Home > Instruction Manual

Instruction Manual

Page 1
Equipment for Engineering Education
Instruction Manual
HM 150.05 Hydrostatic Pressure Apparatus
G.U.N.T. Gerätebau GmbH
P.O. Box 1125 D-22881 Barsb��ttel • Germany Phone (040) 670854-1 Fax (040) 670854-41

Page 2
Instruction Manual
Publication no.:917.00005A15012 12/96
HM 150.05 Hydrostatic Pressure Apparatus
All rights reserved G .U.N.T . G e rätebau Gm bH, B a rsb��ttel , G e rm any, 11/96

Page 3
Table of Contents
1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 Unit Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2.1 Commissioning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Care and Maintenance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
3 Theory on the Centre of Pressure . . . . . . . . . . . . . . . . . . . . . 4
3.1 Determining the Centre of Pressure . . . . . . . . . . . . . . . . . . . . . . . . . 5 3.2 Determining the "Resultant Force". . . . . . . . . . . . . . . . . . . . . . . . . . . 6 3.3 Mode of Functioning of the HM 150.05 Unit . . . . . . . . . . . . . . . . . . . 7
4 Experiments Relating to the Centre of Pressure . . . . . . . . . . 8
4.1 Centre of Pressure with Vertical Positioning of the Water Vessel . . . 8 4.1.1 Performing the Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . 8 4.1.2 Evaluating the Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . 8 4.2 Centre of Pressure with Water Vessel Tilted . . . . . . . . . . . . . . . . . . 10 4.2.1 Performing the Experiment . . . . . . . . . . . . . . . . . . . . . . . . . 10 4.2.2 Evaluating the Experiment . . . . . . . . . . . . . . . . . . . . . . . . . 11 4.3 Centre of Pressure with 90�� Positioning of the Water Vessel . . . . . 13
5 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
5.1 Worksheet for Centre of Pressure (HM 150.05) . . . . . . . . . . . . . . . 14 5.2 Symbols and Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 5.3 Technical Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
HM 150.05 Hydrostatic Pressure Apparatus
All rights reserved G .U.N.T . G e rätebau Gm bH, B a rsb��ttel , G e rm any, 11/96

Page 4
1 Introduction The effect of hydrostatic pressure is of major signi- ficance in many areas of engineering, such as shipbuilding, the construction of dykes, weirs and locks, and in sanitary and building services engi- neering. With the HM 150.05 Hydrostatic Pressure Appa- ratus the following key topics can be investigated by experimentation:
• Pressure distribution in a liquid taking into ac-
count gravity
• "Lateral force" of the hydrostatic pressure • Centre of pressure of the lateral force
T he appendix to this Test Instruction contains prepa- red worksheets which facilitate methodical evalua- tion of the results of the experiments. The apparatus is designed for use in the fields of education.
HM 150.05 Hydrostatic Pressure Apparatus
All rights reserved G .U.N.T . G e rätebau Gm bH, B a rsb��ttel , G e rm any, 11/96
1 Introduction
1

Page 5
2 Unit Description 1. Water vessel 5. Water level scale 2. Detent 6. Rider 3. Slider 7. Weights 4. Stop pin 8. Handles
7 8 6 3 4 2 5 1
HM 150.05 Hydrostatic Pressure Apparatus
All rights reserved G .U.N.T . G e rätebau Gm bH, B a rsb��ttel , G e rm any, 11/96
2 Unit Description
2

Page 6
With HM 150.05 "Hydrostatic Pressure Appara- tus "the correlation between the water level and the dependent side pressure can be investigated. The unit is of robust construction and can be set up quickly. It is therefore highly suitable for every- day use in schools and universities. The unit can be easily transported by means of two handles. A transparent measuring vessel with mm scale and a scale with mm increments permits precise water level and lever arm readings. 2.1 Commissioning The "Hydrostatic Pressure Apparatus" should be placed on a horizontal, waterproof surface . An additional vessel for filling and emptying the water vessel should be provided. 2.2 Care and Maintenance The unit and its accessories require practically no maintenance. To prevent liming, empty the unit after use and dry it with a soft cloth.
HM 150.05 Hydrostatic Pressure Apparatus
All rights reserved G .U.N.T . G e rätebau Gm bH, B a rsb��ttel , G e rm any, 11/96
2 Unit Description
3

