APPARATUS
Beam le"el
i"ot
Ad-ustable counterbalan
2eight hanger 3uadrant Drain "al"e
PROCEDURE
# D
%lose
2ater
D B
Ad-ustable counterbalance
weight
1. Measur Measure e the the dimens dimension ion of quadrant (height of quadrant [D], width of quadrant [B]). After that measure the length of balance arm, and height of quadrant to !i"ot, #. $. %lose %lose drain drain "al"e "al"e and and admit admit water until the water full& 'lled in tan. Mae sure that the water does not s!ill out from the tan.
. *hen !lace !lace weig weight ht + +g g on the the weight hanger. Ad-ust the counterbalance until balance arm is horiontal and mae sure it is stable. (!laced in the middle of the beam le"el indication) /. 0tart 0tart remo"e remo"e the the weigh weightt !rogressi"el& when it is in balance condition.
4ot balance
+. 0lowl& 0lowl& redu reducin cing g water water from from tan b& o!en the drain "al"e until balance arm is horiontal
and stable.
balance
o!en
5. 4e6t, record the mass of load, m and the de!th of immersion, d. 7e!eat abo"e ste! for each weight (+g) b& reducing a further weight from the weight hanger. 8. %ontinue until water le"el reach the lowest scale from bottom of quadrant. 9. astl&, re!eat the !rocedure in re"erse form (!rogressi"el& adding weight at the weight hanger).
OBJECTIVE 1. *o determine the h&drostatic thrust acting on a !lane surface immersed in water. $. *o determine the de!th of centre of !ressure. . *o com!are the e6!erimental and theoretical results.
THEORETICAL BACKGROUND *his e6!eriment to show the h&drostatic thrust acting on a !lane surface immersed in water and centre of !ressure. 7eferring from the de'nition of the centre of !ressure which is the !oint in a !lane at which the total liquid thrust can be said to be acting normal to that !lane. B& achie"ing an equilibrium condition between the moments acting on the balance arm of the test a!!aratus, the forces acting are the weight force a!!lied to the balance and the h&drostatic !ressure thrust on the end face of the quadrant.
A. Fully Submerged Ver!"#l Pl#$e Sur%#"e
2here : d ; *he de!th of submersion < ; *he h&drostatic thrust e6erted on the quadrant h ; *he de!th of centroid h=; *he de!th of centre of !ressure,
h>; *he distance of the line of action of thrust below the !i"ot. *he line of action !asses through the centre of !ressure,
Fully Submerged Ver!"#l Pl#$e Sur%#"e & Hydr'(#!" T)ru(
( )
D HydraostaticThrust , F = ρ gBD d − 2
(4)
(1.1)
Fully Submerged Ver!"#l Pl#$e Sur%#"e( & E*+er!me$#l De+) '% Ce$re '% Pre((ure
Moment , M = Fh (4m) (1.$)
*he weight, 2, a!!lied to the hanger at the end of the balance arm !roduced balancing. *he moment is !ro!ortional to the length of the balance arm, .
Fh = WL (mg) (1.)
0ubstitute (1.1) into (1.)
Fh =WL
(
ρ gBD d −
)
D h =mgL 2
h = {mL} over {ρ BD left (d- {D} over {2} right )} (1./)
(m)
Fully Submerged Ver!"#l Pl#$e Sur%#"e( & T)e're!"#l De+) '% Ce$re '% Pre((ure
*he theoretical result for de!th of centre of !ressure,
'
h=
I x Ah
(1.+)
2here
I x ;
2
nd
moment of area of immersed section about an a6is in the free
surface. ?sing !arallel a6is theorem,
I x = Ic + Ah BD I x = 12
2
(
3
D BD d − 2
+
)
2
(1.5)
[ ( )] 2
D D + d− I x = BD 12 2
2
( m
4
)
(1.8)
De!th of the centre of !ressure below !i"ot !oint is
h =h'+H-d (m) (1.9)
0ubstitute (1.+) into (1.9)
h =h'+H-d h = {{} r!"# {$}} over {%h} + H-d h = {BD left &{{D} {2}} over {12} + {left (d- {D} over {2} right )} {2} right } over {BD left (d- {D} h = {left &{{D} {2}} over {12} + {left (d- {D} over {2} right )} {2} right } over {d- {D} over {2}} + (m)
(1.@)
B. P#r!#lly Submerged Ver!"#l Pl#$e Sur%#"e
P#r!#lly Submerged Ver!"#l Pl#$e Sur%#"e & Hydr'(#!" T)ru(
( )
Bd HydraostaticThrust , F = ρ g 2
2
(4)
(1.1)
P#r!#lly Submerged Ver!"#l Pl#$e Sur%#"e( & E*+er!me$#l De+) '% Ce$re '% Pre((ure
Moment , M = Fh (4m) (1.$)
*he weight, 2, a!!lied to the hanger at the end of the balance arm !roduced balancing. *he moment is !ro!ortional to the length of the balance arm, .
Fh = WL (mg) (1.)
0ubstitute (1.1) into (1.)
Fh=WL
( )
Bd ρ g 2
2
h =mgL
h = {2mL} over {ρ {Bd} {2}}
(m)
(1./)
P#r!#lly Submerged Ver!"#l Pl#$e Sur%#"e( & T)e're!"#l De+) '% Ce$re '% Pre((ure
*he theoretical result for de!th of centre of !ressure,
h =H- {d} over {3} (1.+)
DISCUSSION *his e6!eriment to determine the h&drostatic thrust acting on a !lane surface immersed in water, the de!th of centre of !ressure and to com!are the e6!erimental and theoretical results getting from the e6!eriment. 7eferring from this e6!eriment, the !arameter was obtained which is the dimension of quadrant, height, D and width, B also the height of quadrant to !i"ot, #. *hen the length of balance arm, . During the e6!eriment was conducted another !arameter was obtained which is the de!th of immersion, d, the t&!e of immersion whether it is full& or !artiall& submerged and the mass of load that was using while conducted the e6!eriment.
artiall& submerged,
(
D F = ρ gBD d − 2
)
( )
Bd F = ρ g 2
2
*he de!th of centre of !ressure also was com!uted using,
h = {mL} over {ρ BD left (d- {D} over {2} right )}
artiall& submerged,
h = {2mL} over {ρ {Bd} {2}}
#owe"er, the de!th of centre of !ressure also can get without an e6!eriment. ?sing theoretical which is
h =H- {d} over {3}
And the e6!erimental and theoretical was being com!ared b& calculation
Percentageerror ( ) =
Theoretical− Experimental 1 Theoretical
*aing mass of load, g;1+g as sam!le calculation
*2− *1, 1 =4*, *2
height of the water. *he balance arm is not reall& balancing also can aect the reading of the height and then can aect the dierence number of the e6!erimental and the theoretical de!th of centre of !ressure.
CONCLUSION Based on the e6!eriment, the number of h&drostatic thrust, the de!th of centre of !ressure was achie"ed. 7eferring to the number of h&drostatic thrust, it is become higher when the de!th of immersion of the ob-ect is higher. And the dierence of e6!erimental and the theoretical of the de!th centre of !ressure is /5.8. #ence, the other ob-ecti"e of this e6!eriment which is to com!are the e6!erimental and theoretical results getting from the e6!eriment was also achie"ed.
