SM1 Physics Practical Hydrostatics 12 13

7/26/2019 SM1 Physics Practical Hydrostatics 12 13

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Hydrostatics 3-1

Practical 3 HYDROSTATICS

I. INTRODUCTION

I.1 What is this practical about

The aim of this practical work is to apply the principles taught in the physics tutorials and

lectures on hydrostatics (also named statics of fluids), which is the science of fluids at rest.

You may wear protectie clothes for these e!periments.

I.! Pr"li#i$ar% "&"rcis"s

"lease prepare these e!ercises prior to the practical.

'&"rcis" 1

#igure 1

$e consider the wall of a tank which has water on one side and air on the other side (#ig. 1).

The wall has a s%uare shape& its side length is denoted a and the angle 'etween the wall and

the horiontal is denoted . n the following, represents the density of water whereas air

density is neglected.

*umerical application& a+m, sin + ., +1g/cm3, g+1 m.s-0.

(1) (orc" )"$"rat"* b% +lui*s at r"st

(1.1)ie the literal e!pression of the pressure p in water first as a function of the

altitude and then as a function of the distance along the tank, consideringthe origin at 2.

(1.0)$hat is the literal e!pression of the elementary force #d e!erted on a wall stripas a function of , g, a, and . pecify its modulus and make a sketch to

show how it is oriented.

(1.3)4educe the literal e!pression of the resulting force # acting on the tank wall asa function of , g, a, and . pecify its modulus and make a sketch to show

how it is oriented.

,!- Actio$ poi$t o+ th" r"sulti$) +orc"

4etermine the position of the action point of the resulting #, denoted 5.

,3- Nu#"rical applicatio$calculate # and the coordinates of 5.

water


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Hydrostatics

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'&"rcis" !

#igure 0

6 window has the shape of an e%uilateral triangle (675). ts length is h ((#ig.0). t is part of a

ertical wall. 2ne side of the window is in contact with water of density and the other side

with air. $e will assume that p+ct. The side 75 of the triangle is parallel to the free surface

of water and located at the distance h to it.

,1- (orc" )"$"rat"* b% +lui*s at r"st

$hat is the literal e!pression of the modulus and the orientation of the resulting

force # acting on the window8 ie its e!pression as a function of , h and g.

,!- Actio$ poi$t o+ th" r"sulti$) +orc"

4etermine the coordinates of the action point of the resulting #, denoted 5.

II. /UOYANCY

n this section of the practical the 'uoyancy (also called 6rchimedes9 principle) will 'e

determined %uantitatiely. 7uoyancy is the upward force caused 'y the fluid pressure that

ena'les an o':ect to float or seem at least lighter. t is e%ual to the magnitude of the weight of

the fluid displaced 'y the 'ody.

#igure 1 & 6rchimedes. 4omenico #etti, 10, ;useum < 6lter ;eister =, 4resden,

(ermany).

p+ctp+ct


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Hydrostatics 3-3

>6rchimedes was a reek scientist who lied in yracuse (icily) from 0?@ 7.5. to 010 7.5.

(#igure 1). He is known for his multiple scientific studies, theories and e!periments in

mathematics as well as in physics. 6mong these studies is the one on floating o':ects that sets

the 'asis for what would later 'ecome hydrostatics. He studies rigorously the immersion of a

solid or li%uid 'ody in a fluid that has a lower, e%ual or higher density.A

II.1. A0ailabl" #at"rial

7odies haing different olumes and/or different masses, made out of arious materials

(aluminium, 'rass, iron, inc),

Two circular dynamometers with full scale of 1* and 0* to measure forces (the operating

principle is descri'ed in the appendi!),

4ifferent li%uids& water, salt water,

6 calliper,

6 densimeter.

II.!. Practical or2

1. $ith the material at hand, demonstrate the principle of 'uoyancy. ;easure it for each

'ody immersed in water and write the associated uncertainty for each result.

