lab manual-manomety lab experiment.pdf

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1 | Page Fluid Mechanics Laboratory Department of Civil Engineering and Construction Engineering Management California State University, Long Beach Lab # 1 Fluid Statics and Manometry (Prepared by Dr. Rebeka Sultana) Objectives The purpose of this experiment is to demonstrate both visually and numerically the behavior of liquids under hydrostatic conditions. The students will learn basics of reading liquid surface level and apply hydrostatic principles to measure static pressure using manometers. General Discussion Reading liquid surface level Either fluid is hydrostatic or in motion, measuring liquid level is required to determine the flow depth or pressure head. Immersing a scale in liquid or attaching the scale to the side of a transparent vessel or tank is the simplest way to measure liquid/water level relative to some datum, such as the base of the tank. Changes in liquid level can be recorded by taking repeated (a) (b) Figure 1. Meniscus and potential error to read liquid level due to meniscus

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Page 1: Lab Manual-Manomety Lab Experiment.pdf

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Fluid Mechanics Laboratory

Department of Civil Engineering and Construction Engineering Management

California State University, Long Beach

Lab # 1

Fluid Statics and Manometry (Prepared by Dr. Rebeka Sultana)

Objectives

The purpose of this experiment is to demonstrate both visually and numerically the behavior of

liquids under hydrostatic conditions. The students will learn basics of reading liquid surface level

and apply hydrostatic principles to measure static pressure using manometers.

General Discussion

Reading liquid surface level

Either fluid is hydrostatic or in motion, measuring liquid level is required to determine the flow

depth or pressure head. Immersing a scale in liquid or attaching the scale to the side of a

transparent vessel or tank is the simplest way to measure liquid/water level relative to some

datum, such as the base of the tank. Changes in liquid level can be recorded by taking repeated

(a) (b)

Figure 1. Meniscus and potential error to read liquid level due to meniscus

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measurements using the scale.

When recording liquid level measurement, it is important to view the surface of the liquid

correctly relative to the scale because the meniscus that forms around the scale due to surface

tension. Meniscus is shown in Figure 1 which must be ignored to record the accurate value.

There can be reading error from parallax if the scale is not directly adjacent to the liquid. If the

eye is below the true liquid level and looking upwards, apparent reading on the scale will be

lower than the true reading because of parallax. When eye is above the liquid level and looking

downwards, apparent reading will be higher than the actual liquid level. This effect increases

with distance from the liquid to scale. So, it is important to maintain the correct eye level when

level is read.

Figure 2. Examples of reading Vernier scale

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To increase precision in reading Vernier scale has been developed which allows to read

measurements at 1/10th

accuracy level. Example of how to read Vernier scale is shown in Figure

2.

Hydrostatic Pressure

Atmospheric pressure acts on the top of a liquid surface that is static in a reservoir. But, the

pressure increases at the bottom of the reservoir because of gravity. This pressure is not

influenced by the shape and size of the tank or reservoir in which the liquid is retained. Figure 3

shows the pressure on top of the tank is po and at h unit below the free surface the pressure

increases by following the hydrostatic equation:

hpp o (1)

Figure 3. Fluid pressure in tanks with various shapes (Munson et al., 2012).

If the pressure varies from atmospheric pressure, then additional force works on the liquid.

Pressure difference can be measured by recording the liquid level difference in a U-tube

manometer as shown in Figure 4.

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Figure 4. U-tube manometer with the left-leg closed and pressurized

If the pressure difference is small, then h in Figure 4 can be small and difficult to read the value

with accuracy. For smaller differential pressure change (i.e., liquid level change), inclined

manometer can be used. Inclined manometer (shown in Figure 5) which improves visual

resolution depending on the angle of inclination.

Figure 5. Inclined manometer

The relationship between vertical and inclined height can be defined by the following

relationship:

sin Lh (2)

Therefore, the hydrostatic pressure can be derived as:

ghhp (3)

sin gLp (4)

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where

p = pressure at the datum

= density of the liquid in the manometer

g = acceleration due to gravity

L = Distance change along the inclined scale

θ = angle of inclination of the inclined manometer

When the manometer is inclined at 30o, then vertical level change of 1 unit is magnified by 2

units in the inclined manometer (i.e., Sin30o = 0.5 and 1/0.5 = 2). With 60o inclination, then 1

unit vertical level change is magnified by 1.155 times (i.e., Sin60o = 0.866 and 1/0.866 = 1.155).

