valve (1) to change the three flow rate levels corresponding to thecurrent of 21A < I < 26A (the first flow rate corresponding to I = 22.5A, thesecond flow rate corresponding to I = 22A; The third flow rate corresponds

to I = 21.5A)

o Wait for the water level in the channel to stabilize (the water level in pointgauge is constant), read the following values:

⮚ Water level in manometer tube (1)

⮚ Water level in manometer tube (2)

⮚ Elevation Z before the Vee-notch in the channel by point gauge

The measurement results are recorded in Table 1 of the report

♦ The second measurement:

o Adjust the valve (1) to regulate the five discharge levels corresponding tothe current I = 21.0A to 19.0A

o Continue to open the locks of manometer tubes (3), (4)

o For each discharge level, wait for the water level in the channel tostabilize, taking the following measurements:

⮚ Reading water level from the manometer tube (1) to the manometertube (4)