Contoh soal Mekanika Fluida


5-1 SAE 10 oil with a specific gravity of 0,87 flows through a 6 in diameter pipe. The velocity of flow is 8,0 ft/s. determine : a) the volume flow rate in both cubic feet per second and gallons per minute , b) the weigh flow rate, and c) the mass flow rate
Answer:
Diketehui        : SG oil                        : 0.87
                          Diamter pipa (D)       : 6 inchi
                          Kecepatan alir (v)      : 8 ft/s
Ditanya           : a. Debit alir (Q) dalam ft3/s dan gallon/min?
                          b. Berat minyak (W)?
                          c. Massa minya (M)?
Jawab              :
a.       Untuk Q dalam ft3/s
Q         = A. v
Dimana
A = π r2 = D2   =  (6 inch )2
 = 0,785 (0,25 ft2)
 = 0,19 ft2
Maka
Q         = 0,19 ft2 . 8 ft/s
                        = 1,52 ft3/s
Untuk Q dalam gallons/minute
Q         = 1,52 ft3/s ( ) ( ) = 0,68 gal/min
b.      W        = γ A v
= SG oil. γ air. A v
= 0,87. 9,81 kNm-3. 0,19 ft2 ( )2. 8 ft/s ( )
= 0,37 kN
c.       M         = p A v
= SG oil. p air. A v
= 0,87. 1 grcm-3. 0,0176 m2. 2,44 m/s
= 37,36 kg/s
5-3 The diameter of a 12 ft length of pipe increase uniformly from 12 to 36 inch (see fig 5-13). Kerosene is following through the pipe with a velocity of 6.0 ft/s at the 12 inch end of the pipe. Determine a) velocity at the midlength of the pipe b) velocity at the 36 inchi end of the pipe c) volume flow rate, d) weight flow rate and e) mass flow rate
Answer:
Diketahui        : Panjang pipa (L)        = 12 ft
                          Diameter 1                = 12 inch
                          Diameter 2                = 36 inch
                          Kecepatan alir kerosene (v)   = 6 ft/s dari D1
Ditanya           : a. v ditengah pipa?
                          b. v di akhir pipa?
                          c. Q kerosene?
                          d. W kerosene?
                          e. M kerosene?
Jawab              :
a.       v ditengah pipa
Q12 inch              = Q tengah pipa
A1. v 1            = A2.  v 2
Dimana diameter tengah pipa adalah 24inch, angka ini didapatkan dengan menggunakan rumus phitagoras.
Maka
              (12 inch 0.0833ft/inch)2. 6 ft/s     = 2. v2
                0,78 ft3/s          = 3,13 ft2 v2
            v2                            = 0,25 ft/s
b.      v diakhir pipa
A1 v1    = A2 v2
0,78 ft3/s = 2 v2
v2            = 0,11 ft/s
c.       Q         = 0,78 ft3/s
d.      W        = γkerosen A v
= SG kerosene air Q
= 8,03 kNm-3 0,78 ft3/s
= 0,177 kN
e.       M         = p Q
= 819 kgm-3 0,022 m/s
= 18,018 kg/s
5-12 A nozzle is attached to a pipe as shown in fig 5-19. The inside diameter of the pipe is 100 mm while the water jet exiting from the nozzle has a diameter of 50 mm. if the pressure at section 1 is 500 kPa, determine the water jet velocity. Assume lead loss in the jet negligible
Answer
Diketahui                    : Diameter pipa di titik1          = 100 mm
                                      Diameter pipa di titik2          = 50 mm
                                      Tekanan di titik1 P1              = 500 kPa
Ditanya                       : kecepatan alir di titik2?
Jawab                          :
     H1       =       H2
Dimana P1 = Q γ H
            500 kPa           = A1 v1 γ H
            500 kPa           = (π/4) D2 v1 γ H
            H         =  
            Dimana Q1      = Q2
            A1 v1    = A2 v2
            (π/4) 0,01 m2 v1           = (π/4) 0,0025 m2 v2
                = 0,25
            v1         = v2 0,25
Maka   P2        = A2 v2 γ H
                        = (π/4) 0,0025 m2 v2 γ
                        = 500 kPa


            Di titik 1       -            Hl 1-2   = di titik 2
             + + Z1                  =  + + Z2
            0,0625 v22/ 2. 9,81 m/s            + 0       =  v22/ (2. 9,81 m/s ) + 0,025 m
5-15 The pipe shown in fig 5-22 has a uniform diameter of 150 mm. assume the head loss between points 1 and 2 is 1,2 m and between points 2 and 3 is 2,0 m determine the discharge of water in the pipe and the pressure head at point 2.
Diketahui                    : diameter pipa = 150 mm
                                      Hl 1 -3           = 1,2 m
                                      Hl 2-3            = 2.0 m
Ditanya                       : head tekanan pada titik 2?
Jawab
Di titik 1          -           Hl 1-2              -           Hl 2-3              = di titik 3       (datum titik 3)
 + + Z1      -           1,2       -           2,0       =  + + Z3
0 + 0 + 3,7 – 1,2 – 2,0             = 0 +  + 0
            v = 3,13 m/s
maka untuk head tekanan di titik 2 (datum titik 1):
di titik 1          -           Hl 1-2              = di titik2
 + + Z1      - 1,2     =  + + Z2
0-      1,2       =  +  + 1,2
          = 2,9 m
5-16 Figuer 5-23 shows a siphon discharging oil (specific gravity 0f 0,84) from a reservoir into open air. if the velocity of flow in the pipe is v, the head loss from point 1 to point 2 is 2,0 , and the head loss from point 2 to point 3 is 3,0 , determine the volume flow rate in the siphon pipe and the absolute pressure at point 2.
Diketahui        : SG oil            = 0,84
                          Hl 1-2            = 2,0
                          Hl 2-3            = 3,0
Ditanya               : a. Q??
                             b. P pada titik 2?
Jawab
a.       Untuk Q
Di titik 1          -           Hl1-2   -           Hl 2-3              = ditik 3 (datum titik 3)
 + + Z1      -           2,0 -           3,0 =  + + Z3
10           - 2,0  -3,0 =
            10 ft    = 6
            V2        = 107,26 ft2/s2
            V         = 10,35 ft/s
Maka   : Q = A v         = (3,14/4) (3 inch 0,0833ft/inch)2 = 0,015 ft3/s
b.      P pada titik 2
Di titik 1          - Hl 1-2            = di titik 2 (datum titik 1)
 + + Z1      - 2,0            =  + + Z2
0          -           2 (10,35ft/s)2/2. 32,81 ft/s2 = (P2/0,84 . 9,81 kNm-3) + 1,63 ft + 5 ft
- 3,265 ft = (P2/ 8,240 kNm-3) + 6,630 ft
P2/8,240 kNm-3            = - 9,895 ft (1m/3,281ft)
P2         =          24,85 kPa


           

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