(a)

(b)

Figure 6. Fluid Static and Manometry Apparatus (a) without labels, and (b) with labels

Equipment

F1-29 Armfield apparatus (shown in Figure 6) will be used for this experiment which consists of

the following:

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A reservoir (label 2)

U-tube differential manometer

3 fixed tubes, the tube in the right has variation of x-section (labels 13 and 11)

Inclined manometer (can be adjusted to preset angles of 5o, 30

o, 60

o, and 90

o to the

horizontal) and

A Vernier scale positioned on top of the reservoir.

A color dye will be used to improve visualization of the effect of hydrostatic pressure.

Procedure

This experiment has three exercises.

Exercise 1: Measuring liquid level

(a) Using a level scale

1. Place the F1-29 (Fluid Statics and Manometry) apparatus on a hydraulic bench. Adjust

the feet, if necessary, to level the apparatus using the circular spirit level attached at the

base of the F1-29 unit by bringing the bubble in the spirit level at the center.

2. Keep the outlet valve at the front of the reservoir fully closed.

3. Connect the flexible filling tube to quick release connector at the base of the reservoir.

Connect the other end of the flexible filling tube with the outlet of the hydraulic bench.

4. By keeping the valve in the hydraulic bench completely closed, start the pump in the

hydraulic bench.

5. Slowly open the valve and with a low flow fill the reservoir to a depth approximately 200

or 300 mm. Turn off the pump in the hydraulic bench

6. Ensure the serrated ferrule at the top of the reservoir and each individual tube is open to

atmosphere and not connected with any tapping.

7. Level your eye with the surface of the water in the reservoir. Observe the difference

between the water level in the middle and at the meniscus adjacent to the wall. Use the

front scale of the reservoir to record the depth of liquid level.

8. To understand reading error from parallax, raise your eye level by approximately 100 mm

and observed/record the reading of the water level.

9. Lower your eye level by approximately 100 mm and observe/record the liquid level

change due to parallax.

10. The correct liquid level record is the one that you have recorded when your eye was

leveled with the free liquid surface.

(b) Using a Vernier scale

1. By holding the vertical rod, use the coarse adjustment rod to slide the rod up and down to

adjust the position of the point gauge. When the tip of the point gauge touches the liquid

surface, use the adjustable stop to lock the position of the vertical rod. Figure 7 shows the

Vernier scale with hook and point gauges.

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Figure 7. Vernier scale with the point and hook gauges.

2. Measure the liquid level surface when the tip and its reflection just touch. If the liquid

touches the tip then surface tension will attach the water to the tip and prevent an accurate

measurement. In this case, use the fine adjustment nut to raise the point gauge just above

the liquid level.

Exercise 2: Free Surface Demonstration

1. Ensure the serrated ferrule at the top of the reservoir and each individual tube is open to

atmosphere and not connected with any tapping.

2. Connect the flexible tube with the quick release connectors at both ends from the base of

the reservoir to the connector at the base of the U tube and leave the tube connected.

3. Observe that the tubes of U-tube and vertical tubes fill to the same height and settle at the

same height as in the liquid in the reservoir.

4. Next, open the valve at the base of the reservoir and allow the liquid from the reservoir to

fill in the tubes at the right hand side of the apparatus.

5. Open the valve at the base of the reservoir and allow liquid to flow into the vertical tubes.

Observe that the liquid level in all the tubes is the same even if the cross-sectional areas

of the tubes are different. Record the liquid surface levels in the reservoir, U-tube and in

the vertical tubes.

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6. To observe how liquid level adjusts in an inclined tube (the right most tube from the

reservoir), pull the indexing knob forward and then inclined the tube to an angle of 60o

above the horizontal and push the indexing knob back in to secure the tube at this angle.

Record the reading in the inclined tube.

Note: The indexing knob can be only fixed at the fixed angles. If the knob is pushed at an

angled position but does not secure, that indicates, the tube is not at one of its fixed

angle. Then move the tube up and down to find out the angled position.

7. In the similar process, position the inclined tube to an angle of 30o above the horizontal.

Observe the distance travelled by the fluid along the tube. Note that the meniscus is

severely deformed by inclination and so care should be taken to record the accurate

reading. Record the reading in the inclined tube.

Note: If any tubes do not fill to the same height as the liquid in the reservoir, then there

might be trapped air in the flexible tubing connected with the tube. To remove this

trapped air, connect a flexible tube with the serrated ferrule at the top of the tube.

Connect the syringe at the other side of the flexible tube and force the liquid up until the

air bubble is dislodged.