0. $hat parameters influence the 'uoyancy8

3. 4etermine the density of salt waterB e!plain how the densimeter works and use it to erify

your e!perimental result.

ien is the area of an n-sided regular polygon&

f C is the radius (distance from the centre to a erte!)&

=n

RnS

0sin

0

0

II.3. I#pl"#"$tatio$ '&"rcis"

6 container carries two not misci'le li%uids in the field of graity& oil (oil+ kgDm-3) and

water (water + 1kgDm-3). 6 wooden sphere is also placed into this container (wood +kgDm-3).

1. $here will the sphere finally 'e located8

0. $hat fraction of the sphere is immersed in water8

3. The olume of a spherical cap of height his

=

R

hRhV 3

3

0

whereRis the radius of

the corresponding sphere. 5alculate the height immersed in water.


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Hydrostatics

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III. PR'SSUR' 'ASUR''NT TH' (UNDA'NTA4 4AW

O( HYDROSTATICS

The aim of this chapter is to identify which parameters the pressure difference 'etween twopoints in a fluid depend on.

III.1. A0ailabl" #at"rial

6 water manoscope (see 'elow).

6n a%uarium with water or salt water.

6 Fmm ruler

III.!. Stu*% o+ th" #a$oscop"

6 manoscope consists of a manometer that is connected to a fle!i'le pipe and plastic plunger

(#igure 0). 6 manometer measures the pressure difference 'etween the gas olume confined

in a closed essel and the atmospheric pressure. t performs a relatie pressure measurement.

The difference in fluid height in the G-shaped tu'e partially filled with li%uid and connected

to the enironment at 'oth ends of the tu'e is named h.

#igure 0& $orking principle of a manoscope.

1. !plain how the water manoscope works. "ropose a method that ena'les the manoscope

to 'e cali'rated.

0. f the manoscope can 'e read with millimeter precision, what is the smallest pressure

difference that can 'e measured with the water manoscope8

III.3. Practical or2

1. How does the pressure ary under water within a horiontal plane80. "lot the pressure or pressure difference as a function of depth under water and salt water.

h

Ii%uid

#le!i'le pipe

crew for angular

ad:ustment

;em'rane

;anometer


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Hydrostatics 3-F

3. 7ased on a dimensional analysis, show that the slope of the linear regression is

homogeneous to a mass density times an acceleration.

E. f the measurements a'oe had 'een made with a li%uid that had twice the density of the

li%uid you used, what would hae 'een then the measured alues for the arious heights

h8

I5. A6D'/UR6 H'ISPH'R'S

>n 1FE 2tto on uericke, mayor of ;agde'urg thought of an e!periment to show the

e!istence of atmospheric pressure. He used two metallic hemispheres with a seal. 6fter haing

pumped the air out of the sphere, 1 horses were needed to pull the hemispheres apart. The

scene 'elow (#igure 3) shows this e!periment in ;agde'urg in the presence of the emperor

#erdinand .A

#igure 3& a) 2tto on uereicke, ') hemispheres, c) historical e!periment.

Ceproduce this e!periment and e!plain how it demonstrates the effect of atmospheric

pressure.

I5.1. '&"rcis"

6 sphere is made out of two hemispheres of diameter D. Jacuum is created inside the two

hemispheres. $hat force does the operator need to apply to separate the hemispheres if D

+ ?@mm andp0+ 1'ar8


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Hydrostatics

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5. APP'NDI7

Op"rati$) pri$cipl" o+ th" *%$a#o#"t"r

6 dynamometer measures forces or moments. Here it is used to measure forces. The

dynamometers used in this practical make use of Hooke9s law stated 'y Co'ert Hooke in 1@?

'y this Iatin phrase& ut tension, sic vis, meaning >like the tension is the forceA. n other words>the elongation is proportional to the forceA.

#igure E& a-') Iinear dynamometer, c) 4ynamometer with spiral spring.

These dynamometers contain a spring with known stiffness. f su':ected to a force (applied 'y

the 'odies of this study), the spring is deformed and is elongated. 6fter a cali'ration that takes

the spring stiffness into account, the scal" (see #igure F) allos th" a#plitu*" o+ th" +orc"

measured in *ewton (*) to b" r"a* *ir"ctl%.

#igure F& a) longation of the spring, ') 5ali'rated scale.

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SM1 Physics Practical Hydrostatics 12 13