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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

    = 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, 30o, 60o, and 90o 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 h