Exercise 3: Effect of changes in air pressure

1. Ensure that liquid level in all the tubes is same as is in the reservoir. This is done by

keeping all the serrated ferrules open to atmosphere. Keep the inclined manometer at 60o

angle with the horizontal

(a) (b)

Figure 8. Applying pressure in the reservoir by a syringe (a) depress the plunger, and (b)

withdraw the plunger

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2. To apply pressure in the reservoir, attach one end of one of the flexible tube to the

serrated ferrule at the top of the reservoir. Attach the syringe (with the plunger

withdrawn) on the other side of the flexible tube and apply pressure in the reservoir by

depressing the plunger. This will lower the fluid level surface slightly in the reservoir and

the levels will rise to a common height in all of the other tubes including the piezometer

tube inside the reservoir as shown in Figure 8:

3. Record the height difference between the liquid surface in the reservoir and the

manometers.

4. Next reduce the pressure in the reservoir by first disconnecting the syringe and allowing

all the tubes to return to the same level. Reconnect the syringe (with the plunger

depressed) to the other end of the flexible tube similar to step 2 (see Figure 8). Withdraw

the plunger which will reduce the pressure in the reservoir less than atmospheric. So, the

fluid level in the reservoir will slightly increase and in the manometer the level will

decrease.

5. Record the height difference between the liquid surface in the reservoir and the

manometers.

6. To observe how pressure change will affect the liquid level in the U-tube, connect the

reservoir and the U-tube by connecting the flexible tube with the connectors at the base

of the reservoir and the U-tube. Keep the valve at the end of the reservoir open. Then

apply pressure on the right leg of the U-tube and record the level difference between the

liquid levels in the two legs of the U-tube as shown in Figure 9a. Note that because of

applied pressure in one leg of the U-tube, liquid level in other leg of the U-tube as well as

in the reservoir changes because of the connection between the U-tube and the reservoir.

(a) (b)

Figure 9. Applying pressure in the U-tube (a) connected to the reservoir, and (b) not

connected to the reservoir

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7. Next remove the flexible connector between the reservoir and the U-tube, and apply

pressure on the right leg of the U tube like in step 6 (Figure 9b). Note that the liquid level

in the reservoir will not change this time. Record the liquid level difference between the

U-tube legs.

8. Similarly, pressure can be applied to any one of the tubes and difference in liquid level

can be studied. Keep the valve open at the end of the reservoir and connect the U-tube

with the reservoir using the flexible connector. Apply pressure to two independent fixed

tubes (Figure 10) using Y adaptor and record the liquid level difference in the tubes. Also

observe the change in liquid levels by reducing the pressure by withdrawing the plunger

in the syringe.

Figure 10. Applying pressure in the fixed tubes using Y flexible tubes.

Record the experimental data in Table 1.

Calculations

1. For inclined manometer, convert the inclined height to vertical height using Equation 2.

2. Calculate the air pressure applied in the reservoir, U-tube and fixed tubes using the

vertical height change in the liquid level. Use Equation 3 and 4.

Discussions

Discuss your results by addressing the followings-

1. Discuss advantages and disadvantage (in terms of accuracy) of different methods of

liquid level measurement.

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2. Compare the liquid levels in the reservoir, U-tube, fixed tubes, and inclined tube and

confirm that surface of water is always horizontal. Discuss how liquid level changes in

the inclined tube but vertical height remains the same.

3. Comment on the effect of change of pressure in the reservoir, U-tubes and fixed tubes.

Discuss the amount of level change in the tubes of different sizes.

References

Armfield, 2012, “Fluid Statics and Manometry”, Instruction Manual.

Munson, B. R., T. H. Okiishi, W. W. Huebsch, A. P. Rothmayer, 2012, “Fundamentals of Fluid

Mechanics”, 7th

edition, John Wiley, Chapter 10.

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Table 1. Fluid static and manometry data

Liquid level measurement using a level scale Liquid level (mm)

Eye at the liquid level

Eye 100 mm below the liquid level

Eye 100 mm above the liquid level

Liquid level measurement using Vernier scale Liquid level (mm)

Point gauge

Hook gauge

Free surface Demonstration Liquid Level (mm) Vertical height (mm)

At Reservoir

U-tube

Fixed tube

Inclined tube at 60o

Inclined tube at 30o

Pressure change in the reservoir Level change in the

reservoir (mm)/Pressure

change ΔP (kN/m2)

Level change in the U tube

(mm)/Pressure change ΔP

(kN/m2)

Apply the pressure

Reduce the pressure

Pressure change in the U-tube Level change in U-tube

(mm)/Pressure change

ΔP (kN/m2)

Level change in Reservoir

(mm)/ Pressure change ΔP

(kN/m2)

connection with the reservoir

No connection with the reservoir

Pressure change in the two

fixed tubes

Level change in the legs

(mm)

Level change in the U-tubes

(mm)

Apply pressure

Reduce pressure