Page 7
3 Theory on the Centre of Pressure The hydrostatic pressure of liquids is the "gravita- tional pressure" phyd. It rises due to the intrinsic weight as the depth t increases, and is calculated from:
phyd = ��⋅g⋅t.
(1)
�� - Density of water
g - Acceleration due to gravity (g=9,81 m/s
2
) t - Distance from liquid surface To calculate forces acting on masonry dams or ships�� hulls, for example, from the hydrostatic pres- sure, two steps are required:
• Reduce the pressure load on an active surface
down to a resultant force Fp, which is applied at a point of application of force, the "centre of pressure", vertical to the active surface.
• Determine the position of this centre of pressu-
re by determining a planar centre of force on the active surface. It is first demonstrated how the centre of pressure can be determined. The resultant force Fp is then calculated.
HM 150.05 Hydrostatic Pressure Apparatus
All rights reserved G .U.N.T . G e rätebau Gm bH, B a rsb��ttel , G e rm any, 11/96
3 Theory on the Centre of Pressure
4

Page 8
3.1 Determining the Centre of Pressure A linear pressure profile is acting on the active sur- face shown, because the hydrostatic pressure rises proportional to the depth t. The resultant force Fp is therefore not applied at the centre of force C of the active surface, but always slightly below it, at the so-called centre of pressure D! To determine the distance e of the centre of pressure from the planar centre of force, the following model demonstration is used: Imagine an area A in front of the active surface, formed by the height h and the pressure profile of the hydrostatic pressure p1-p2. This area is in the form of a trapezium. The centre of pressure D lies on the extension of the planarcentre of force of this area A. A can be broken down into partial areas A1 and A2. The respective planar centres of force are identified by black dots. A balance of moments between the areas is then established around the point O1 in order to find the common planar centre of force (dynamic effect in direction Fp):
��M
(O1)=0: A⋅(
h 2
+e) = A1⋅
h 2
+A2⋅
2h 3 (2) Where A1 = p1⋅h, (3) A2 = p2−p1 2
⋅h and
(4) A = A1+A2 (5) the result is
h
2
yc
2h 3
Fp
O1
A2 A1 p2 p1
Planar center of gravity h
��
e
p1 p2
h
t1 t2 Fp
A Active surface C
��
e
yc
D
HM 150.05 Hydrostatic Pressure Apparatus
All rights reserved G .U.N.T . G e rätebau Gm bH, B a rsb��ttel , G e rm any, 11/96
3 Theory on the Centre of Pressure
5

Page 9
e = 1 6 h⋅
p2−p1
p2+p1 . (6) With the hydrostatic pressure p2 = ��gcos��⋅(yc+ h 2
) and
(7) p1 = ��gcos��⋅(yc− h 2
) the result is
(8) e = 1 12

h2 yc . (9) e is the distance of the centre of pressure from the planar centre of force of the active surface which we are looking for. 3.2 Determining the Resultant Force The hydrostatic pressure acting on the active sur- face can be represented as resultant force Fp, of which the line of application leads through the centre of pressure D. The size of this resultant force corresponds to the hydrostatic pressure at the planar centre of force C of the active surface: pc = ��⋅g⋅tc (10) pc - Hydrostatic pressure at the planar centre of force of the active surface tc - Vertical distance of the planar centre of force from the surface of the liquid In visual terms, the pressure at the planar centre of force corresponds to precisely the mean value between the highest and lowest pressure, becau-
tc t1 t2 yc h
2
Fp
Active surface Aactiv
��
C D
HM 150.05 Hydrostatic Pressure Apparatus
All rights reserved G .U.N.T . G e rätebau Gm bH, B a rsb��ttel , G e rm any, 11/96
3 Theory on the Centre of Pressure
6

