Fluid Measuring System.pdf

8/14/2019 Fluid Measuring System.pdf

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PERCOBAAN:

FLUID MEASURING SYSTEM

1. Tujuan:

(a) Verifikasi secara experimental anggapan persamaan Bernoulli.

(b) Mengamati dan mengukur karakter Venturi Meter, Orifice, dan Rotameter.

2. Theory:

(a). Bernoulli Equation

Assume that the following apply:

Steady flow Incompressible flow Flow along a streamline No frictional forces

The Bernoulli equation, which expresses the principle of conservation of linear momentum

under special circumstances, can written as :

2

2

221

2

11

22gz

VPgz

VP

(1)

In addition, let assume 21 zz . Therefore, we have

22

2

22

2

11 VPVP

(2)

Let us consider the continuity equation (conservation of mass) and limit it to the same

assumption as above. Then we have

2211 AVAV

where

4

21

1

DA

4

22

2

DA (3)

2

2

1

1

2

1

2

D

D

A

A

V

V (4)

Solving forP2from equation (2)


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2

1

2

1

2

2

112

V

V

VPP

Substituting for V

2 / V

1 from equation (4)

2

1

4

2

1

2

112

D

D

VPP

Noting that

11 AVm

11

A

mV

21

2

1A

mV

4

2

1

2

1

2

12 12 D

D

A

mPP

(5)

orpressure at any locationxis given by

4

1

2

1

2

1 1

2 xD

D

A

mPxP

(6)

or, since

g

xPxh

)()(

one can write

4

1

2

1

2

2

1)(

12

)(xD

D

Ag

mhxh

(7)

Hence the pressure head at any location along the test section can be expressed in term of the

pressure at a reference location (inlet).

(b). Venturi meter


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Assuming that there is no loss of energy along the pipe, and that the velocity and

piezometric heads are constant across each of the sections considered, then Bernoullis

theorem states that

u21

2g + h1=

u22

2g + h2=

u2n

2g + hn (8)

Where u1, u2 and un are the velocities of flow through section 1, 2, and n. The equation of

continuity is

u1A1= u2A2= unAn= Q (9)Q denotes the volume flow or discharge rate.

Substituting in equation (8) for u1 from equation (9)

u22

2g

A2

A1

2

+ h1=u2

2

2g+ h2 (10)

And solving this equation for u2 leads to

u2=

vuut2g(h1 h2)1

A2A1

2

(11)

So that the discharge rate, from equation becomes:

Q = A2vuut2g(h1 h2)

1 A2A1

2 (12)

In practice, there is some loss of energy between sections 1 and 2, and the velocity is not

constant across either of these sections. Consequently, measured values of Q usually fall

a little short of those calculated from equation (3) and it is customary to allow for this

discrepancy by writing:

Q = CA2

vuut

2g(h1 h2)

1 A2A1

2 (13)

C is known as the coefficient of the meter, which may be established by experiment. Its


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value varies slightly from one meter to another and even for a give meter it may vary

slightly with the discharge, but usually lies within the range of 0.92 to 0.99.

(c). Orifice meter

The governing equation is similar to eq.(13) of the venturi meter, but with different values of

coefficient and characteristic.

Q = CAo

vuut2g(h5 h6)1

AoA5

2

(14)

3. Gambar alat:

7

9

5 6 7


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Gambar 1

Schematic diagram Venturi meter

Table 1Lokasi Pressure tap locations dan diameters pada lokasi pressure tap

Pressure location A B C D

Diameter (mm) 26 16 26

x (mm) from A 0 46 156

4. Pengamatan dan perhitungan

(a) Lakukan percobaan untuk 5 macam flowrate yang berbeda. Isikan pada Tabel 2.

(b) Buatlah perhitungan teoritis nilaih(x)untuk setiap flowrate dan bandingkan

dengan hasil percobaan.

h(x) = h1+ _m2

22gA21 "1

D1

D(x)4

#h(x) = h1+ _m2

22gA21 "1

D1

D(x)4

#Note: Untuk perhitungan tekanan teoritis pada titik 2, 3, 4, 5, 6, 7, 8, dan 9,

jarak diukur dari titik 1 dan tekanan pada titik 1 dianggap tekanan masuk.

Hitung % error antara nilai teori diatas dengan hasil percobaan.

%ERROR = jhcalc hexpj

hexp 100%%ERROR =

jhcalc hexpj

hexp 100%

atau

A

BC

D


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%ERROR = jhcalc hexpj

hcalc 100%%ERROR =

jhcalc hexpj

hcalc 100%

Pilihan tergantung pada nilai mana yang saudara anggap lebih teliti (beri alasan

terhadap nilai yang dianggap teliti tersebut!). Isikan pada Tabel 3.

(c) Grafikkan xh vs.x untuk nilai teoritis dan percobaan untuk setiap flow ratesecara terpisah.

(d) UntukVenturi meter dan Orifice meter, plot Cvs.NRe dan bandingkan dengan

textbook. Beri komentar.

(e) Plot head loss untuk rotameter vs. kecepatan fluida.

5. Diskusi

(a) Jelaskan apakah anggapan Bernoulli terbukti pada percobaan ini?

(b) Perhatikan pada bagian venturi, uraikan apa yang dimaksud dengan head

recovery? Mengapa dapat terjadi? Apakah hal serupa terjadi pada orifice?

Mengapa?

(c) Beri komentar terhadap plot Cvs.NReVenturi meter dan Orifice meter. Apakah

nilai flow rate yang akan diukur berpengaruh terhadap ukuran alat yang sebaiknya

dipakai?

(d) Coba amati pola alir (dengan mengamati gerakan/lintasan kotoran yang melayang

bersama aliran). Dapatkah pola alir ini membantu menjelaskan keterangan saudara

pada bagian (a). Uraikan argumentasi saudara!(e) Manakah alat ukur yang paling hemat energi? Manakah yang paling sensitif?

Manakah yang paling sederhana?

(f) Berbagai alat ukur tersebut ada yang korelasi antara bacaan dan flow rate bersifat

linear. Ada pula yang tidak. Sebutkan masing-masing. Manakah yang lebih baik,

linear atau non linear, ditinjau dari segi kalibrasi, segi pemakaian?


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Table 2Nilai tekanan percobaan sebagai fungsi flow rate: m dalam (kg/sec) danh dalam (mm air).

Q m(kg/sec)

h1 h2 h3 h4 h5 h6 h7 8h 9h


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Table 3Nilai teoritis tekanan sebagai fungsi flow-rate: m (kg/sec) danh (mm air).

Q

m (kg/sec)

h1

% error inh1

h2

% error inh2

h3

% error inh3

h4

% error inh4

h5

% error inh5

h6

% error inh6

h7

% error inh7

h8

% error inh8

h9

% error inh9

Fluid Measuring System.pdf

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