Page 10
se of the linear pressure distribution. If the wall is tilted by an angle ��: pc = ��⋅g⋅cos ��⋅yc. (11) The resultant force Fp can now be calculated: Fp = pc⋅Aactive (12) Important!To calculate the resultant force the planar centre of force of the active surface is applied, but the line of application of the resultant force Fp runs through the centre of pressure (see section 3.1). 3.3 Mode of Functioning of the HM 150.05 unit The unit��s water vessel is designed as a ring segment with constant cross-section. The force due to weight G of the water always produces the same moment of momentum referred to the centre of motion O as the resultant force Fp of the active surface running through the centre of pressure D. Consequently, this apparatus can be used to de- termine the force of pressure Fp and the centre of pressure. To illustrate the point, imagine the ring segment completely filled. The force due to weight G applied to the centre of volume of the water can be broken down into two components:
• A radially applied component Gr running preci-
sely through the centre of motion, and
• a tangential component Gt with a lever arm r
acting on the centre of motion O. The radial component Gr exerts no momentum on centre of motion O, because its lever arm is zero. Now, regardless of the water level:
r
Gr Gt Fp yp
G O D
HM 150.05 Hydrostatic Pressure Apparatus
All rights reserved G .U.N.T . G e rätebau Gm bH, B a rsb��ttel , G e rm any, 11/96
3 Theory on the Centre of Pressure
7

Page 11
Fp⋅yp = Gt⋅r (13) That is to say, the force due to weight G of the water volume always exerts the same moment of momentum as the force Fp at the centre of pressure D. The derivation of (13) leads via determination of the centre of force of a ring segment and its volu- me.
HM 150.05 Hydrostatic Pressure Apparatus
All rights reserved G .U.N.T . G e rätebau Gm bH, B a rsb��ttel , G e rm any, 11/96
3 Theory on the Centre of Pressure
8

Page 12
4 Experiments Relating to the Centre of Pressure 4.1 Centre of Pressure with Vertical Positioning of the Water Vessel 4.1.1 Performing the Experiment 4.1.1.1 Counterbalancing the Water Vessel
• Set the water vessel (1) to an angle of �� =0��
using the detent (2) as shown
• Counterbalance the unit with a rotating slider
(3): The stop pin (4) must be precisely in the middle of the hole for this 4.1.1.2 Performing the Measurement
• Mount the rider (6), set the lever arm on the
scale (e.g. l=150 mm)
• Top up with water until the unit is balanced
(stop pin (4) at centre of hole)
• Read off water level s and enter it in the
prepared worksheet (see Appendix)
• Increase the appended weights (7) in incre-
ments of 0.5 - 1 N andrepeat the measurement 4.1.2 Evaluating the experiment Measured values: s - Water level reading l - Lever arm of the force due to weight FG - Force due to weight of the appended weights
1 3 4 2
��
0�� 30�� 60 �� 90��
l 4 6 7 s
HM 150.05 Hydrostatic Pressure Apparatus
All rights reserved G .U.N.T . G e rätebau Gm bH, B a rsb��ttel , G e rm any, 11/96
4 Experiments Relating to the Centre of Pressure
9

Page 13
4.1.2.1 Determining the Centre of Pressure At a water level s, below the 100 mm mark, the height of the active surface changes with the water level. If the water level is above that mark, the height of the active surface is always 100 mm. Meaning: s - Water level e - Distance of centre of pressure D from planar centre of force C of the active surface lD - Distance to centre of motion of the unit: For a water level s < 100 mm: (pressure has a triangular profile) e = 1 6
⋅s
(1) lD = 200mm − 1 3
⋅s
(2) For a water level s > 100 mm: (pressure has a trapezoidal profile) e = 1 12
⋅ (100mm)2
s−50mm (3) lD = 150mm + e (4) 4.1.2.2 Determining the Resultant Force The resultant force corresponds to the hydrostatic pressure at the planar centre of force C of the active surface. Thus, the height of water level s must again be differentiated: Meaning: Aact - Superficial content of active surface b=75 mm - Width of liquid vessel pc - Hydrostat. pressure at planar centre of force
s
lD
50mm C D
Trapezoidal profile Active surface
s
lD
e C D
Triangular profile Active surface
HM 150.05 Hydrostatic Pressure Apparatus
All rights reserved G .U.N.T . G e rätebau Gm bH, B a rsb��ttel , G e rm any, 11/96
4 Experiments Relating to the Centre of Pressure
10

Page 14
Fp - Resultant force for hydrostat. pressure on active surface: For s < 100 mm: (triangular profile) pc = ��⋅g⋅ s 2 and Aact = s⋅b (5) For s>100 mm: (trapezoidal profile) pc = ��⋅g⋅(s−50mm) and Aact = 100mm⋅b(6) The resultant force is produced as Fp = pc⋅Aact . (7) 4.1.2.3 Balance of Moments Calculated variables: FG - Appended weight l - Lever arm of appended weight referred to cen- tre of motion O To check the theory, a balance of moments around the centre of motion O can be established and checked:
��M
(O)=0: FG⋅l = Fp⋅lD
(8) 4.2 Centre of Pressure with Water Vessel Tilted 4.2.1 Performing the Experiment
• Set an angle �� and counterbalance the water
vessel as described under 4.1.1.1.
• Enter the characteristic values in the prepared
worksheet: Lowest water level st and highest water level sh of the active surface
• Perform the measurement as described under
4.1.1.2.
s 50 mm 100 mm
Fp
C D
Aact Fp FG lD l
O
0�� 30�� 60 �� 90 ��
��
sh st
Active area
HM 150.05 Hydrostatic Pressure Apparatus
All rights reserved G .U.N.T . G e rätebau Gm bH, B a rsb��ttel , G e rm any, 11/96
4 Experiments Relating to the Centre of Pressure
11

Page 15
4.2.2 Evaluating the experiment The difference between evaluation of the tilted vessel and that of the vertical vessel lies in the translation of the water levels onto the tilted active surface: A factor cos�� must be taken into account here. 4.2.2.1 Determining the centre of pressure When the water vessel is at a tilt, too, a triangular pressure profile is produced when the water level is below sh; above that level a trapezoidal profile is produced. Measured values: s - Water level reading
�� - Tilt angle of vessel
Meaning: st - Water level at lowest point of vessel sh - Water level of active surface at rim e - Position of centre of pressure h - Height of active surface lD - Distance between centre of pressure/centre of motion For a water level s < sh a triangular profile as follows applies: h = s−st cos�� (9) e = 1 6
⋅h
(10) lD = 200mm − 1 3
⋅h
(11) For a water level s > sh a trapezoidal profile as follows applies:
��
s
sh
e h
ld st
HM 150.05 Hydrostatic Pressure Apparatus
All rights reserved G .U.N.T . G e rätebau Gm bH, B a rsb��ttel , G e rm any, 11/96
4 Experiments Relating to the Centre of Pressure
12

Page 16
e = 1 12
⋅ (100mm)2
s−st cos��
−50mm
(12) lD = 150mm + e (13) 4.2.2.2 Determining the resultant force Meaning: Aact - Superficial content of active surface b=75 mm - Width of liquid vessel pc - Hydrostat. pressure at planar centre of force of active surface For s<sh with h from section 4.2.2.1: pc = ��⋅g⋅ s−st 2 and Aact = h⋅b (14) For s>sh the trapezoidal profile as follows applies: pc = ��⋅g⋅(s−st − 50mm⋅cos��) , (15) Aact = 100mm⋅b (16) The resultant force is produced as Fp = pc⋅Aact . (17) 4.2.2.3 Balance of moments The results can be checked with the balance of moments, as described in section 4.1.2.3.
��
s
sh st Fp 50mm⋅cos��
Aact
HM 150.05 Hydrostatic Pressure Apparatus
All rights reserved G .U.N.T . G e rätebau Gm bH, B a rsb��ttel , G e rm any, 11/96
4 Experiments Relating to the Centre of Pressure
13

Page 17
4.3 Centre of pressure with 90�� positioning of the water vessel The angle ��=90�� represents a special case. The resultant pressure profile has the form of a triangle, because the hydrostatic pressure is equal at every point on the active surface. For this reason, the centre of pressure C lies preci- sely at the planar centre of force D of the active surface e = 0 (18) and has the lever arm lD = 150mm. (19) The resultant force is produced as Fp = ��⋅g⋅(s−st)⋅(100mm⋅b) (20) The result can be checked with the balance of moments from section 4.1.2.3.
s
lD Fp st
C=D
HM 150.05 Hydrostatic Pressure Apparatus
All rights reserved G .U.N.T . G e rätebau Gm bH, B a rsb��ttel , G e rm any, 11/96
4 Experiments Relating to the Centre of Pressure
14

Page 18
5 Appendix 5.1 Worksheet for Centre of Pressure
Angle �� [��] Lowest water level st [mmWC] Highest water level sh [mmWC] Lever arm l [mm] Appended weight FG [N] Water level reading s [mm] Calculated lever arm lD [mm] Resultant force Fp [N] Angle �� [��] Lowest water level st [mmHOW] Highest water level sh [mmHOW] Lever arm l [mm] Appended weight FG [N] Water level reading s [mm] Calculated lever arm lD [mm] Resultant force Fp [N] Angle �� [��] Lowest water level st [mmWC] Highest water level sh [mmWC] Lever arm l [mm] Appended weight FG [N] Water level reading s [mm] Calculated lever arm lD [mm] Resultant force Fp [N]
HM 150.05 Hydrostatic Pressure Apparatus
All rights reserved G .U.N.T . G e rätebau Gm bH, B a rsb��ttel , G e rm any, 11/96
5 Appendix
15

Page 19
5.2 Symbols and Units
��
Density of liquids g/cm
3
phyd Hydrostatic pressure
mmHOW
pc
Hydrostatic pressure in planar centre of gravity of active surface mmHOW
Fp
Resultant force in centre of pressure N
FG
Force due to weight of appended weights N
G
Force due to weight of water in measuring vessel N
h
Height of active surface mm
b
Width of liquid container mm
s
Water level reading/scale mm
sh
Water level at highest point of active surface mm
st
Water level at lowest point of measuring vessel mm
e
Distance between centre of pressure and planar centre of gravity mm
lD
Lever arm of resultant force Fp mm
l
Lever arm of force due to weight mm
yp
Distance between centre of pressure and liquid level along the active surface mm
yc
Distance between planar centre of gravity and liquid level along the active surface mm
Aact Superficial content of active surface mm
2
5.3 Technical data Dimensions: LxWxH 400x500x360 mm
3
Capacity of measuring vessel: approx. 1.8 l Weight: approx. 10 kg
HM 150.05 Hydrostatic Pressure Apparatus
All rights reserved G .U.N.T . G e rätebau Gm bH, B a rsb��ttel , G e rm any, 11/96
5 Appendix
16
Search more related documents:Instruction Manual
Download Document:Instruction Manual

Recent Documents:

Set Home | Add to Favorites

All Rights Reserved Powered by Free Document Search and Download

Copyright © 2011
This site does not host pdf,doc,ppt,xls,rtf,txt files all document are the property of their respective owners. complaint#nuokui.com
TOP